Most other National Football League teams behave this way, too. In research to be published in the forthcoming issue of The Journal of Personality and Social Psychology, we examined every instance over a recent 10-year period in which N.F.L. teams faced a choice in the final minutes between kicking an extra point to tie the game or going for a 2-point conversion to win. The teams overwhelmingly chose to avoid the risk of immediate defeat: Of the 47 times teams faced this situation, they opted to kick the extra point 42 times (89 percent).

This bias can be costly. Teams that chose to avoid the 2-point conversion won the game only 40 percent of the time, which is well below the average rate of successful 2-point conversions (about 50 percent). Surely some of those teams should have known they were underdogs if the game went into overtime, and mistakenly avoided a risk they should have taken.

This error is not limited to the N.F.L. We also looked at all instances in the past five years in which teams in the National Basketball Association trailed by 2 points with less than 24 seconds to play. In this situation, a team can attempt a 2-point shot that would send the game to overtime or try a (more difficult) 3-point shot that would win the game immediately.