Do players turn “clutch” when chasing a personal goal?

Phil Birnbaum looks into a Bill James piece that claims that players perform better when approaching round number goals, such as 20 wins. Birnbaum argues that the difference could be attributed more to opportunity, and presents some compelling evidence for his claim in the piece. Personally, I think Birnbaum is probably right, and there’s not enough evidence for me to reject the null hypothesis, that players perform the same on average in all situations, in this case.