The analysis and evidence here suggest that the market for star athletes in professional sports could be subject to “destructive competition”—a competitive process which drives some participants from a market even though it is inefficient for them to leave. When pursuing a league championship, the talent which turns an average team into a contender contributes disproportionately to the team's success. Teams which fail to earn enough on the last stars they sign to offset losses on their inframarginal talent will abandon a competitive market for star athletes. Other situations that involve input rivalry between producers might yield similar results.