Inverted-U curve

A graph of the relationship between arousal and performance, where performance rises as arousal increases up to an optimum point, then falls again as arousal continues to increase.

The inverted-U curve is often associated with the Yerkes-Dodson law, named after psychologists Robert Yerkes and John Dodson who published a study of mice and electric shocks in 1908. The Yerkes-Dodson finding was that learning performance improved with moderate shock intensity and declined at high intensity, producing the characteristic inverted-U shape when plotted.

The contemporary view of the Yerkes-Dodson relationship is more nuanced than the simple curve suggests. Modern research has established that there is no single universal curve but rather a family of curves whose shape depends on the complexity of the task being learned. Simple, well-rehearsed tasks tolerate high arousal and may even be performed better at high arousal. Complex, novel tasks require lower arousal, with the optimum shifted toward the lower end of the curve.

The inverted-U is useful as a model for explaining why a horse, dog, or any other animal can perform a familiar task at high arousal but not learn a new one. It is also useful for explaining why pushing through a training session when the animal is becoming over-aroused tends to produce poor results: the animal is on the descending limb of the curve and additional pressure makes performance worse, not better.

The model has limitations. It treats arousal as a single dimension, which is an oversimplification, and it does not directly address the valence of the arousal (whether the animal is in a positive or negative emotional state). Contemporary work on affective state and welfare uses a more dimensional framework that captures both arousal and valence.

Despite its limitations, the inverted-U remains one of the most useful single concepts in applied training, because it directly explains the relationship between trying harder and getting worse results.