When watching games, it always seemed to me that teams were more likely to attempt three point shots when trailing by three. Of course, that is rational and to be expected as the game nears its final minute (expected, but not easy). But this bias for three pointers seems to occur throughout the game. When there is plenty of time left, one would presume that teams should be taking the best shot available - one which maximizes expected points, regardless of whether it is a two or a three. But the psychological pull of "evening the score" seems to bias shot selection when trailing by three.
The chart below summarizes the percentage of shot attempts that are from three point range as a function of score difference. The dataset consists of all shots taken over the past four NBA seasons. To keep things restricted to a normal game flow context, I excluded both the last five minutes of the game and the first five minutes. Scoring differences of minus 10 or less and plus 10 or greater are grouped together.
The scale may be misleading here. While there is variation, it's in a pretty tight band from about 24-27%. Part of this is due to a healthy sample size, with at least 14,000 shots in each grouping. As expected, there does appear to be a slight bump in three point attempts when trailing by three. Perhaps not as expected is a similar bump when trailing by five. Teams are least likely to attempt three point shots when trailing by four.
When the score difference is between -2 and 2, three point rates tend to be low. They start climbing again when a team leads by at least three. I was surprised that teams with a large lead are more likely than the trailing team to take three pointers. I would have expected the opposite relation. Maybe causality goes the other direction in this case? Maybe teams that take a higher percentage of three point shots tend to find themselves with a lead? Nah. Couldn't be.