Why no one bats .299 in late September

This paper shows that people strive for round-number goals, showing evidence from Major League baseball players, high school students taking the SAT, and from laboratory subjects answering hypothetical surveys of behavior.

As can be seen in the figure, baseball players are 4 times more likely to end the season with a 0.300 batting average than a 0.299 average! How does this happen? Players that are at 0.298 or 0.299 are more likely to have at-bats (rather than having a pinch hitter), they are slightly more likely to have hits at those at bats, and once a batter hits the magic 0.300 point, batters often take walks and sit out for pinch hitters.

The SAT takers were 10-20 percentage points more likely to re-take the test if they had an exam ending in -90 (e.g. 1190) than one ending in -00 (e.g. 1200).

Last, the authors gathered laboratory participants and asked them how they would react given certain situations. To give an example situation, imagine running laps around a track and you are getting tired. You have run either 28, 29, 30 or 31 laps (depending on what condition you are in). Do you want to run one more lap? They found that participants in the just under a round number condition (29 laps) were more likely to run one more, and participants in the just over the round number (31) were less likely to do one more.

Are these round number goals rational? In other words, is a baseball player more likely to get a lucrative contract with a 0.300 batting average than a 0.299? Do highly selective colleges have round number cut-offs for admissions? The authors examined data from university admissions that showed no discontinuities in the probability of admission as a function of SAT score, suggesting that such round number goals are not, in fact, rational.

Pope D, & Simonsohn U (2010). Round Numbers as Goals: Evidence From Baseball, SAT Takers, and the Lab. Psychological science : a journal of the American Psychological Society / APS PMID: 21148460