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.

Showing a graphic of arousal versus performance
Inverted U Curve, adapted from Inverted U Theory, also known as Yerkes-Dodson Law (1908).

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…

Influence of Sport on where the peak of the Inverted U Curve is, adapted from Inverted U Theory, also known as Yerkes-Dodson Law (1908)
Influence of Sport on where the peak of the Inverted U Curve is, adapted from Inverted U Theory, also known as Yerkes-Dodson Law (1908)

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.

Influence of task difficulty on where the peak of the Inverted U Curve is, adapted from Inverted U Theory, also known as Yerkes-Dodson Law (1908)
Influence of task difficulty on where the peak of the Inverted U Curve is, adapted from Inverted U Theory, also known as Yerkes-Dodson Law (1908)

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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