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The Inverted-U Theory

Balancing performance and pressure with the yerkes-dodson law.

By the Mind Tools Content Team

Have you ever worked on a project with a tight-but-achievable deadline, where your unique knowledge and skills were vital for a successful result? Even though you found it challenging, you may well have done some of your very best work.

Or, think back to a task where you felt little pressure to deliver. The deadline may have been flexible, or perhaps the work wasn't challenging. Chances are, you did an average job at best.

There's a subtle relationship between pressure and performance. When people experience the right amount of pressure, they often perform brilliantly. However, if there's too much or too little pressure, performance can suffer.

In this article, you'll learn how the Inverted-U Theory – also known as the Yerkes-Dodson Law – can help you to understand the relationship between pressure and performance. The result will be that you'll get the best from a happy and engaged team!

Click here to watch our video on the Inverted-U Theory/Yerkes-Dodson Law.

What Is the Inverted-U Theory?

The Inverted-U Theory was created by psychologists Robert Yerkes and John Dodson in 1908. Despite its age, it's a model that has stood the test of time. [1]

The theory describes a clear relationship between pressure and performance. In the original research, pressure was exerted by electric shocks – to motivate rats to escape from a maze!

The Inverted-U Theory gets its name from the curve created when the correlation between pressure (or "arousal") and performance is shown on a graph. See figure 1, below.

Figure 1: The Inverted-U Curve.

From " The Relation of Strength of Stimulus to Rapidity of Habit‐Formation " by Robert Yerkes and John Dodson. Published in the Journal of Comparative Neurology (1908). Work now in the public domain.

According to Yerkes and Dodson, peak performance is achieved when the level of pressure we experience is appropriate for the work we're doing. When we're under too much or too little pressure, performance declines, sometimes severely.

Understanding the Inverted-U Curve

The left hand side of the graph, above, shows the situation where people aren't being challenged. Here, they see no reason to work hard at a task, or they're in danger of approaching their work in a "sloppy," unmotivated way.

The middle of the graph shows where people work at peak effectiveness. They're sufficiently motivated to work hard, but they're not so overloaded that they're starting to struggle. This is where people can experience "flow," the enjoyable and highly productive state in which they can do their best work. (For more on this, see our article, The Flow Model .)

The right hand side of the graph shows where they're starting to fall apart under pressure. They're overwhelmed by the volume and scale of competing demands on their attention, and feeling a serious lack of control over their situation. They may exhibit signs of hurry sickness , stress, or out-and-out panic.

In reality, the exact shape of the curve will depend on both the individual and their situation. It's also important to recognize that seemingly small changes in professional or personal life can lead to rapid repositioning on the curve.

What's the Difference Between Pressure and Stress?

The Inverted-U Theory shows that pressure can be positive – up to a point. Stress, however, is never positive, and it's important not to confuse the two ideas.

When the levels of pressure we're experiencing are right for the work we're doing, we're stimulated in a beneficial way: motivated, engaged, and excited about doing our best. But stress happens when people feel out of control, and it's a wholly negative thing.

The Inverted-U Theory is about using pressure wisely, always aware of where the benefits end and stress begins.

For more information about how to identify and manage stress, see our article, Minimizing Workplace Stress .

You can take steps to manage the way you experience pressure by using techniques such as Relaxation Imagery , Centering , and Deep Breathing . You can also use Affirmations to maintain a positive outlook and control. Consider teaching these techniques to your teams, too – though you'll also need to have the right organizational processes in place to ensure that pressure levels remain beneficial.

The Four Influencers of the Inverted-U Theory

The impact of pressure can be complex. But four key factors, or "influencers," affect how the Inverted-U Theory plays out in practice*:

• Skill Level.
• Personality.
• Trait Anxiety.
• Task Complexity.

1. Skill Level

Someone's level of skill with a given task will directly influence their performance, in terms of both their attitude and their results.

For a while, a new task is likely to be challenging enough. Later, if it starts to feel too easy, some form of extra pressure might be needed to help the person re-engage with their role.

Don't worry about people becoming too skilled or too confident. You can use the other influencers to balance this, so that they feel the optimum amount of positive pressure. Increased skill and confidence can only bring benefits to individuals and organizations.

2. Personality

A person's personality also affects how well they perform.

For instance, some psychologists believe that people who are extroverts are likely to perform better in high-pressure situations. People with an introverted personality, on the other hand, may perform better with less pressure.

The Inverted-U Theory prompts us to match our own personalities – and those of our people – to appropriate tasks. Observation, detailed knowledge of individuals, and open communication, are all important when we're allocating roles and responsibilities.

Although not addressed directly within the Inverted-U Theory, it's important to remember that people can experience various forms of personal pressure (from their family lives, for instance, or from underlying concerns about their role or organization). Try to bear these pressures in mind when setting deadlines and allocating tasks.

3. Trait Anxiety

Think of trait anxiety as the level of a person's "self-talk." People who are self-confident are more likely to perform better under pressure. This is because their self-talk is under control, which means that they can stay "in flow," and they can concentrate fully on the situation at hand.

By contrast, people who criticize or question themselves are likely to be distracted by their self-talk, which can cause them to lose focus in more challenging situations.

The more that people are able to lower their anxiety about a task (with practice, or with positive thinking, for example) the better they'll perform.

4. Task Complexity

Task complexity describes the level of attention and effort that people have to put into a task in order to complete it successfully. People can perform simple activities under quite high levels of pressure, while complex activities are better carried out in a calm, low-pressure environment.

But even when someone's skill levels are high, they may still benefit from a calm environment in which to carry out their most complex work. Conversely, people carrying out low-complexity tasks may need extra stimulation in order to feel motivated and achieve their potential.

Using the Inverted-U Theory

The simplest way to use the Inverted-U Theory is to be aware of it when you allocate tasks and projects to people on your team, and when you plan your own workload.

Start by thinking about existing pressures. If you're concerned that someone might be at risk of overload, see if you can take some of the pressure off them. This is a simple step to help them improve the quality of their work.

By contrast, if anyone is underworked, it may be in everyone's interest to shorten some deadlines, increase key targets, or add extra responsibilities – but only with clear communication and agreement.

From there, balance the factors that contribute to pressure, so that your people can perform at their best. Remember, too little pressure can be just as stressful as too much!

Try to provide team members with tasks and projects of an appropriate level of complexity, and work to build confidence in the people who need it.

Also, manage any negativity in your team, and train your people so that they have the skills they need to do the jobs they're given. Our article on Training Needs Assessment (TNA) will help you do this. Tools like the Four Dimensions of Relational Work can also help you match tasks to people's personalities and interpersonal skills.

However, bear in mind that you won't always be able to balance the "influencers." Motivate and empower your people so that they can make effective decisions for themselves.

The Inverted-U Theory illustrates the relationship between pressure and performance. Also known as the Yerkes-Dodson Law, it explains how to find the optimum level of positive pressure at which people perform at their best. Too much or too little pressure can lead to decreased performance.

Various factors affect how much people react to pressure in different situations. There are "four influencers" that can affect how much pressure people feel:

The Inverted-U Theory helps you to observe and manage these four factors, aiming for a balance that supports engagement, well-being, and peak performance.

You can use the model by managing these four influencers, and by being aware of how they can positively or negatively influence your people's performance.

*Originator unknown. If you know the originator of the "Four Influencers," please contact us.

[1] Yerkes, R.M. and Dodson, J.D. (1908). 'The Relation of Strength of Stimulus to Rapidity of Habit-Formation,' Journal of Comparative Neurology and Psychology, 18(5), 459-482. Available here .

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The Yerkes-Dodson Law of Arousal and Performance

Charlotte Nickerson

Research Assistant at Harvard University

Undergraduate at Harvard University

Charlotte Nickerson is a student at Harvard University obsessed with the intersection of mental health, productivity, and design.

Learn about our Editorial Process

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

The concept of optimal arousal in relation to performance on a task is depicted here. Performance is maximized at the optimal level of arousal, and it tapers off during under- and overarousal.

Key Takeaways

• The Yerkes-Dodson law states that there is an empirical relationship between stress and performance and that there is an optimal level of stress corresponding to an optimal level of performance. Generally, practitioners present this relationship as an inverted U-shaped curve.
• Research shows that moderate arousal is generally best; when arousal is very high or very low, performance tends to suffer (Yerkes & Dodson, 1908).
• Robert Yerkes (pronounced “Yerk-EES”) and John Dodson discovered that the optimal arousal level depends on the complexity and difficulty of the task to be performed.
• This relationship is known as the Yerkes-Dodson law, which holds that a simple task is performed best when arousal levels are relatively high, and complex tasks are best performed when arousal levels are lower.
• The Yerkes-Dodson law’s original formulation derives from a 1908 paper on experiments in Japanese dancing mice learning to discriminate between white and black boxes using electric shocks. This research was largely ignored until the 1950s when Hebb’s concept of arousal and the “U-shaped curve” led to renewed interest in the Yerkes-Dodson law’s general applications in human arousal and performance.
• The Yerkes-Dodson law has more recently drawn criticism for its poor original experimental design and it’s over-extrapolated scope to personality, managerial practices, and even accounts of the reliability of eyewitness testimony.

How the Law Works

The Yerkes-Dodson law describes the empirical relationship between stress and performance.

In particular, it posits that performance increases with physiological or mental arousal, but only up to a certain point. This is also known as the inverted U model of arousal.

When stress gets too high, performance decreases. To add more nuance, the shape of the stress-performance curve varies based on the complexity and familiarity of the task.

Task performance is best when arousal levels are in the middle range, with difficult tasks best performed under lower levels of arousal and simple tasks best performed under higher levels of arousal.

Original Experiments

The Yerkes-Dodson law has seen a number of interpretations since its inception in 1908. In their original paper, Robert Yerkes and John Dodson reported the results of two experiments involving “discrimination learning” – the ability to respond differently to different stimuli – and dancing mice (Teigen, 1994).

The mice received a non-injurious electric shock whenever they entered a white box but no shock when they entered the black box next to the white box.

In the first set of experiments, Yerkes and Dodson gave the mice very weak shocks; however, they found that these mice took two long to learn the habit of choosing the black box over the white box (choosing correctly 10/10 times over three consecutive days).

When the researchers increased the strength of the shock, the number of trials needed for the mice to learn the habit decreased – until they reached the third and strongest level of electric shock.

When the electric shock was at its strongest, the number of trials needed for the mice to learn which box to enter went up again. This finding went against Yerkes and Dodson” hypothesis that the rate of habit-formation would increase linearly with the increasing strength of the electric shock.

Instead, a degree of stimulation that was neither too weak nor too strong optimized the rate of learning (Yerkes and Dodson, 1908; Teigan, 1994).

Because of this unexpected result, Yerkes and Dodson elaborated on their original experimental design to provide “a more exact and thoroughgoing examination of the relation of strength of stimulus to rapidity of learning” (1908).

The researchers made it easier to discriminate between the white and black boxes by letting more light into the white box and used five rather than three levels of shock.

Contrary to what we now know as the Yerkes-Dodson law, the weakest stimulus gave the slowest rate of learning, while the strongest stimulus led to the fastest rate of learning.

This confused Yerkes and Dodson, who wrote, “The results of the second set of experiments contradict those of the first set. What does this mean?” (1908).

One hypothesis the researchers made was that these contradictory results came from the easiness of the discrimination task.

To test this hypothesis, Yerkes and Dodson made the discrimination task more difficult than in the first set of experiments by allowing less light into the white and black boxes.

The researchers used four levels of shock, but fewer mice in each condition than before – two rather than four. In this set of experiments, the most efficient learning seemingly occurred at the second-weakest shock level (Teigen, 1994).

From these three sets of experiments, Yerkes and Dodson concluded that both weak and strong stimuli can result in low rates of habit formation and that the stimulus level most conducive to learning depends on the nature of the task.

“As the difficultness of discrimination is increased, the strength of that stimulus which is most favorable to habit-formation approaches the threshold” (Yerkes and Dodson, 1908; Teigen, 1994).

Replication Studies

Following the original formulation of the Yerkes-Dodson law, researchers replicated the original study, using animals such as chicks (Cole, 1911) and kittens (Dodson, 1915).

Cole (1911) gave chicks an easy, medium, and difficult discrimination task, with four levels of shock for the medium task and three levels of shock for the other tasks.

In the easy task, the rapidity of learning increased with the strength of shock; in the medium-difficulty task, the strongest shock seemingly decreased the rate of learning, and in the difficult task, the strong shock increased the variability of performance – three chicks learned more rapidly due to the strong shock, while two others failed to learn the discrimination task (the sixth chick died over the course of the experiment).

Although Cole (1911) only observed one U-curve (in the medium-difficulty condition), he concluded that his results were in agreement with Yerkes-Dodson.

Dodson (1915), meanwhile, trained four kittens to discriminate between light and dark-colored boxes by giving them a “medium-strength” shock when they entered the darker box.

These kittens performed better at the discrimination task than those given a “strong” electric shock. When the task was made easier (again, by letting more light into the boxes), the strong and medium-strength shocks proved equally effective. With an easier task, learning improved with shock strength (Teigen, 1994).

Dodson himself later found that both the strength of rewards and punishments were related to the rapidity of learning in a U-shaped manner.

For example, rats who had been starved for up to 41 hours prior to the experiment showed higher rates of discrimination learning than those who were not. However, if they were starved longer (and food was more rewarding as a result), learning became less efficient (Dodson, 1917).

Later scholars generally agreed that the Yerkes-Dodson law was about the relationship between punishment and learning.

Young (1936), following a review of the research of Yerkes and Dodson (1908), Cole (1911), and Dodson (1915), added a later confounding study by Vaughn and Diserens (1930) showing that maze learning was more efficient in human subjects given either light or medium punishments in the form of electric shocks, but not with heavy punishment or no punishment.

To quote Young, “For the learning of every activity, there is an optimum degree of punishment” (1936). The 1930s and 1940s saw an evolution of the Yerkes-Dodson law.

Writers such as Thorndike (1932), Skinner (2019), and Estes (1944) did away with the idea of punishment as a fundamental learning principle, and others introduced a distinction between learning and performance (Teigen, 1994).

Researchers reinterpreted the Yerkes-Dodson law as describing the relationship between motivation and performance.

Some, such as Hilgard and Marquis (1961), concluded that the law was evidence that “under certain conditions, the drive may actually interfere” with learning.

Introductory textbooks as well as scholars on the subject, have described the Yerkes-Dodson law in terms of motivation and performance (e.g., Bourne and Ekstrand, 1973).

In these descriptions, the Yerkes-Dodson law has become more about motivated behavior in general than the psychology of learning.

The shape described by the Yerkes-Dodson law has also changed from U-curves to the inverted U: while learning (as measured by the number of trials needed for mastery) is optimal at the lowest point of a U-curve (the least trials needed), performance is optimal, at its highest, at the highest point of the inverted U-curve.

This expansion in scope, it has been argued, renewed interest in the Yerkes-Dodson law from 1955 to 1960 (Teigen, 1994).

Broadhurst (1957) replicated the original Yerkes-Dodson experiment with a better design by using four motivation levels and three difficulty levels with ten rats in each condition.

Again, the rats had to discriminate between light and dark boxes, but they were motivated by different levels of air deprivation: 0, 2, 4, or 8 seconds.

For the easy discrimination task, the highest performance was seen in the 4-second air deprivation group, while the optimum moved to 2 seconds for the medium and difficult task groups.

Broadhurst also proposed testing motivational differences in individual rats by conducting the experiment on rats differing in “emotionality” (Broadhurst, 1957; Teigen, 1994).

Eyewitness Testimony

Expert witnesses have cited the Yerkes-Dodson law in court.

Witness for the defense: The accused, the eyewitness, and the expert who puts memory on trial, Elizabeth Loftus, a psychologist and expert witness in memory and the fallibility of memory, eyewitness testimony explains,

“I approached the backboard located in front of the jury box and, with a piece of chalk, drew the upside-down U shape that represented the relationship between stress and memory known to psychologists as the Yerkes-Dodson law” (Loftus and Ketcham, 1991).

Although this curve bore more similarity to Hebb’s inverted U-curve of arousal, Loftus used the curve to relate arousal (or “stress”) to the efficiency of memory (rather than, as has been formulated by others, learning, performance, problem-solving, the efficiency of coping, or another concept).

The Yerkes-Dodson effect states that when anxiety is at low and high levels, eyewitness testimony is less accurate than if anxiety is at a medium level. Recall improves as anxiety increases up to an optimal point and then declines.

When we are in a state of anxiety, we tend to focus on whatever is making us feel anxious or fearful , and we exclude other information about the situation.

If a weapon is used to threaten a victim, their attention is likely to focus on it. Consequently, their recall of other information is likely to be poor.

Work Stress

The Yerkes-Dodson law has seen frequent citations in managerial psychology, particularly as researchers have argued that the increase in work stress levels is a “costly disaster” (Corbett, 2015).

Corbett (2015) examines the lineage of this law in business writing and questions its application, calling it a “folk method.”

In particular, Corbett criticizes how the law has been extrapolated from its initially limited animal experiments to almost every facet of human task performance, with studies examining tasks as unrelated as product development teamwork, piloting aircraft, competing in sports, and solving complex cognitive puzzles.

This has proved, Corbett argues, to create a situation where the law has become so ambiguous as to be unfalsifiable (2015).

Corbett argues that the generally uncritical portrayal of the Yerkes-Dodson law in textbooks has added a veneer of scientific legitimacy to the management practice of increasing work stress levels at a time when more robust research is increasingly showing that increasing levels of work-related stress corresponds to decreasing mental and physical health.

Corbett, taking an argument from Micklethwait and Wooldridge (1996) posits that management theory is generally incapable of self-criticism, has confusing terminology, rarely “rises above common sense,” and is riddled with contradictions (2015).

In response, he suggests that managerial psychology embraces evidence-based managerial practices.

Arousal and Performance

The renewal of interest in the Yerkes-Dodson law in the 1950s corresponded to the introduction of the concept of arousal (Teigen, 1994).

Hebb (1955), who wrote seminally on the concept of arousal, introduced the inverted U-curve to describe the relationship between arousal and performance.

This idea of arousal shifted the idea of “drive” from the body to the brain and could be framed as either a behavioral, physiological, or theoretical concept. Although not referenced in Hebb’s original paper, writers continued to describe the Yerkes-Dodson law in terms of arousal in textbooks and research literature (Teigen, 1994).

These reformulations of the Yerkes-Dodson law have used terms such as fear, anxiety, emotionality, tension, drive, and arousal interchangeably.

For example, Levitt (2015) holds that the Yerkes-Dodson law describes “that the relationship between fear, conceptualized as drive, and learning is curvilinear,” reporting findings on human maze learning as support for his view.

Using the arousal concept in the formulation of the Yerkes-Dodson law has also seen the law being linked to phenomena such as personality traits and the effects of physiological stimulants.

For instance, in accounting for the theoretical differences in intellectual performance between introverts and extroverts under time pressure, different noise conditions, and at different times of day (e.g., Revelle, Amaral, and Turriff, 1976; Geen, 1984; and Matthews, 1985) as well as participants differing in impulsivity working under the influence of caffeine (e.g., Anderson and Revelle, 1983).

Critical Evaluation

Yerkes and Dodsons’ original experimental design, scholars generally agree, was deeply flawed by modern standards – so much so that W. P. Brown wrote that the law should be “buried in silence” (Teigen, 1994; W. P. Brown, 1965).

Yerkes and Dodsons’ performance vs. stimulus curves were based on averages from just 2-4 subjects per condition; the researchers performed no statistical tests (Gigerenzer and Murray, 2015), and the highest level of shock used in 3, 4, and 5 shock conditions were of different strengths.

The authors assumed that the linear response curve in the second set of experiments (with the easily discriminated white and black boxes) was simply the first part of a U-curve, which would have been fully uncovered given that they had subjected the mice to higher levels of shocks (Teigen, 1994).

Indeed, this experimental design has been misreported by later scholars, such as Winton (1987), who described the original study as a 3 x 3 design with three different levels of discrimination difficulty and three levels of shock strength.

Additionally, Yerkes and Dodson, as Teigen (1994) points out, failed to discuss the concepts involved in the speed of habit formation. Several of the original replicating studies, such as Dodson’s kitten experiment (1915), also showed poor experimental design.

In this experiment, there were only two kittens in the “less difficult” and “easy” discrimination conditions and no U-curves. Nonetheless, Dodson concluded that the results were compatible with the original Yerkes-Dodson experiment (Teigen, 1994).

Anderson, K. J., & Revelle, W. (1983). The interactive effects of caffeine, impulsivity and task demands on a visual search task. Personality and Individual Differences, 4(2), 127-134.

Bourne, L. E., & Ekstrand, B. R. (1973). Psychology: Its principles and meanings (Dryden, Hinsdale, IL).

Broadhurst, P. L. (1957). Emotionality and the Yerkes-Dodson law. Journal of experimental psychology, 54(5), 345.

Brown, W. P. (1965). The Yerkes-Dodson law repealed. Psychological reports, 17(2), 663-666.

Cole, L. W. (1911). The relation of strength of stimulus to rate of learning in the chick. Journal of Animal Behavior, 1(2), 111.

Corbett, M. (2015). From law to folklore: work stress and the Yerkes-Dodson Law. Journal of Managerial Psychology.

Dodson, J. D. (1915). The relation of strength of stimulus to rapidity of habit-formation in the kitten. Journal of Animal Behavior, 5(4), 330.

Dodson, J. D. (1917). Relative values of reward and punishment in habit formation. Psychobiology, 1(3), 231.

Estes, W. K. (1944). An experimental study of punishment. Psychological Monographs, 57(3), i.

Geen, R. G. (1984). Preferred stimulation levels in introverts and extroverts: Effects on arousal and performance. Journal of Personality and Social Psychology, 46(6), 1303.

Gigerenzer, G., & Murray, D. J. (2015). Cognition as intuitive statistics. Psychology Press.

Hebb, D. O. (1955). Drives and the CNS (conceptual nervous system). Psychological review, 62(4), 243.

Hilgard, E. R., & Marquis, D. G. (1961). Hilgard and Marquis” conditioning and learning.

Levitt, E. E. (2015). The psychology of anxiety.

Loftus, E., & Ketcham, K. (1991). Witness for the defense: The accused, the eyewitness, and the expert who puts memory on trial. Macmillan.

Matthews, G. (1985). The effects of extraversion and arousal on intelligence test performance. British Journal of Psychology, 76(4), 479-493.

Revelle, W., Amaral, P., & Turriff, S. (1976). Introversion/extroversion, time stress, and caffeine: Effect on verbal performance. Science, 192(4235), 149-150.

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Thorndike, E. L. (1932). The fundamentals of learning.

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Young, P. T. (1936). Social motivation.

Inverted U Theory Explained

The inverted u theory describes the relationship between arousal and performance. The theory hypotheses that arousal levels that are either too high or too low can result in gradual decreases in performance. In between these high and low arousal levels, is an optimum level of arousal for performance, which can be seen in the inverted u curve below.

History of the Inverted u Theory

The inverted u theory may also be referred to as the Yerkes-Dodson law due to its creation by two researchers – Yerkes and Dodson. In 1908, these researchers were trying to understand the relationship between the strength of a stimulus and forming habits in mice. They found that there was a negative relationship between the two i.e. the harder it is to form a habit, the less strong the stimulus needs to be to make the habit stick. This study formed the foundation if the inverted u theory, which has stood the test of time.

Understanding the Inverted-U Curve

The inverted u theory takes its name from the shape of the curve. The peak of the curve highlights the arousal level needed for optimum performance. Either side of the peak, where arousal levels are either too high, or too low, suggests gradual decreases in performance.

What is arousal?

Arousal has been defined as the blend of physiological (i.e. heart rate, muscle tension) and psychological (i.e attention) levels of activation within an athlete, which varies from low (i.e deep sleep) to high arousal (i.e. extreme excitement) (Hackfort, Schinke & Strauss, 2019).

Factors Influencing the Curve

The peak of the inverted u curve, where the optimal levels of arousal are needed for optimal performance, may look different for every individual. There are many factors that might influence where the peak of the curve is, examples of these factors include (1) the individual athlete, (2) the sport, (3) difficulty of the task and (4) the skill level of the athlete – we’ll delve into a few of these factors below…

Task Difficulty

Tasks or sports that involve high levels of coordination may benefit from lower levels of arousal to ensure high focus and attention can be sustained. In contrast, sports or tasks that use major muscle groups may need higher levels of arousal than high-coordination tasks.

Skill Level

Similar to the high-coordination sports and tasks outlined above, beginners may also need lower levels of arousal to maintain focus and avoid distractions and performance declines. In contrast, an expert in a task or sport may not need the same levels of focus and attention as a beginner, and can complete the task with a higher arousal level.

Examples of the Inverted U Theory in Sport

An example of the Inverted u theory can be found in Snooker. This sport requires a high level of fine skill and focus of attention, and therefore players may benefit from a lower arousal level for optimal performance. There are many ways that a lower optimal arousal level can be achieved, such as listening to calm or relaxing music, or using visualisation or meditation to remain composed.

In contrast, sports like boxing and rugby naturally favour higher optimum arousal levels due to their physical nature. Even so, arousal levels that are too high can lead to mistakes and poor performance.

Why is the Inverted U Theory Important in Sport?

From an applied sport psychology perspective, the inverted u theory can help to understand the circumstances in which an athlete can perform at their best. As highlighted, this might look different even for athletes competing in the same sport, but this understanding can benefit athletes and their support staff to achieve and maintain their optimal performance zone – this can include arousal level, mindset, physical fitness and warm ups, and many other factors that influence performance.

How Can This Theory Help Athletes?

Achieving the optimum performance level is important for athletes. This theory can build an understanding of what ideal performance looks and feels like. Through this understanding, athletes can begin to tailor their preparation for competition.

Thinking specifically about how to achieve an optimum level of arousal, athletes can consider ways to increase or decrease their arousal level. Common strategies include listening to music (upbeat to increase arousal, calm and relaxing to lower arousal levels), meditation, and the use of psychological skills such as imagery and self-talk through mental skills training .

How can this theory help coaches?

Coaches also play a part in the preparation to perform. Often, coaches are present at competitions, so understanding how an athlete performs best can help the coach to support in managing the arousal levels. Training sessions can be tailored to replicate demands of competition, encouraging athletes to train under pressure, or perhaps exploring performing at different levels of arousal.

What is the Difference Between Pressure and Stress?

Whilst pressure can be thought of positively, stress is not. Excessive amounts of pressure naturally lead to stress, and excessive or chronic stress can lead to both mental and physical illnesses. It is important to understand the different pressures that we face in different situations in order to manage and use them to our advantage. This links back to athletes and coaches understanding their optimum performance zones.

Responding to stress and pressure

There are several variables that influence the way people respond to pressure and stress. Individual differences in optimal arousal levels, the level of pressure and stress the person is under, and the coping strategies employed can all influence our responses.

Stress can lead to feelings of being overwhelmed, or out of control, therefore it is important to manage and reduce stress as much as possible.

Coping Strategies

The effectiveness of coping strategies is dependent on the individual. Generally, coping strategies can be categorised into 3 types:

• Avoidance coping – the problem/situation is avoided. For example, using tv or music to distract from the situation and avoid thinking about it.
• Emotion-focused coping – the emotion attached to a problem or situation is dealt with, rather than the problem itself. Practicing meditation and mindfulness are examples of this.
• Problem-focused coping – the problem or situation is addressed directly, such as through setting boundaries or seeking support.

There are no right or wrong answers as to which coping strategies to use. For example, avoidance coping might be effective in the short term, but ineffective in the long run, as the problem/situation will continue, whereas problem-focused coping may have more long-term effectiveness in managing a problem or situation.

Final Thoughts

In summary, the inverted u theory describes (but does not explain) the relationship between arousal level and performance. Each individual will have an arousal level that is optimal for peak performance. Arousal levels that are above or below the optimum can lead to gradual declines in performance.

Further Reading

Hackfort et al. (2019) –  Dictionary of Sport Psychology: Sport, Exercise, and Performing Arts. 

Yerkes & Dodson (1908) – The relation of strength of stimulus to rapidity of habit formation . 

Written by Nicole Wells

Nicole is a BSc Psychology graduate from University of Lincoln whom is currently completing a PhD in Sport psychology whilst working towards BASES Sport and Exercise Psychology Accreditation.

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Nicole Wells

• Nicole Wells https://sportscienceinsider.com/author/nicole-wells/ Catastrophe Theory in Sport Explained
• Nicole Wells https://sportscienceinsider.com/author/nicole-wells/ Arousal In Sport – What Does The Research Suggest?

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Hypothesis that states that performance improves with increasing levels of arousal up to an optimal point beyond which further increases in arousal produce a detrimental effect on performance. Therefore, athletes may perform badly because they are over- or under-aroused. The hypothesis is qualitative, and does not attempt to quantify the relationship between arousal and performance. The optima vary between people doing the same task and one person doing different tasks. A basic assumption in the hypothesis is that arousal is unidimensional and that there is, consequently, a very close correlation between indicators of arousal; this is not the case. See also catastrophe theory.

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Arousal, anxiety, and performance: a reexamination of the Inverted-U hypothesis

Affiliation.

• 1 Department of Exercise Science and Sport Studies, Rutgers, the State University of New Jersey, USA.
• PMID: 14768844
• DOI: 10.1080/02701367.2003.10609113

Until recently, the traditional Inverted-U hypothesis had been the primary model used by sport psychologists to describe the arousal-performance relationship. However, many sport psychology researchers have challenged this relationship, and the current trend is a shift toward a more "multidimensional" view of arousal-anxiety and its effects on performance. In the current study, 104 college-age participants performed a simple response time task while riding a bicycle ergometer. Participants were randomly assigned to one of eight arousal groups (between 20 and 90% of heart rate reserve) and were told they were competing for a cash prize. Prior to the task, the Competitive State Anxiety Inventory-2 and Sport Anxiety Scale (SAS) were administered to assess the influence of cognitive and somatic anxiety. As hypothesized, regression analysis revealed a significant quadratic trend for arousal and reaction time. This accounted for 13.2% of the variance, F change (1, 101) = 15.10, p < .001, in performance beyond that accounted for by the nonsignificant linear trend. As predicted by the Inverted-U hypothesis, optimal performance on the simple task was seen at 60 and 70% of maximum arousal. Furthermore, for the simple task used in this study, only somatic anxiety as measured by the SAS accounted for significant variance in performance beyond that accounted for by arousal alone. These findings support predictions of the Inverted-U hypothesis and raise doubts about the utility theories that rely on differentiation of cognitive and somatic anxiety to predict performance on simple tasks that are not cognitively loaded.

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Article contents

Arousal control in sport.

• Martin Turner Martin Turner Faculty of Health Sciences, Staffordshire University
•  and  Marc Jones Marc Jones Faculty of Health Sciences, Staffordshire University
• https://doi.org/10.1093/acrefore/9780190236557.013.155
• Published online: 24 January 2018

Sport and stress are intertwined. Muhammad Ali once said, “I always felt pressure before a big fight, because what was happening was real.” As this quote attests, sport is real, unscripted, with the potential for psychological, and often physical, harm. The response to stress, commonly described as “flight or fight,” is an evolutionary adaptation to dangerous situations. It guides behavior and readies a person to respond, to fight, or flee. However, the stress response is not evoked solely in situations of mortal danger; it occurs in response to any situation with the potential for physical or psychological harm, such as sport. For example, the possibility of missing out on a life-changing gold-medal win in an Olympic Games, or losing an important competition that you were expected to win.

Stress in sport is often illustrated by the archetypal image of an athlete choking; snatching defeat from the jaws of victory. But stress can also help athletes perform well. Stress also plays a role in behavior away from the competition arena, influencing interactions with significant others, motivation and performance in training, and how athletes experience and manage injury and retirement from sport. In sport stress, the psychophysiological responses to stress are not just abstract theoretical concepts removed from the real world; they reflect the thoughts, feelings, and experiences of athletes.

It is important to understand the arousal response to stress in sport. Both theory and research suggest a connection between arousal and athletic performance. Recent approaches propose ideas about how the nature of arousal may differ depending on whether the athlete feels positively (as a challenge) or negatively (as a threat) about the stressor. The approach to seeing stress as a challenge supports a series of strategies that can be used to help control arousal in sport.

• cognitive appraisal
• psychophysiology
• performance
• reappraisal
• approach focus

The Autonomic Nervous System

The following quote from ex-soccer player David Beckham, about taking a penalty in the 2002 World Cup, illustrates the strong physiological arousal observed in response to stress: “It was an important moment for me, the nation and the team . . . but I’ve never felt pressure like that in a game before. I just couldn’t breathe.” The fact that the stress of competitive sport performance manifests in physical symptoms is due to the interaction between how a person thinks and the workings of the autonomic nervous system (ANS). Key elements of a person’s response to stress are changes in the ANS, which controls functions of the body that are geared to survival and connect with the involuntary muscles, such as lungs, stomach, and kidneys (Lovallo, 2004 ). The ANS is part of the peripheral nervous system, which refers to all the nerves outside of the central nervous system (i.e., the brain and spinal cord). The peripheral nervous system comprises the somatic system (connection with the voluntary muscles) and the ANS. Both the ANS and the somatic system are influenced by the central nervous system.

The ANS can further be subdivided into the sympathetic and parasympathetic branches. The sympathetic branch is responsible for mobilizing the body ready for action, reflected in the classic flight or fight response, which is associated with the emotions of anger and fear (Canon, 1932 ). Because this response is geared toward sustaining an attack or fleeing, it is a short-term response and places a strain on the body, which is why prolonged anger and fear carry the potential for harm (Lazarus, 1999 ). The parasympathetic nervous system is concerned with calming, or reducing the arousal. The activity of the sympathetic nervous system is generally all or nothing, that is, the entire body is affected (Lovallo, 2004 ).

The sympathetic nervous system exerts its influence through hormonal activity. Stimulation of the adrenal medulla (center of the adrenal gland) results in secretion of adrenaline and noradrenaline (epinephrine and norepinephrine). The pituitary gland also releases adrenocorticotrophic hormone (ACTH), which that stimulates the adrenal cortex (outer part of the adrenal gland) to release corticosteroids, and the hormone most often considered in response to stress is cortisol. Cortisol mobilizes energy resources to provide “fuel” for the body and thus plays a crucial role in metabolism, alongside other important functions, including anti-inflammatory effects, inhibiting immune functioning, and impacting the cardiovascular system, for example, through inducing vasoconstriction (Dickerson & Kemeny, 2004 ).

Early Models of Arousal and Sport Performance

There are two early major approaches to explaining the arousal-performance relationship that have been applied to sport: drive theory and the inverted U-hypothesis.

Drive Theory

Drive theory was outlined by Hull ( 1943 ) and then later modified by Spence ( 1956 ); it is sometimes referred to as the Hull-Spence theory of behavior (Spence, 1956 ). Drive theory was originally proposed to explain the relationship between complex tasks and arousal, although it has also been applied to explain the relationship between simple tasks (equivalent to complex tasks that are well learned) and arousal. Performance (P) is a multiplicative function of drive state (D) and habit strength (H):

In brief, for well-learned tasks, there is a positive linear relationship between arousal and performance. Drive theory has been used to explain behavior in stressful settings, perhaps most notably by Zajonc ( 1965 ), who adopted drive theory to explain social facilitation. The facilitating effects of arousal occur because heightened arousal increases the likelihood of an athlete’s dominant response tendency (habit strength). If the dominant (well-learned) response is the most appropriate, as is likely for skilled performers, then performance improves. However, the literature does not support for the central tenet of drive theory—that heightened arousal (drive state) is associated with improved performance (Martens, 1971 ). In addition, Martens suggested that it is very difficult to determine habit hierarchies. To explain, it is difficult to know when a task becomes so well learned that arousal will always have a positive influence on performance. Perhaps more damagingly, there are many examples of excessive arousal disrupting performance, so the face validity of the theory does not appear to hold. For example, even highly skilled performers can point to examples in which excessive arousal disrupted performance (e.g., a world class tennis player double faulting on a crucial point).

Furthermore, Oxendine ( 1984 ) did suggest that a linear relationship may exist for gross motor activities. Thus, drive theory may hold for tasks for which power is required but co-ordination is not needed. Anecdotally, this would make sense, but determining when an activity relies solely on power is difficult. For example, even tasks like scrummaging in rugby or weightlifting require coordination. In short, there is limited evidence for drive theory in sport (Zaichkowsky & Baltzell, 2001 ).

Inverted-U Hypothesis

In the inverted-U hypothesis performance is best at a moderate level of arousal. Both low and high levels of arousal are associated with decrements in performance. The original work done on the inverted-U hypothesis related to the strength of stimulus and habit-formation (learning) in mice (Yerkes & Dodson, 1908 ). Mice learned most quickly which chamber of two to enter when the punishment for choosing the wrong chamber was an electric shock of moderate intensity. This finding was supported by later work with rats (Broadhurst, 1957 ). From these rodent-based studies, it is difficult to see how the inverted-U hypothesis has become such a commonly used explanation for the arousal-performance link in humans. Perhaps the idea that moderate levels of arousal are suitable for performance has an intuitive appeal. This hypothesis was supported by some research in attention. For example, under high physiological arousal, the attention field narrows (cf. Easterbrook, 1959 ), which has a positive effect on performance if it blocks out unimportant distractions but a negative effect if the narrowing is so great that task-relevant cues are missed.

Some research evidence shows that anxiety (often associated with high arousal) relates to performance in the manner of an inverted U shape. Specifically, the best performances of 145 high school basketball players occurred under moderate levels of anxiety (Klavora, 1979 ), and the performance of university female basketball players was higher following medium levels of anxiety (Sonstroem & Bernardo, 1982 ). However, despite this support, the inverted-U hypothesis has been met with some criticism (cf. Neiss, 1988 ; Raglin, 1992 ; Zaichkowsky & Baltzell, 2001 ):

This hypothesis describes, but does not explain, the relationship between arousal and performance.

The symmetrical U shape is not a realistic representation of a competitive sport situation. Performance tends to deteriorate much more dramatically with high arousal.

Arousal itself is multidimensional and accordingly, the inverted-U hypothesis may be simplistic.

While the inverted-U hypothesis has some intuitive appeal, research has begun exploring how cognitive and physiological aspects of arousal interact to affect performance and contribute to the experience of athletes under stress. Much of this research has considered the role of arousal as part of the anxiety response.

Contemporary Approaches to Arousal and Sport Performance

Anxiety is characterized by feelings of apprehension and tension along with activation or arousal of the autonomic nervous system (ANS; Spielberger, 1966 ). Two elements of anxiety outlined in this definition, cognitive and physical, explain why more recent approaches to understanding arousal have considered both elements in their approaches.

Multidimensional Anxiety Theory (MAT)

One of the most influential theories in sport research is the multidimensional theory of competitive state anxiety (MAT; Martens, Burton, Vealey, Bump, & Smith, 1990 ).

In MAT cognitive anxiety refers to “fear of failure and negative expectations about performance” while somatic anxiety refers to “individuals’ perceptions of their physiological state” (Hardy, Jones, & Gould, 1996 ; p. 142). Adopting a multidimensional approach to the study of competitive anxiety means that an individual could be high in cognitive anxiety and low in somatic anxiety, or vice versa, high in both or low in both. Furthermore, this approach implies that cognitive and somatic anxiety have separate antecedents and different temporal patterning in the lead up to competition (Parfitt, Jones, & Hardy, 1990 ) and that they are affected differently by different anxiety control techniques (Burton, 1990 ) and crucially have different relationships with performance.

The conceptualization of competitive anxiety as a multidimensional construct meant that new measurement tools had to be developed. Martens and colleagues developed the Competitive State Anxiety Inventory-2 (CSAI-2) and published it alongside the MAT (Martens, Burton, Vealey, Bump, & Smith, 1990 ). The CSAI-2 was originally developed to assess cognitive and somatic anxiety, but an additional cognitive factor (self-confidence) emerged during the development. According to MAT, cognitive anxiety has a negative linear relationship, self-confidence a positive linear relationship, and somatic anxiety an inverted-U relationship with performance. Because the CSAI-2 and MAT were published simultaneously, the theory and the measurement tool are linked. Therefore, limitations in one may affect the other, and it is difficult to determine whether unsupportive research findings are a result of limitations in the theory, the measuring tool, or both.

Some research supports the central tenets of MAT. For example, a sample of swimmers, showed a curvilinear trend, similar to the inverted U, between somatic anxiety and performance. They demonstrated a negative linear trend between cognitive anxiety and performance and a positive relationship between self-confidence and performance (Burton, 1988 ). However, some conflicting evidence has also emerged. For example, in a sample of pistol shooters, a curvilinear trend, similar to the inverted U, between somatic anxiety and performance was observed, but no significant relationship between cognitive anxiety and performance was detected, and there was a negative relationship between self-confidence and performance (Gould, Petlichkoff, Simons, & Vevera, 1987 ; Hardy, Jones, & Gould, 1996 ). Collectively, empirical support for these predictions has been equivocal, with support primarily for the positive association between self-confidence and performance (e.g., Craft, Magyar, Becker, & Feltz, 2003 ; Woodman & Hardy, 2001 ). While the relationship between self-confidence and performance was consistent across sports in their meta-analysis, Craft et al. found that both cognitive anxiety and somatic anxiety seem more influential in individual sports (e.g., tennis, badminton), and data from the highest level of athlete (national competition level or higher) showed a positive relationship between cognitive anxiety and performance and somatic anxiety and performance. This finding suggests that for this more elite group, anxiety may be helpful for performance, and thus, it indirectly supports the drive theory.

In short, it is probably correct to say that the relationship between anxiety and performance is more complex than outlined in MAT. While there is support for some of MAT’s predications (e.g., somatic anxiety does appear to have a curvilinear relationship with performance), this relationship does not appear to be consistent across all groups of athletes (e.g., national level athletes). Perhaps support for MAT has been equivocal because much of it has utilized the CSAI-2 (Martens et al., 1990 ) and the construct validity of the CSAI-2 has been questioned (see Kerr, 1997 ; Lane et al., 1999 ). For example, when Jones and Uphill ( 2004 ) asked university athletes to imagine completing the CSAI-2 as if they were competing in the most important competition of the season as if they were either highly anxious (n = 83) or highly excited (n = 87), both the cognitive and somatic anxiety subscales from the excited group were substantially higher than the norms reported by Martens et al. ( 1990 ). In short, individuals scored highly on the cognitive and somatic anxiety intensity subscales of the CSAI-2 when experiencing an emotion (i.e., excitement) other than anxiety.

Because of concerns that the CSAI-2 does not adequately capture the competitive anxiety experience of performers, several researchers advocated using a modified version of the CSAI-2 that incorporated a directional subscale. The CSAI-2(d) measures not only the intensity of symptoms (as assessed by the original CSAI-2) but also considers the perception of these symptoms (e.g., Jones & Swain, 1992 ; Jones, 1995 ). This directional subscale provides a measure of whether the symptoms reported on the cognitive and somatic anxiety subscales are perceived as being facilitative or debilitative for performance. This modification of the CSAI-2 allowed researchers to test the control model of debilitative and facilitative competitive state anxiety (Jones, 1995 ), which proposes that athletes with a positive belief in their ability to cope, and in goal attainment, will interpret anxiety symptoms as facilitative (helpful), whereas those with negative expectancies will interpret their symptoms as debilitative (unhelpful) for performance (Jones, 1995 ). Both elite and successful competitors have reported more facilitative perceptions of anxiety symptoms in comparison to nonelite and unsuccessful competitors, respectively, when no differences in anxiety intensity levels were present (Jones, Swain, & Hardy, 1993 ; Jones & Swain, 1995 ). Research has generally supported the tenets of Jones’s theory and that athletes with a positive perception of anxiety symptoms perform better (see Cumming & Ramsey, 2008 for a review). However, the conceptual worth of this research has been questioned, and a positive perception of symptoms may simply represent the absence of any real levels of perceived anxiety (Lundqvist, Kentta, & Raglin, 2010 ). That is, in a sample of 84 Swedish athletes, Lundqvist et al. found that most of the anxiety items identified as facilitative for performance were rated at an intensity of “not at all,” and the absence of any perceived anxiety for these items is probably the main reason the athletes in this sample rated them as facilitative to performance.

One further limitation of MAT is that it considers the relationship between cognitive anxiety, somatic anxiety, and performance in a series of two-dimensional relationships (Hardy, 1990 ). But athletes are rarely cognitive anxious in the absence of somatic anxiety and vice versa, so how cognitive anxiety relates to performance may be influenced by somatic anxiety and how somatic anxiety relates to performance may be influenced by cognitive anxiety. The interaction between psychological and physiological arousal is discussed in more detail in the next two approaches outlined, reversal theory and catastrophe theory.

Reversal Theory

In reversal theory (Apter, 1989 ) the experience of arousal is different depending on the metamotivational states (or frames of mind) that an individual is in at any given time. There are four pairs of metamotivational states: telic-paratelic; conformist-negativistic; mastery-sympathy; autic-alloic. When one of each pair is active, the other is inactive. Thus, if a person is in a conformist state, they cannot be in a negativistic state. A person can reverse between opposite states for a number of reasons, including, for example, frustration from not achieving a goal, an external event, or satiation, which is being in the same metamotivational state for an extended period of time (Blaydon, Lindner, & Kerr, 2000 ). Although there are four pairs of metamotivational states, typically one or more of the states will be salient (Frey, 1999 ), reflecting a person’s motives at a particular time. For example, when the telic state is most salient, a person is goal oriented and has a preference for low levels of arousal.

Metamotivational states may be related to participation (e.g., Lindner & Kerr, 2000 ), change at different stages of competition (Males, Kerr, & Gerkovich, 1998 ), and perceptual and cognitive responses to exercise (Thatcher, Kuroda, Thatcher, & Legrand, 2010 ), and they may help explain athletes’ emotional responses to injury (Thatcher, Kerr, Amies, & Day, 2007 ). Reversal theory is supported in sport settings; the application of metamotivational states can explain the range of emotions experienced in sport, and these relate to performance and participation (see Hudson, Males, & Kerr, 2016 , for a review). However, Hudson et al. noted that additional robust research is needed, particularly for evidence to demonstrate that reversals can be controlled or that motivational states can be reliably induced at will in the context of sport and exercise. Another potential limitation of this approach is that interpretation of arousal does not seem to relate to some high-intensity emotions, such as happiness, an emotion frequently experienced in sport settings.

Catastrophe Theory

The catastrophe theory (Fazey & Hardy, 1988 ; Hardy, 1990 ) considers how cognitive anxiety and physiological arousal (not somatic anxiety, which is a perception of physiological state) interact to influence performance. The relationship between cognitive anxiety and performance is different depending on the level of physiological arousal and the relationship between physiological arousal and performance is different depending on the level of cognitive anxiety. Simply, according to catastrophe theory, it is not possible to know how cognitive anxiety relates to performance unless the level of physiological arousal is known and vice versa.

The left-hand side of the three-dimensional relationship where physiological arousal is low shows that increases in cognitive anxiety will help performance, whereas the opposite occurs when physiological arousal is high (the right-hand side). To best explain catastrophe, it is easiest to consider the back and front faces of the three-dimensional relationship as well as the relationship between physiological arousal and performance, in which cognitive anxiety acts as a splitting function. When an individual is experiencing low levels of cognitive anxiety, the relationship between physiological arousal and performance is in the shape of a gentle inverted U. When cognitive anxiety is high, increases in physiological arousal facilitate performance up to an optimum level, but increases past the optimum level result in a severe performance decrement (i.e., a catastrophe). To regain composure and optimum performance, a large reduction in physiological arousal is necessary. Only when cognitive anxiety is high do increases in physiological arousal above the optimum lead to sharp catastrophic decreases in performance.

Hysteresis describes the distinct relationship between physiological arousal and performance under conditions of high cognitive anxiety depending on whether physiological arousal is increasing or decreasing. Hysteresis has been demonstrated in eight crown green bowlers (Hardy, Parfitt, & Pates, 1994 ) who completed a bowling task under conditions of low cognitive anxiety, where their individual data would not be compared, and high cognitive anxiety where they were told their scores would be compared to elite crown green bowlers. Physiological arousal was manipulated using physical exercise, and half the participants did the task with physiological arousal increasing and half with physiological arousal decreasing. While there was evidence of a substantial reduction in performance under conditions of high cognitive anxiety as physiological arousal was increasing, there was no evidence of a substantial decrease in physiological arousal necessary before the bowlers “flipped” back to the upper performance surface of the model. There is other support for the central tenets of catastrophe theory (e.g., Edwards & Hardy, 1996 ; Hardy, Woodman, & Carrington, 2004 ). Although catastrophe theory has been criticized as being too complex to test and therefore of dubious value to sport psychologists (Gill, 1994 ), elements of the theory have been tested, and as Hardy, Jones, and Gould ( 1996 ) point out, complexity is not a reason for rejecting a theory. Indeed, more contemporary theories have not only considered the interaction between psychological variables and physiological states but also that subtle differences in physiological responses may indicate positive or negative approaches to stress.

Challenge and Threat States

Another approach that outlines how a person may respond positively and negatively under stress is the biopsychosocial (BPS) model of challenge and threat (Blascovich & Mendes, 2000 ). Challenge and threat are two distinct psychophysiological responses to stressors that occur in motivated performance situations (like sport) where success is important and there are perceived (via demand appraisals) dangers to esteem, uncertainty, and a requirement for effort (see Blascovich, Mendes, Vanman, & Dickerson, 2011 ; Seery, 2011 ). Building on the BPS model and related work (Obrist, 1981 ; Dienstbier, 1989 ) the theory of challenge and threat states in athletes (TCTSA; Jones et al., 2009 ) and integrative framework of stress, attention, and visuomotor performance (Vine, Moore, & Wilson, 2016 ) offer more recent transactional approaches specific to athletic performance by proposing a framework for psychological, emotional, physiological, and behavioral (attentional) reactions in sport. In the BPS model, the TCTSA, and Vines’ framework, importance is placed on whether an individual experiences a challenge state or a threat state, rather than the magnitude of arousal evinced. Both a challenge and a threat state involve augmented arousal, but in a challenge state this physiological reaction is adaptive, and in a threat state it is maladaptive. In sum, the TCTSA builds on previous theory (Obrist, 1981 ; Dienstbier, 1989 ; Blascovich & Mendes, 2000 ) and offers an integrative, interdisciplinary approach to the understanding of the human stress response in competitive situations,

While the aforementioned challenge and threat approaches place emphasis on the cardiovascular components of challenge and threat states, Vine et al. offer a more detailed account of the attentional consequences of challenge and threat in visually guided motor skills, whereas Jones et al. offer a more detailed account of the cognitive antecedents and performance consequences of challenge and threat.

Specifically in the TCTSA (Jones et al., 2009 ), a challenge state is experienced when sufficient, or nearly sufficient, resources to meet the demands of a situation are perceived, whereas a threat state is experienced when insufficient resources to meet the demands of a situation are perceived. Demand appraisals comprise perceptions of danger, uncertainty, and required effort in a situation, while resource appraisals comprise three interrelated constructs: self-efficacy, perceptions of control, and goal orientation. Jones et al. ( 2009 ) suggest that high levels of self-efficacy, perceived control, and focus on approach goals, represent sufficient resources to cope in a motivated performance situation and are therefore indicative of a challenge state. Conversely, low levels of self-efficacy, perceived control, and focus on avoidance goals, represent insufficient resources to cope in a motivated performance situation and are indicative of a threat state. Physiologically, a challenge state is accompanied by increased sympathetic adrenomedullary (SAM) activity and catecholamine release (i.e., epinephrine and norepinephrine), which is proposed to promote efficient energy use through increased blood flow to the brain and muscles, higher blood glucose levels (fuel for the nervous system), and an increase in free fatty acids that can be used by muscles as fuel (e.g., Dienstbier, 1989 ). A challenge state is fast acting and represents the efficient mobilization of energy for action.

A threat state is also marked by increased SAM activity, but it is also characterized by increased pituitary adrenocortical (PAC) activity accompanied by cortisol release, which tempers the positive effects of SAM activity. Therefore, the mobilization of energy is less efficient than in a challenge state as blood flow (and therefore glucose) to the brain and muscles is restricted (e.g., Dienstbier, 1989 ). A threat state is considered a “distress system” that is maladaptive for performance situations. Indeed, growing research indicates that a challenge state is associated with better cognitive and motor performance than a threat state (e.g., Blascovich, Seery, Mugridge, Norris, & Weisbuch, 2004 ; Moore, Vine, Wilson, & Freeman, 2012 ; Turner, Jones, Sheffield, & Cross, 2012 ) and maintained health (cf. O’Donovan et al., 2012 ). For example, in one study researchers examined the relationship between CV reactivity and the performance of 42 elite male cricketers in a pressured batting test (Turner, Jones, Sheffield, Slater, Barker, & Bell, 2013 ). The batting test required the cricketers to score 36 runs from 30 deliveries and athletes were allocated runs by a national coach. After baseline CV recording, athletes were informed that their performances would be compared to those of all other cricketers and would be seen by all coaching staff, and that their scores would be considered when future team selection was made. The athletes’ CV reactivity to being informed about the batting test was recorded as it is with the netball athletes. Challenge CV reactivity was related to superior performance compared to threat CV reactivity. That is, athletes who exhibited challenge CV reactivity recorded a better score in the batting test than athletes who exhibited threat CV reactivity. In another study (Moore, Vine, Wilson, & Freeman, 2012 ), researchers assessed the cognitive appraisals, emotions (anxiety), CV reactivity (CO and TPR), visual gaze, putting kinematics, muscle activity, and golf putting performance of novice golfers. Participants in a challenge condition, manipulated using instructional sets, exhibited greater challenge CV reactivity and challenge appraisals than participants in a threat condition. Furthermore, participants who exhibited challenge CV reactivity reported more favorable emotions; displayed more effective visual gaze, putting kinematics, and muscle activity; and performed more accurately in the golf putting task than participants who exhibited threat CV reactivity.

Although research investigating the impact of the resource appraisals on challenge and threat states is in its fledgling stage (e.g., Turner et al., 2014 ), the theoretical background for the three resource appraisals is strong and stems from these models: the BPS model (Blascovich & Mendes, 2000 ), the model of adaptive approaches to competition (Skinner & Brewer, 2004 ), and the model of debilitative and facilitative competitive state anxiety (Jones, 1995 ). Therefore, strategies that help athletes to increase their resource appraisals to meet or exceed perceived demands, can promote a challenge state and are therefore valuable (Turner & Barker, 2014 ). In other words, rather than using arousal attenuation or activation strategies, which can be useful at times, athletes should primarily focus on increasing their self-efficacy, perceived control, and approach goals.

Strategies for Confidence, Control, Approach Focus, and Reappraisal

The strategies for promoting a challenge state broadly fit within two themes. The first theme reflects strategies that can be adopted by coaches to create an environment in which a challenge state is more likely. The second theme reflect psychological skills that can be learned by athletes to get themselves into a challenge state.

Creating a Challenge Environment

One method by which challenge has been promoted uses instructional sets. More specifically, past research has used instructional sets to manipulate challenge and threat states. In line with theory (Blascovich & Mendes, 2000 ; Jones et al., 2009 ), challenge instructions typically emphasize the perception of high resource appraisals, and some experiments also attempt to lower the perception of demand appraisals. The use of instructional sets stems from a consistent body of research demonstrating that psychophysiological responses to stressors can be influenced by what participants are told prior to a stressful task (e.g., Allred & Smith, 1989 ) and that instructional sets can modify perceptions of challenge and threat (e.g., Taylor & Scogin, 1992 ; Hemenover & Dienstbier, 1996 ; Alter, Aronson, Darley, Rodriguez, & Ruble, 2010 ; Feinberg & Aiello, 2010 ).

In one study (Feinberg & Aiello, 2010 ), challenge instructions focused on perceiving a cognitive task “as a challenge to be met and overcome” (p. 2079), while threat instructions focused on the difficulty of the task and the importance of working “as quickly and efficiently as possible” (p. 2079). Results demonstrated that challenge appraisals and performance increments followed challenge instructions, while threat appraisals and performance decrements followed threat instructions. However, this study did not include measurements of arousal or physiological reactivity. Growing research demonstrates that challenge and threat instructions can also influence physiological markers of challenge and threat. Another study (Tomaka, Blascovich, Kibler, & Ernst, 1997 ) showed that participants given threat instructions about an upcoming mental arithmetic task experienced threat CV reactivity and cognitively appraised the task as threatening. Conversely, participants given challenge task instructions experienced challenge CV reactivity and cognitively appraised the task as a challenge. Importantly, challenge instructions urged participants to “think of the task as a challenge” (p. 72), while threat instructions reminded participants that the task would be “scored for speed and accuracy” (p. 72). Using similar instructions but in relation to a golf putting task, Moore et al. ( 2012 ) found that those who received challenge instructions appraised the task as a challenge, exhibited challenge CV reactivity, and they displayed more effective visual gaze, putting kinematics, and muscle activity, which aided performance in the putting task, compared to those who received threat instructions.

More recent research (Turner, Jones, Sheffield, Barker, & Coffee, 2014 ) confirmed that challenge instructions only increased the perceptions of resource appraisals from the TCTSA, and threat instructions only decreased the perceptions of resource appraisals, keeping task demands the same between conditions. In other words, challenge instructions promoted high self-efficacy, high perceived control, and a focus on approach goals; threat instructions promoted low self-efficacy, low perceived control, and a focus on avoidance goals. Both sets of instructions increased perceptions of danger, uncertainty, and effort, thus maintaining perceived demands and only altering perceived resources. In two laboratory studies, a throwing across task and a climbing well task, Turner et al. ( 2014 ) found that challenge instructions led to challenge CV reactivity, whereas threat instructions led to threat CV reactivity.

The research suggesting that a challenge state can be promoted using instructional sets has important implications for how leaders manage individual and team approaches to stressors. Leaders can have an important influence on their subordinates’ responses to stressful situations (e.g., Smith, Smoll, & Weichman, 1998 ; Baker, Côté, & Hawes, 2000 ), and therefore they could use this influence to promote a challenge state. Leaders can ensure that their communications with subordinates prior to stressful situations include primers for high confidence, control, and approach goals, while retaining references to the gravity and importance of the occasion. The use of particular instructional sets can also form part of the social support offered by the leader and others within a team setting.

A significant body of research indicates that social support provides a buffer for the adverse effects of stress (e.g., Cohen & McKay, 1984 ; Haslam, O’Brien, Jetten, Vormedal, & Penna, 2005 ). Cobb ( 1976 ) suggests that psychological support reflects the provision of information (e.g., effective coping response) and therefore it is important to provide the right information to those entering stressful situations. Social support can buffer stress in many different ways, but for the purposes of this article, one important mechanism is through informational support (House, 1981 ). Informational support provides those in receipt with coping guidance, similar to challenge instructions, and contributes to positive appraisal by helping those in receipt clarify their understanding of threatening stimuli (e.g., Aspinwall & Taylor, 1997 ). Informational social support can be used to help convince an individual that they can cope with the stressor (Cohen & McKay, 1984 ). Therefore, information offered to individuals that promotes high perceived resources, such as the instructions used in past research (e.g., Tomaka et al., 1997 ; Turner et al., 2014 ), may help those who receive them to enter a challenge state. In addition, Rees and Hardy ( 2004 ) found that social support positively influences performance, regardless of the level of stress, and more recently, Freeman and Rees ( 2008 ) found that high levels of esteem support predicted smaller threat appraisals and greater challenge appraisals, with subsequent better golf performance. The role of social support in challenge and threat states is yet to be fully tested, and some research has found that social support has little effect on challenge and threat states (Moore, Vine, Wilson, & Freeman, 2014 ). However, some suggest that social support could help enhance the resource appraisals, or could actually be a resource appraisal itself (e.g., Haslam & Reicher, 2006 ). Coaches may play an important role in social support, and a recent study (Nichols, Levy, Jones, Meir, Radcliffe, & Perry, 2016 ) of athletes’ perceptions of coach behaviors found a positive association between supportive coach behaviors and challenge and unsupportive coach behaviors and threat. This finding illustrates that coaches can influence the self-reported challenge and threat states of athletes. Interestingly, in a study of soccer coaches coaching behaviors (Dixon, Turner, & Gillman, 2016 ) found positive associations between challenge appraisals and social support and between threat appraisals and autocratic behavior as well as a significantly negative association between threat appraisals and positive feedback. Therefore, the ways coaches appraise stressors are also important for how they behave towards their athletes.

Recently, research has identified a hormone that plays a big role in social bonding that also may influence the human stress response. Oxytocin is produced in the hypothalamus, and in low stress situations, it may physiologically reward those who maintain good social bonds with feelings of greater well-being. But when oxytocin operates in high stress situations, it may encourage people to seek out social contact. Further, oxytocin released during positive (supportive) social contact, even if this social contact is only anticipated, actually reduces the severity of the body’s stress response (Taylor, 2006 ). Recent research (Kubzansky, Mendes, Appleton, Block, & Adler, 2012 ) indicates that when people are put under social stress (e.g., public speaking), oxytocin is associated with a challenge state and a healthier recovery profile after the stress. Research also suggests that oxytocin may help to lower blood pressure and cortisol levels (Light, Smith, Johns, Brownley, Hofheimer, & Amico, 2000 ). In summary, when facing a stressful situation, oxytocin may help people to better deal with stress.

Part of creating a challenge environment may also involve helping individuals to adapt to stressful situations via experiential learning, which places individuals in demanding situations. Past performance accomplishments are a powerful source of self-efficacy (Bandura, 1997 ; Feltz & Lirgg, 2001 ), and, as is recognized in MAT and catastrophe theory, self-efficacy plays an important role in the relationship between arousal and performance. Self-efficacy is also an important resource appraisal in the TCTSA. Therefore, helping athletes to flourish in stressful situations may provide important sources of self-efficacy for subsequence stressors. One way to achieve this experiential learning is through systematic desensitization (Wolpe, 1973 ). In brief, the athlete is subjected to stress regularly and systematically, thus promoting acclimatization to future stressors. This exposure to stress may foster resilience, a construct that has been put forth in relation to challenge and threat states by Seery ( 2011 ). For Seery, the exhibition of a challenge state and potential positive (or less negative) outcomes, is suggestive of resilience in motivated situations, and individuals who have a history of facing some adversity should exhibit greater resilience than those who have experienced no or high adversity. Past research offers some evidence for Seery’s notion of resilience, where repeated exposure to stressors has been shown to lead to an increase in challenge over time (Quigley, Barrett, & Weinstein, 2002 ). In other words, situations that become more familiar may promote a challenge appraisal and challenge CV responses due to enhanced coping perceptions (Blascovich et al., 1999 ; Quigley et al., 2002 ). Also in support of his assertions, Seery, Leo, Lupien, Kondrak, and Almonte ( 2013 ) found that relative to a history of either no adversity or nonextreme high adversity, a moderate number of adverse life events is associated with less negative responses to pain and more positive psychophysiological responses while taking a test. The precise impact of exposure on the demand and resource appraisals is not yet known, and future research should investigate exposure in line with the TCTSA.

Psychological Skills: Imagery, Reappraisal, Relaxation

Psychological skills are techniques that can be applied by individuals to regulate their own internal states such as cognitions and emotions. Two main psychological skills have emerged in literature that can promote a challenge state: reappraisal and imagery.

Reappraisal is an important strategy for regulating emotions (see Gross, 1998 , for review), and two studies have examined the effects of reappraisal on challenge and threat states (i.e., Jamieson, Mendes, Blackstock, & Schmader, 2010 ; Jamieson, Nock, & Mendes, 2012 ). In Jamieson et al.’s ( 2010 ) study, prior to an exam, reappraisal condition participants were told that “recent research suggests that arousal doesn’t hurt performance” and that “people who feel anxious during a test might actually do better.” They were also encouraged to “simply remind yourself that your arousal could be helping you do well” (p. 2). By being prompted to perceive their anxiety as helpful, participants in the reappraisal condition exhibited higher catecholamine levels, indicative of SAM activity (challenge state), perceived their anxiety as helpful, were more confident about performance and demonstrated better performance in the exam compared to a control group. Jamieson et al. ( 2012 ) similarly used a reappraisal condition to encourage participants facing a speech task that their arousal is functional and can help them to succeed. Results showed that participants in the reappraisal condition had higher perceived resources and exhibited higher increases cardiac output as well as lower increases in total peripheral resistance compared to the control group; a psychophysiologically adaptive response. In sport, after responding to a pressure task with a threat state, a reappraisal group shifted toward a challenge cardiovascular response, although this difference was not statistically significant (Moore, Vine, Wilson, & Freeman, 2015 ). The reappraisal group also outperformed the control group during the pressurized task. Importantly, reappraisal does not dampen arousal but aims to reshape how arousal is perceived (Jamieson et al., 2013 ), which contrasts with theories such as MAT and catastrophe theory, where arousal level is seen as important for performance.

Another way to promote a challenge state is through the use of imagery, a technique that involves realistically recreating or creating events in the absence of physical practice. Imagery can be used for a variety of purposes, but notably, it is effective for regulating emotions (e.g., Hecker & Kaczor, 1988 ), enhancing self-confidence (Callow, Hardy, & Hall, 2001 ), and promoting coping under stress (e.g., Vadocz, Hall, & Moritz, 1997 ; for reviews, see Martin, Moritz, & Hall, 1999 ; Cumming & Ramsey, 2008 ), all of which are important aspects of a challenge state. The mechanisms for how imagery works are still under debate, but nonetheless, imagery is a well-researched skill that has been shown to be valuable for motivated performance situations (Durand, Hall, & Haslam, 1997 ). Three studies have expressly applied imagery to enhance a challenge state (Hale & Whitehouse, 1998 ; Williams, Cumming, & Balanos, 2010 ; Williams & Cumming, 2012 ). Hale and Whitehouse ( 1998 ) showed that an imagery-based video and audiotaped manipulation that prompted challenge perceptions resulted in less cognitive anxiety, less somatic anxiety, more self-confidence, and perceptions that symptoms were facilitative. In Williams et al. ( 2010 ) a challenge imagery script that emphasized resources (challenge appraisals), promoted high self-efficacy, high perceived control, and potential gain led to lower threat appraisals, positive emotion perceptions, and higher confidence. Similar scripts were used by Williams and Cumming ( 2012 ) who also found that the challenge script led to challenge appraisals and the threat script led to threat appraisal and a perception that emotional responses were debilitating for performance. Imagery offers a useful way to promote a challenge state, but more research is needed to test the psychophysiological implications of effective imagery use.

Although to date no studies have explicitly explored the effect of relaxation strategies on challenge and threat states, the use of relaxation techniques may be helpful in regulating arousal and may have the potential to reduce the intensity of the felt threat state and potentially its impact on performance, whereas energizing strategies may help enhance the felt experience of a challenge state. This is because increasing or decreasing physiological arousal would appear to have a blanket effect on the intensity of an individual’s emotional state (e.g., Hohmann, 1966 ; Zillmann, Katcher, & Milavsky, 1972 ).

Relaxation techniques have been classified as muscle-to-mind techniques, which are more physical in nature (e.g., breathing techniques), or mind-to-muscle techniques (imaging being in a relaxing environment), which are more cognitive in nature (Harris, 1986 ). However, the autonomic nervous system and cognitive aspects of emotion are linked, illustrated in the fact that an intervention designed to reduce somatic (physical) anxiety also reduced, albeit to a lesser degree, cognitive anxiety in soccer players (Maynard, Hemmings, & Warwick-Evans, 1995 ) and field hockey players (Maynard & Cotton, 1993 ). A number of strategies have been proposed to reduce arousal (e.g., progressive muscular relaxation, centering), whereas strategies to increase arousal include up-beat music and exercise itself (Jones, 2003 ).

One approach that has a particular focus on arousal control in sport is biofeedback (Zaichkowsky & Fuchs, 1988 ). This approach is based on the principle that athletes can learn to voluntarily control their arousal levels by receiving concurrent feedback from an instrument that measures aspects of the autonomic nervous system response. The athlete can experiment with different thoughts and feelings to reduce or increase arousal. It is then anticipated that the ability to control arousal levels transfer to the athletic field. For example, a 20-year-old small-bore rifle shooter underwent an intervention comprising relaxation strategies, thought stopping and biofeedback which resulted in lower levels of urinary adrenaline and noradrenaline (physiological markers indicative of anxiety) in subsequent competitions (Prapavessis, Grove, McNair, & Cable, 1992 ). Biofeedback is also often used as a strategy to regulate Heart Rate Variability (HRV), which is proposed to be a measure of autonomic flexibility. That is, the interplay between sympathetic and parasympathetic influences heart rate and is proposed to represent the capacity for emotional responding (Appelhans & Luecken, 2006 ). HRV training utilizes the link between respiration and HRV wherein breathing in accelerates heart rate and breathing out lowers heart rate. In HRV training, breathing is regulated to around 6 breaths per minute (Vaschillo, Lehrer, Rishe, & Konstantinov, 2002 ). Greater HRV is associated with more positive emotional response to stressors (e.g., Bornas et al., 2005 ) and both performance of stressful tasks (e.g., Hansen et al., 2003 ); there is also some support for the application of HRV training in sport (e.g., Maman & Kanupriya, 2012 ), although more research is needed.

The area of arousal control in sport has moved through initial simplistic theories of arousal toward more complex psychophysiological explanations for the relationship between arousal and performance. More current theory suggests that arousal control is less about arousal magnitude or severity and more about the underlying endocronological processes that regulate arousal. Also, the notion that the perception of arousal symptoms may provide a stronger link to performance has garnered much support. Regardless of the decades of theoretical debate already present in this area, arousal control is a topic that will continue to be examined and discussed, particularly as advancements are made in how psychophysiological reactivity is measure at a biochemical and neurological level. For example, one approach that has received little research in sport is the role of Neuropeptide Y (NPY). NPY has been consistently associated with a positive response under stress, and this has been demonstrated in military settings, including special forces personnel in the United States (Morgan, Wang, Southwick, Rasmousson, Hazlett, Hauger, & Charney, 2000 ). NPY is a 36-amino-acid peptide, and receptors for NPY in the brain are similar (i.e., amygdala, hippocampus, locus coeruleus) to those of ACTH, which ultimately stimulates the release of cortisol. Furthermore, NPY and ACTH have counterbalancing functional effects; thus, NPY may, in effect, attenuate the stress response (Nulk, Schuh, Burrell, & Matthews, 2011 ).

Theoretical developments have also yielded advances in strategies to help performers regulate arousal; the ability to perform under pressure id still considered a fundamental aspect of athletic success. Arousal control is not only about being relaxed, it is also about recognizing the optimum state for performance and finding methods by which to arrive at that state. This idea is perhaps best summed up by Lewis Moody (retired England Rugby Union World Cup winner):

“Before you play, you have to get yourself in the right frame of mind. If you’re not mentally right, you won’t be able to produce your best. Everyone’s different though—you have to do what works for you. Some guys run around shouting and screaming whereas others prefer to chill out” (Moody, 2005 ).

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The theory of inverted u: a comprehensive exploration.

Dive deep into the theory of Inverted U, also known as the Yerkes-Dodson Law. Understand how it affects performance, productivity, and stress management across various life aspects.

Understanding the Inverted U Theory: An Introduction

The Theory of Inverted U , also known as the Yerkes-Dodson Law , is a critical psychological concept that explores the complex relationship between arousal, stress, and performance. Introduced by psychologists Robert Yerkes and John Dodson in 1908, the law suggests that a certain level of stress can enhance performance, but there's a threshold beyond which performance deteriorates.

This theory is a fundamental framework to understand productivity, stress management, decision making, and even motivation. This article aims to present an in-depth exploration of this mental model with relatable examples and practical applications.

Unpacking the Inverted U Model

The Inverted U model visualizes the correlation between pressure (stress or arousal) and performance. This correlation is divided into three primary phases:

Ascending Phase (Increasing Returns) : At this stage, as stress or stimulation increases, performance also improves. The pressure can act as a catalyst to drive focus and energy.

Peak Point (Optimal Performance) : This is the ideal stress-performance equilibrium. At this point, an individual or system is at their peak performance—the right amount of stress fuels motivation and focus without causing overwhelm.

Descending Phase (Decreasing Returns) : Past the optimal point, any additional stress results in deteriorating performance. Here, stress outweighs the individual's coping mechanisms, leading to errors, decreased productivity, or even burnout.

A Day in the Life: The Inverted U Model in Action

To better grasp this theory, imagine a regular workday. In the morning, as you sip your coffee, your arousal levels gradually increase. You start working and as the pressure mildly intensifies, you find yourself becoming more efficient - this is the ascending phase of the model.

Come mid-day, you're entirely engrossed in your work, handling tasks effectively - you're at the peak point of the inverted U, experiencing optimal stress levels and showcasing your best performance.

As the day progresses, if the workload continues to pile up, you might start feeling overwhelmed. The excessive stress leads to fatigue and mistakes - you've entered the descending phase of the model, where increased stress leads to decreased performance.

Practical Applications of the Inverted U Theory

Understanding the theory of Inverted U allows us to optimize performance and well-being in various contexts, from personal growth to professional environments, education, and even sports training.

Workplace Productivity

Effective stress management is crucial in the workplace. Leaders and managers can utilize this model to ensure employees aren't overloaded with work and to prevent burnout. For instance, setting realistic deadlines, promoting a healthy work-life balance, and recognizing employees' efforts can help maintain an optimal stress-performance balance.

Education and Learning

The Yerkes-Dodson law is equally applicable in the realm of education. It helps teachers, parents, and students understand the impact of stress on academic performance. Moderate pressure can encourage students to study and prepare well for exams. However, excess stress might impair focus, memory recall, and overall learning.

Sports and Performance Psychology

In sports, the right amount of arousal can boost performance. Athletes often perform their best when they're mildly stressed - it enhances focus and adrenaline flow. However, too much anxiety can lead to poor performance. Coaches and athletes can use this model to devise optimal training strategies, taking care to avoid overtraining and promoting proper rest and recovery.

Conclusion: Harnessing the Power of the Inverted U Theory

The Theory of Inverted U or the Yerkes-Dodson Law offers vital insights into the intricate interplay of stress and performance. By understanding this relationship, we can strive for balance, optimizing productivity without compromising well-being.

Whether you're a professional trying to maximize your work output, a student seeking to optimize study habits, or a sports coach aiming to improve team performance, this mental model offers a powerful framework to inform your strategy.

Remember, the goal isn't to eliminate stress, but to harness it - striking the right balance is the key to unlocking peak performance.

The Quest for the Inverted U

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The quest for the inverted U, although not without historical precedents, received its major modern impetus with the publication of Daniel E. Berlyne’s Conflict, Arousal and Curiosity (1960). In this and in later volumes Berlyne developed a conception of motivation that was in sharp contrast to the prevailing formulations of psychiatry, psychology, and behavior theory.

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Walker, E.L. (1981). The Quest for the Inverted U. In: Day, H.I. (eds) Advances in Intrinsic Motivation and Aesthetics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3195-7_3

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The Inverted “U-Shaped” Dose-Effect Relationships in Learning and Memory: Modulation of Arousal and Consolidation

In the ample field of biological non-linear relationships there is also the inverted U-shaped dose-effect. In relation to cognitive functions, this phenomenon has been widely reported for many active compounds, in several learning paradigms, in several animal species and does not depend on either administration route (systemic or endocerebral) or administration time (before or after training). This review summarizes its most interesting aspects. The hypothesized mechanisms supporting it are reported and discussed, with particular emphasis on the participation of emotional arousal levels in the modulation of memory processes. Findings on the well documented relationship between stress, emotional arousal, peripheral epinephrine levels, cerebral norepinephrine levels and memory consolidation are reported. These are discussed and the need for further research is underlined.

INTRODUCTION

The so called “inverted U-shaped dose-effect curve” (IUSDEC) is a nonlinear relationship which has been frequently reported when studying the negative or positive actions of pharmacological and non-pharmacological treatments on cognitive functions and memory. The effects of increasing dosages of a given compound appear to increase up to a maximum, and then the effects decrease. At the present time it is not easy to elucidate the mechanisms on which the IUSDEC is based and in many instances researchers have described it without attempting any interpretation. Even when an attempt was made, not all mechanisms have been clarified. In some cases (cholinesterase inhibitors) a pharmacological mechanism has been proposed but most of the interpretations rest on the effects of emotional arousal modifications.

Arousal has been invoked as an essential endogenous modulator of memory processes ( Gold and Zornetzer 1983 ; McGaugh 1989a ; Lupien and McEwen 1997 ). The “arousal hypothesis” of IUSDEC is based on the finding that the arousal state can interact with exogenously supplied mnemoactive or presumptive mnemoactive agents to alter their effectiveness at any given dosage. On the other hand, there is considerable evidence that retention can be modulated by the administration of hormones and neuromodulators that are normally released during experiences comparable to those observed during training, as well as evidence that retention can be influenced by treatments that alter the functioning of these systems ( McGaugh 1989a ). Moreover it is of interest that IUSDEC has been reported after both pre-training and post-training treatments. Some doubts on the importance of active compounds (and the related IUSDEC) in specific mnemonic processing can be advanced in the case of pre-training administration. In fact, it is sufficient to surmise that the active compound lowers pain thresholds and improves olfactory and/or visual acuity: if so, learning would be affected, without any direct interference on memory processing. On the other hand, in post-training administration the possibility of alterating sensory or motor function is avoided, and thus are avoided their possible, but not assessable, effects on mnemonic processing. Indeed, since IUSDEC has been reported many times following post-training administration, the dose-response effects measured in these experimental conditions can be much more closely related to specific actions on mnemonic processing ( McGaugh 1989b ). Nevertheless, a caution must be expressed before proposing shorp divisions. In fact, if it may be accepted that arousal level influences learning by acting on how the animal acquires the information to be memorized, it cannot be excluded that also during consolidation this same factor may still act on memorization ( Gold and Zornetzer, 1983 ). Thus, even during consolidation, when the animal is neither called to perform any overt behavior nor receives further sensorial inputs, trace processing cannot be thought to be completely unrelated to the emotive/motivational condition of the experimental subject. In fact it is accepted that what may be called an “appropriate” level of neural activation, lasting some time after the training events, is a necessary condition to achieve viable engram elaboration ( McGaugh, 1989a ). In other words, if the post-training treatment entails an alteration of the background matrix of neural activity currently referred as arousal, engram elaboration may nevertheless be influenced, even if the treatment, per se, is not directly mnemoactive. Presently the experimental findings on IUSDEC in modulation of arousal and consolidation will be reported, starting from the well documented relationships between stress, peripheral epinephrine levels, cerebral norepinephrine levels and learning. All of these show that the combined effect of training and drugs on mnemonic processing follows a biphasic nonlinear trend.

THE INVERTED U-SHAPED RELATIONSHIP BETWEEN LEARNING AND AROUSAL LEVEL: ROLE OF SYSTEMIC EPINEPHRINE AND BRAIN NOREPINEPHRINE

Early investigations showed that retention is modulated by post-training peripheral administration of the adrenal medullary hormone epinephrine ( Gold and Van Buskirk, 1975 , 1976 ; Gold, 1984 ; McGaugh and Gold, 1988). Typically, retention is enhanced by low to moderate dosages and impaired by higher ones. The IUSDEC suggests that plasma epinephrine might be involved in amnesia as well as in memory enhancement ( Gold and van Buskirk, 1975 ). Stressful stimulations, including the mildly stressful ones typically used in studies of learning and memory in animals, cause release of epinephrine from the adrenal medulla; therefore, findings indicating that memory is influenced by post-training injections of epinephrine are consistent with the view that memory storage is modulated by the release of endogenous epinephrine ( Gold and McGaugh, 1975 ). On this point it has been repeatedly shown that plasma epinephrine concentrations are altered by various stressors including the footshocks which are part of the training paradigm. In a study concerning the relationships between footshock intensity, stress amine levels and memory, animals received sham, low, or high footshock training and plasma samples were taken immediately after training. Low footshock training caused an increase in plasma epinephrine similar to that shown by handled, not-footshocked rats; furthermore, low footshock intensity did not produce an optimal inhibitory avoidance retention performance. In contrast, high footshock training, at an intensity that produced very good retention performance, resulted in higher plasma epinephrine levels ( McCarty and Gold, 1981 ). It was also found that in experiments where rats are trained with a mild footshock punishment and given post-training systemic epinephrine, the dose that yields optimal enhancement of memory produces (shortly after training) plasma epinephrine levels comparable to those found in untreated animals, trained with a high footshock intensity that yields good retention ( Gold and McCarty, 1981 ). Gold and van Buskirk (1976) found that the same epinephrine dose that enhanced retention performance after low footshock training could produce amnesia if administered after high footshock training. All these findings support the view that treatments or conditions which alter the endogenous plasma epinephrine levels in response to training, either by increasing or decreasing them, interfere with memory processing, according to an IUSDEC, probably by modifying the emotional arousal level. Therefore, under weak training conditions, those treatments which appear to mimic the adrenergic response to more severe training procedures enhance memory retention.

Stress footshock and other stressors result in a transient decrease in rat’s brain norepinephrine content, due to the release and metabolization of this amine prior to its resynthesis. Not surprisingly concentration variations of brain norepinephrine after inhibitory avoidance training with low and high footshocks were found to be analogous to those described above for plasma epinephrine ( Gold and van Buskirk, 1978 ). Low footshocks had no significant effect on brain norepinephrine concentration. High training footshocks were followed by a transient 20% decrease in brain norepinephrine concentration. It should be stressed that the magnitude of this transient post-training decrease is closely correlated with later retention performance over a wide range of experimental conditions. Moreover, it was convincingly shown that epinephrine plasma level modulates brain norepinephrine concentration, thus proving a direct correlation between peripheral and central amine concentrations. The animals which receive a subcutaneous epinephrine injection (0.1 mg/kg) after low footshock training exhibit enhanced retention performance compared to saline-injected rats trained with high footshocks. In addition, both these groups of animals exhibit a 20% decrease in brain norepinephrine concentration. On the other hand, a higher amnesia-producing epinephrine dose (0.5 mg/kg) elicits a 40% decrease in brain norepinephrine concentration ( Gold and Van Buskirk, 1978 ). Thus, not only modulation of plasma epinephrine levels but also modulation of brain norepinephrine levels, due to arousal and pharmacological treatments, directly influence memory retention, and this influence is expressed as an inverted U-shaped relationship.

More recent studies have advanced our understanding of how epinephrine and norepinephrine influence memory consolidation. It has been shown that there is a peripheral-central neuronal pathway mediating the effects of epinephrine on memory consolidation. The nucleus of the solitary tract appears to act as an interface between the peripheral endocrine/autonomic milieu and the neural mechanisms regulating memory consolidation. Epinephrine activates β-adrenoceptors on vagal afferents terminating on brainstem noradrenergic cell groups in the nucleus of the solitary tract. Temporary inactivation of this nucleus with a local infusion of lidocaine blocks epinephrine effects on memory consolidation ( Williams and McGaugh 1993 ). Post-training electrical stimulation of the ascending vagus nerve induces memory enhancement similar to that produced by epinephrine ( Clark et al., 1998 ). Noradrenergic projections from the nucleus of the solitary tract innervate forebrain structures involved in learning and memory and influence norepinephrine release via descending projections to the nucleus paragigantocellularis in the lower medulla, which projects to the locus coeruleus ( Van Bockstaele et al., 1998 ). Noradrenergic neurons in this structure project to the amygdala. In fact, epinephrine affects memory consolidation by activating noradrenergic projection to the amygdala. Infusions of norepinephrine or β-adrenoceptor agonists into the amygdala after training enhance memory consolidation ( Ferry and McGaugh 1999 ) and the activation of both β- and_α-adrenoceptors in the basolateral nucleus of the amygdala appears to be necessary to mediate these noradrenergic influences on memory consolidation ( Ferry et al., 1999a , 1999b ; Hatfield and McGaugh 1999 ). In vivo microdialysis and high-performance liquid chromatography studies indicate that an increase of central epinephrine, due to systemic administration of this hormone ( Williams et al., 1998 ) or consequent to emotionally arousing training experiences ( Clark et al., 1998 ; Quirarte et al., 1998 ), induces the release of norepinephrine in the amygdala. Interestingly, footshock stimulation induces a release of nor-epinephrine in the amygdala which varies according to the intensity of the stimulus ( Galvez et al., 1996 ; Quirarte et al., 1998 ). Finally, epinephrine infusion into the nucleus of the solitary tract enhances training-induced nor-epinephrine release in the amygdala and improves retention performance ( Clayton and Williams 2000 ). These findings support the hypothesis that norepinephrine release in the amygdala plays a critical role in mediating emotional arousal effects on memory consolidation.

IUSDEC AND THE MODULATION OF AROUSAL AND CONSOLIDATION

Other compounds, besides amines, may modify memory retention following a biphasic non- linear dose-effect relationship, probably acting on arousal emotional levels interacting on the plasma epinephrine—brain norepinephrine system. For instance, a close relationship between amine and endorphins or glucose levels has been repeatedly reported ( Gold and Zornetzer, 1983 ; McGaugh, 1989a ). Not surprisingly, it has been suggested that there is a relationship between the levels of these compounds and arousal. It is quite interesting that the inversion of the effect on memory retention at high epinephrine dosages was due to the fact that epinephrine caused the liberation of β-endorphins at these dosages ( Introini-Collison and McGaugh 1987 ). Endorphins, systematically administered in the rat, caused disruption of passive avoidance retention, and facilitated active avoidance extinction, following an IUSDEC ( Gaffori and De Wied 1982 ). A quite clear-cut proof that the memory impairment induced by high doses of epinephrine is due to opioid peptide release was the demonstration that this effect was blocked by naloxone ( Introini-Collison and McGaugh 1987 ). On the other hand, the systemic administration of opioid antagonists, by itself, caused memory enhancement, either in a passive avoidance test in the mouse ( Introini-Collison and McGaugh 1987 ) or on recognition memory in the monkey ( Aigner and Mishkin 1988 ). The procognitive effect followed a IUSDEC.

It has been suggested that epinephrine effects on memory might be mediated, at least in part, by the release of glucose ( Gold, 1988 ). Post-training systemic injections of glucose produce non-linear, dose-dependent effects on inhibitory avoidance retention, similar to those reported after epinephrine administration ( Gold, 1986 ). Moreover, plasma levels of glucose measured shortly after training vary according to the footshock intensity used in training. Interestingly, the systemic, post-training glucose administration enhanced the retention performance of a habituation response in the open-field in the mouse, whereas insulin administration acted in the opposite way. The effects of both compounds followed a IUSDEC ( Kopf and Baratti 1999 ). Since glucose readily enters the brain, it may be that glucose affects memory by directly affecting brain glucoreceptors ( Oomura et al., 1988 ). Moreover post-training cerebroventricular glucose administration produces dose-dependent effects on retention ( Lee et al., 1988 ).

Facilitation of memory processes is reported when amphetamine is administered shortly after a training experience. In a manner similar to several other adrenergic agents, systemic amphetamine administration exerts a IUSDEC action on memory processes. In early studies memory facilitation was reported after post-training amphetamine administration at low dosages: higher dosages proved ineffective in altering an appetitive discrimination response ( Krivanek and McGaugh 1969 ). Similarly, high doses of post-training amphetamine resulted in memory disruption in a single-trial inhibitory avoidance paradigm ( Weissman, 1967 ). Amphetamine acts through peripheral catecholamine mechanisms: central administration of amphetamine did not affect retention ( Martinez et al., 1980 ).

It is well known that emotional arousal also activates the hypothalamic-pituitary-adrenocortical axis, elevating plasma levels of corticosterone. Ample evidence indicates that glucocorticoids influence long-term memory consolidation ( De Kloet et al., 1999 ; Roozendaal 2000 ). It has been shown that their effects on memory follow an inverted-U shape relationship. Acute corticosterone administration influences the spatial memory deficit induced by adrenalectomy in adult rats in a biphasic way ( McCormick et al., 1997 ). Acute post-training administration of low doses of glucocorticoids enhances memory consolidation, in a manner highly similar to that of epinephrine on spatial memory ( Sandi et al., 1997 ) and on fear conditioning ( Pugh et al., 1997 ; Cordero and Sandi 1998 ). On the other hand, it appears that adrenergic and glucocorticoid hormonal systems interact, influencing memory consolidation. In fact, blockade of the corticosterone stress response, by means of the corticosterone synthesis inhibitor metyrapone, prevents the inhibitory avoidance retention enhancement induced by post-training epinephrine injections or exposure to psychological stress ( Roozendaal et al., 1996 ; Liu et al., 1999 ).

In humans, the IUSDEC relationship reported between glucocorticoid levels and cognitive function was explained as due to increased arousal. Circadian variations of the effect of corticosterone oral administration on a free recall test in young humans were measured ( Fehm-Wolfsdorf et al., 1993 ). Corticosterone administration suppressed the increased cognitive performance in the morning when endogenous corticosterone levels are at their peak, while it had no effect on cognitive performance when administered at night, when corticosterone is at the lowest concentration. Probably the high endogenous corticosterone levels in the morning corresponded to the peak of the inverted-U shape function between corticosterone levels and cognitive performance, and the corticosterone administration at that time shifted the performance towards a decrease. On the contrary, the corticosterone administration in the evening (at low endogenous corticosterone levels) may not have been sufficient to increase cognitive performance toward the peak of the inverted-U shape function influencing the processes of arousal and selective attention. The inverted-U shape relationship between corticosteroids and memory led to the question of whether this process involves opposing or synergic processes that could be mediated by the two types of adrenal steroid receptors reported to exist in the brain: mineralcorticoid receptors (Type I) and glucocorticoid receptors (Type II). When the performance in the Y-maze of rats administered with either Type I or Type II receptor antagonists was measured, only the Type II antagonist-treated group showed impaired spatial memory performance ( Conrad et al., 1996 ). Successively the authors showed that if a IUSDEC explains the results obtained with memory performance at different corticosterone doses, it may only be related to Type II receptor activation ( Conrad et al., 1999 ).

The report that glucocorticoid effects on memory consolidation enhancement depend on the emotionally arousing content of the administered stimulation ( Sandi, 1998 ; Buchanan and Lovallo 2001 ), is consistent with extensive evidence indicating that noradrenergic activation in the amygdala is involved in mediating glucocorticoid effects on memory consolidation ( De Quervain et al., 1998 ; Roozendaal 2000 , 2002 ). The infusion into the basolateral amygdala, immediately after training, of the specific Type II agonist RU28362 enhances retention performance while the infusion of the Type II antagonist RU38486 impairs retention performance ( Roozendaal and McGaugh 1997 ). Selective lesions of this nucleus block retention enhancement induced by post-training systemic injections of dexamethasone ( Roozendaal and McGaugh 1996 ). Thus glucocorticoid effects on memory consolidation depend on basolateral amygdala function. Moreover, noradrenergic cell groups of the nucleus of the solitary tract and of the locus coeruleus express high densities of Type II receptors ( Harfstrand et al., 1987 ). Post-training activation of these receptors on noradrenergic cell groups in the nucleus of the solitary tract induces memory enhancement ( Roozendaal et al., 1999 ). As recalled above, this nucleus projects directly to the amygdala and infusion of a β-adrenoceptor antagonist into the basolateral nucleus blocks this glucocorticoid-induced memory enhancement ( Roozendaal et al., 1999 ).

Not all agents that influence memory, presumably acting on arousal levels, act through peripheral adrenergic mechanisms. Post-training subcutaneous injections of ACTH affect later avoidance retention performance. The effects on memory are dose dependent; immediate post-training, systemic administrations of moderate doses of ACTH enhance, and higher doses impair memory storage in a passive avoidance paradigm in the rat ( Gold and van Buskirk 1976 ). It has been shown that ACTH interaction with the level of training-related stress is quite similar to that of amines: a single post-trial administration of ACTH will enhance retention after training with a weak footshock and will impair retention of training with a strong footshock ( Gold and Zornetzer 1983 ). But, on the other hand, systemic ACTH injections do not produce reliable changes in epinephrine and norepinephrine plasma levels. ACTH, then, does not initiate adrenomedullary or sympathetic activity which would normally follow a footshock, and this hormone must therefore act through other (probably central) mechanisms ( McCarty and Gold, 1981 ). ACTH cerebroventricular administration either post-training or 1 h before retention testing enhanced or disrupted the passive avoidance response in the rat according to the dosage-arousal levels ( Sahgal et al., 1983 ).

Similarly, vasopressin effects on learning and memory were discussed as due to emotional arousal level modulation ( Sahgal 1984 ; Ambrogi Lorenzini et al., 1991 ). Indeed, the initially reported results showing that post-training vasopressin administration facilitated memory processes in a dose-dependent manner, were presented as proof that vasopressin peculiarly enhanced mnemonic capacity ( De Wied et al., 1976 ). Later investigations showed that this effect presumably was due to arousal modifications. Sahgal et al., (1983) found that post-trial cerebroventricular administration of vasopressin improved the performance of some rats in a passive avoidance task, while impairing that of others, and argued that exogenous vasopressin may increase the rats’ state of arousal. Thus the amine levels-footshock intensity relationship suggests that if an animal is in a state of low arousal before vasopressin treatment, then an increase in arousal will facilitate performance. However, if the animal is in an optimal or high arousal state, a further increase in arousal will impair performance. It was proposed that vasopressin may be involved in the selection of a high arousal state, or in the regulation of arousal by the noradrenergic dorsal bundle ( Sahgal 1984 ). Finally, oxytocin, another neurosecretory product of the hypothalamo-neurohypophyseal system, appears to have effects opposite to those of vasopressin. Oxytocin impairs passive avoidance performance after post-trial systemic administration and this effect is dose-dependent in a biphasic manner ( Bohus et al., 1978 ; Boccia et al., 1998 ).

As stated in the Introduction, in several papers the hypothesis of a relationship between IUSDEC and the emotional arousal state is not discussed or presented. For instance, it was found that the administration of D-cycloserine (an NMDA agonist) enhances recognition memory in monkeys, after systemic pre-test administration ( Matsuoka and Aigner 1996 ) and that γ-L-glutamyl-L-aspartate and D-2-amino-5-phosphonovalerate (both NMDA antagonists) after intracerebroventricular post-training administration disrupt the retention of an active avoidance response in the mouse ( Mathis et al., 1991 ). The post-training intracerebroventricular administration of 2-deoxy-D-galactose (a compound antagonizing glycoprotein fucosylation) disrupts the retention of a passive avoidance response in the rat ( Ambrogi Lorenzini et al., 1997 ). The pre-training systemic administration of the nootrope minaprine enhances an active avoidance response in the rat ( Ambrogi Lorenzini et al., 1993 ). The intracerebroventricular administration of the neuropeptide PACAP-38 enhances the passive avoidance response in the rat ( Sacchetti et al., 2001 ). The same compound elicites a similar dose-response effect on the excitability of an in vitro rat hippocampal slice preparation ( Roberto et al., 2001 ). The post-training intrahippocampal administration of nifedipine (a Ca ++ channel blocker of the class of dihydropyridines) enhances retention of inhibitory step-down avoidance in the rat ( Lee and Lin 1991 ; Quevedo et al., 1998 ). In all these instances the Authors described a IUSDEC, but did not discuss its possible mechanisms. In some instances that finding was explained by simply suggesting down-regulation or tolerance. In the case of cholinesterase inhibitors, the hypothesis that the activation of presynaptic autoreceptors may play a role in reducing the activity of these compounds was advanced ( Braida et al., 1998 ). In an early study it was reported that systemic post-training administration of physostigmine affects memory processing of an appetitive maze learning task in rats, again following a IUSDEC trend ( Stratton and Petrinovich 1963 ). Similarly, more recent acetylcholinesterase inhibitors (MF201, MF268) were found to antagonize scopolamine-induced amnesia of spatial memory tasks in the rat at low but not at high dosages (pre-trial oral administration) ( Braida et al., 1996 , 1998 ), as was found to occur with other cholinergic agonists and cholinesterase inhibitors, which improve performance at low doses but are ineffective at higher ones ( Flood et al., 1981 ; Wanibuchi et al., 1994 ; Waite and Thal 1995 ).

As initially stated, the IUSDEC is a widely described and poorly understood phenomenon. Thus, in the present paper it is not possible to clarify all the unanswered questions, possibly related to facets and mechanisms not yet adequately investigated. This non-linear relationship has been reported for many active compounds, in several learning paradigms, in some animal species and does not depend on either administration route (systemic or endocerebral) or on administration time (before or after training). The IUSDEC response is possibly a multifactorial phenomenon, and the single components may not be easy to isolate experimentally. Nevertheless some mechanisms, at least, have been well studied. Therefore, for some compounds the “arousal hypothesis” is worth discussing in some depth. On the other hand in many instances the IUSDEC in learning and memory was not attributed to emotional arousal modifications. Although this hypothesis was not discussed in these papers, arousal levels may be involved in even these circumstances, since there is no experimental evidence which completely excludes it. However, the IUSDEC cannot be exhaustively explained by modification of the emotional state. The fact that the IUSDEC has been reported equally for compounds exhibiting quite opposite (positive or negative) effects on learning and memory is not of secondary importance. It may be more difficult to propose this hypothesis for compounds which cause amnesia at low dosages, the effect disappearing at higher ones. Nevertheless, the “arousal hypothesis” appears to be quite interesting and possibly heuristic, and may help to explain at least some of the IUSDEC evidence in learning and memory consolidation. But it must be remembered, when considering this hypothesis, that there are several mechanisms, simultaneous or otherwise, which concur to elevate or decrease emotional arousal levels (adrenal output, pituitary hormones, interoceptive and exteroceptive environmental stimulation and activation of the reticular formation, emotional commutations of the sensorial input). Thus memory processes may be modified by modulating the non specific physiological response to a training experience. So when their net action produces the optimal emotional arousal level, a generalized mnemonic facilitation may result. Conversely, where their net effect decreases arousal beneath a certain level, memorization may be disrupted. Indeed this is true both for pre- and post-training administration because, as recalled in the Introduction, the arousal level may be critical not only during acquisition but also during the early stage of the consolidation process ( Gold and Zornetzer, 1983 ). In a more generalized way, we may surmise that the IUSDEC can be the expression of an “escape” mechanism, which is actuated when sufficiently high concentrations of a given active compound are reached. Sustaining the “escape” mechanism could be a hierarchic organization of mnemonic processing organization, whose components would be progressively more impervious to external influences. Anyhow, since the IUSDEC is a well-documented phenomenon in memorization, the present scarcity of interpretations must be an encouragement to further investigations in this field. Indeed, at least within the “arousal hypothesis” of IUSDEC, there are some findings which may point the way for future research, like the recent ones on how epinephrine and glucocorticoids modulate long-term memory consolidation in animals and human subjects: release of norepinephrine and activation of β-adrenoceptors within the basolateral amygdala appear to be critical in mediating adrenal stress hormone regulation of memory consolidation.

Acknowledgments

The authors wish to express their warmest thanks to Prof. Carlo Ambrogi Lorenzini for his valuable advice and constructive criticism during the course of this work. The authors also wish to thank Dr. Beatrice Passani for her critical suggestions.

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Inverted U Theory in Sport – What is it and why is it important?

The Inverted U Theory in Sport

In this post we will discuss the Inverted U theory in sport:

• Why is it important?
• What is involved?
• What is the Inverted U Theory in Sport
• Sporting examples of the Inverted U Theory
• How can this theory help athletes and coaches

This post is part of our series discussing the relationship between arousal and performance. You may also want to check out our other articles below:

• Drive Theory in Sport
• Catastrophe Theory in Sport
• Personality Types

Why is the Inverted U Theory in Sports Important?

All those involved in sports should understand the principles and purpose of the Inverted U theory.  

The Inverted U theory in sports aims to explain the relationship between arousal levels and performance. The theory also suggests how different levels of arousal can lead to either an increase or decrease in performance.

In 1908, researchers Yerkes and Dodson published a study that forms the foundation of the Inverted U theory. The Inverted U theory began to explain the relationship between performance and arousal different to that of the drive theory . The Inverted U theory differs by suggesting that too much arousal can lead to a decrease in performance. 

Researchers have then developed the Inverted U Theory further resulting in the Catastrophe Theory by Fazey and Hardy (1988) . You can read our article on the Catastrophe theory here .

Sports coaches and athletes need to understand the impact on arousal and performance and how an athlete’s performance can potentially increase and/or decrease with different levels of anxiety . You may also want to check out out article on personality types .

If sports coaches understand the link between arousal and performance, this could result in better performances and reduce the risk of a decline in performance. The inverted U Theory is still taught as part of many sports qualifications and coaching qualifications , helping demonstrate the importance of the theory.

All those involved in sports should understand the principles and purpose of the Inverted U theory.

What is involved in the Inverted U theory?

The two factors involved in the Inverted U theory in sport are:

• An athlete’s arousal or anxiety level
• Performance level

What is the Inverted U Theory in Sport?

The Inverted U theory in sport suggests that if an athlete’s arousal is low/none existent then this will result in a low-performance level. As an athlete’s arousal level increases, the performance will gradually increase up to a point of maximum performance. The point of peak performance in the Inverted U theory is called the optimum point.

If arousal continues to increase after the optimum point, The Inverted U Theory suggests performance will decrease gradually. 

Sporting Examples of the Inverted U Theory in Sport

A sporting example to help explain the Inverted U Theory would be a boxer who is just about to enter a boxing match. 

A low arousal level at the start of the match would result in the boxer’s performance level being low. The low arousal level could lead to a slower reaction time or lack of concentration levels.

Alternatively, too much arousal could lead to loss of strategy or increase the risk of foul play and potentially being penalised. 

Whereas, if the boxer had the optimum level of arousal at the start of the boxing match, they would perform at their best.

For the Inverted U Theory, it is important to note that each sport requires different optimum performance levels. Therefore, the Inverted U theory can be described as being on a continuum of arousal and the arousal level for peak performance for one sport may be different to another. For example, a boxer would have a different peak performance arousal level compared to a snooker player. 

How Can This Theory Help Athletes and Coaches?

The Inverted U Theory builds on the drive theory (you can read our article on the drive theory here) and further explains the importance for coaches to understand the relationship between arousal and performance.

Sports coaches need to be aware that performances can drop due to an increase or decrease in arousal levels. 

However, there are criticisms among researchers as the Inverted U theory does not explain sudden drops in performance. The Inverted U theory suggests performance gradually improves or declines. However, this is not always the case and researchers have created a new theory called the Catastrophe Theory.

The Inverted U theory in sports links both arousal levels and performance levels. The Inverted U theory states that performance will gradually increase if arousal increases to an optimum point. Too much arousal after this point will then lead to a gradual decline in performance. Read our next article in this series here .

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New to sports coaching?  Then you may want to check out our guide to sports coaching. Here you will be able to learn techniques and strategies that will excel your coaching career. Topics include  Stages of Learning ,  Methods of Training  and  Leadership Styles .

You may also be interested in the following articles:

• Stages of Learning
• The Best GPS Sports Vests
• Downloadable Sports Session Planner Template
• What are the different Leadership Styles used in sports
• Learn The Different Methods of Practice

References:

   Yerkes, R.M. , & Dodson, J.D. (1908). The relation of strength of stimulus to rapidity of habit-formation. Journal of Comparative Neurology and Psychology, 18, 459-482.

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