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 (driving a familiar route), high arousal helps — it keeps you alert and fast. 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 the original rat-maze data from Yerkes and Dodson. The actual law is qualitative. The Gaussian is a convenient, widely used approximation.

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).