How do decision-makers evaluate alternative strategies when performance outcomes differ in variance? We introduce variance-induced perception bias (VIPB), the tendency to overestimate the expected performance of strategies with greater variance. Across four preregistered experiments, including a laboratory study with eye-tracking, we show that observers consistently misjudge strategies that generate a wider distribution of outcomes. High variance strategies are more likely to produce extreme successes, and observers selectively attend to these salient outliers and generalize from them. The bias intensifies under information overload and when rankings highlight top performers. Framing evaluations around the worst rather than the best outcomes reduces, but does not eliminate, the effect. VIPB extends beyond perception: when asked to choose directly, people imitate the higher-variance strategy even though it delivers lower average returns. Our findings reveal how selective attention to high performers distorts strategic judgment and choice, highlighting variance as a variable that shapes strategic choices.