The inverted U relationship
Performance varies predictably with arousal level. At very low arousal (lethargy, inattention), performance is poor. Performance improves as arousal increases: alertness sharpens focus, motivation drives effort, and task engagement deepens. But the relationship does not continue upward; performance peaks at moderate arousal and then declines as arousal exceeds optimal levels.
High arousal produces anxiety, scattered attention, and impulsive errors. An athlete who is slightly nervous performs better than one who is apathetic, but excessive pre-game anxiety degrades coordination and decision-making. A student moderately stressed by an upcoming test studies effectively; panic diminishes performance. The curve is an inverted U because both extremes impair.
Task complexity and optimal arousal
Optimal arousal shifts with task complexity. Simple, well-practiced tasks tolerate higher arousal; a tennis serve is harder to choke on than a delicate motor control task. Complex tasks requiring flexible thinking need lower arousal; overthinking disrupts problem-solving. An athlete performing a familiar skill can tolerate high pressure; a novice learning a new sport needs calmer conditions.
Understanding this curve explains performance under pressure. Relaxation alone is not always optimal; moderate arousal (called flow in positive psychology) combines focus with engagement. Athletes learn to manage arousal to stay in the optimal zone. In work and learning, recognizing that both numbness and panic impair performance leads to more nuanced interventions than simply 'reduce stress'.