Yerkes-Dodson Arousal Performance Curve

The Yerkes-Dodson law (1908) holds that performance improves with arousal up to an optimal level, then declines. The resulting curve is an inverted U.

The second part of the law, often forgotten: the optimal arousal level depends on task complexity. For simple, well-practiced tasks like driving a familiar route, high arousal helps, because it keeps you alert and quick. For complex tasks requiring fine judgment or working memory (a chess endgame, a surgery), even moderate arousal can degrade performance by narrowing attention and increasing error rates.

This calculator uses a Gaussian model to approximate the inverted-U:

Performance = 100 * exp(-0.5 * ((arousal - optimal) / width)^2)

This is a computational model, not data. The Gaussian is a convenient and widely used approximation; the actual law is qualitative.

It is worth knowing how thin the original evidence is, because the inverted U gets cited as though it were a measured constant of human performance. Yerkes and Dodson tested Japanese dancing mice, not rats and not people, training them to discriminate between two boxes under electric shocks of varying strength. They found that the shock level producing fastest learning was lower for the harder discrimination. That is the whole finding. The smooth inverted-U curve everyone draws came decades later, mostly from Donald Hebb’s 1955 work on arousal, and the two got welded together under the Yerkes-Dodson name. The relationship holds up reasonably well as a rule of thumb. Just do not treat the curve below as measurement.

Optimal arousal levels (modeled):

• Complex task: optimal ~ 3/10, narrow curve
• Moderate task: optimal ~ 5/10
• Simple task: optimal ~ 7/10, wider curve

What counts as arousal? In this model, arousal includes physiological activation (heart rate, cortisol, adrenaline) as well as cognitive load, stress, and emotional intensity. A score of 1 is half-asleep; 10 is full panic.

Why does high arousal hurt complex tasks? The leading explanation is attentional narrowing: high arousal focuses attention on dominant responses and shuts out peripheral information. This is useful for a sprinter (dominant response = run) and harmful for a chess player (needs wide, creative search).