We study the role of stereotyped beliefs in explaining the gender competition gap. We collect data on the performance and competitiveness of men and women in all tasks previously studied in the literature. We have identified 23 unique tasks. The competition gap varies by task, with stereotypically male tasks displaying larger gaps. In an online experiment, we elicit beliefs about how each gender performed and find significant gender differences: both men and women believe their own gender performs better, yet both think others believe men outperform women. Our main finding is that across the tasks and studies used in the literature, actual gender performance differences correlate weakly with competition gaps, while beliefs about these differences explain 54\% of the variation. In our lab experiment, we manipulate task stereotypes by altering task framing and selectively disclosing information about others' beliefs. When the task is framed as a "Math task" rather than a "Memory task", a significantly larger share of participants believe that men outperform women. Similarly, informing participants that previous participants believed women perform better shifts beliefs in favor of women. While these treatments have no direct effect on competitiveness, they significantly influence the gender competition gap via a causal mediated pathway through beliefs about male advantage."