Effective teamwork is essential in structured, performance-driven environments, from professional organizations to high-stakes competitions. As tasks grow more complex, high performance requires not only technical proficiency but also interpersonal skills that enable effective coordination. Prior research has identified social skills and familiarity as key drivers of team performance, but their combined effects—particularly in temporary teams—remain underexplored due to data and design limitations. We analyze a large panel dataset of temporary teams in a competitive environment. The data capture millions of interactions in the real-time strategy game Age of Empires 2, where players are assigned quasi-randomly to teams and must coordinate under pressure. We isolate individual contributions to team success by comparing observed outcomes to predictions based on task proficiency. Our findings confirm a robust "team player effect": certain individuals consistently improve team outcomes beyond what their technical skills predict. This effect is amplified by team familiarity—teams with shared experience benefit more from the presence of such individuals. The effect also grows with team size, suggesting that social skills help overcome coordination challenges in larger groups. These results demonstrate the team player effect's robustness in a quasi-randomized, high-stakes setting. Social skills and familiarity interact complementarily—not additively—offering broader implications for team-based production in organizations and labor markets.