This bias appears to be costly in the N.B.A. as well. The teams that attempted the 3-point shot won the game more often (17.3 percent) than those that attempted the 2-point shot (14.5 percent).

Basketball fans in a laboratory environment make this same mistake. In one study, we asked participants to imagine that they were the coach of an N.B.A. team that was down by 2 points in the final seconds. Just as N.B.A. teams did, our participants avoided the superior strategy, opting for the 2-point shot 81 percent of the time.

Why do people make this error? Part of the explanation lies in our tendency to treat problems in isolation rather than as part of a larger whole. Just as investors often mistakenly evaluate stocks individually rather than as part of a portfolio, coaches and fans often evaluate decisions in terms of their immediate impact and give less consideration to how those decisions fit in the larger context of the game.

In our laboratory study, we found that whether participants opted for the 2-point or 3-point shot was unrelated to their beliefs about how the team would perform in overtime. They made their decision by focusing almost entirely on the prospect of losing immediately, neglecting how the future was likely to play out.

But there is more to the story than myopia. People also seem to be unnecessarily wary of risks that they feel they are choosing to take (as opposed to risks they feel they are forced to take).

In a study that highlights this point, we asked football fans to imagine that a team had scored a touchdown in the final seconds of a game. Then we told half the fans that the team trailed by 1 point and the other half that the team trailed by 2 points. We then told all the fans that the team was going to attempt a 2-point conversion.

Those who were told the team was down by 1 point (and thus had the viable option of kicking the extra point to force overtime) thought the 2-point conversion was more likely to fail than did those whose team had to attempt a 2-point conversion just to force a tie. That is, the same decision was thought to be riskier when it was seen as optional than when it was seen as unavoidable.

“Live to fight another day” is often a good rule of thumb, but it is not always the best strategy to pursue. Good judgment, in sports and elsewhere, sometimes requires the presence of mind to take the risk of an immediate setback to achieve lasting success.