Stat Chat: The Answer (Pt. 2)

Juliette Pope/The Miscellany News.

Analyzing a psychological process and determining the circumstances under which it impacts behavior is all well and good. However, I find that the real fun often comes from thinking about how we might alter our behavior to be our best selves. In general, most psychological phenomena are adaptive; that is, while there may be a downside to them, there is likely also an upside. Otherwise, the behavior would have been nixed by evolution long ago. Yet, this may not ring true in the context of sports. While people have played with balls and sticks for at least 3,000 years, that is not nearly enough time for significant evolutionary changes to take place on the biological level. Strategies and rules have evolved in sports, sure, but our basic psychology remains the same. While athletes’ psychological bent may be adaptive in the rest of their lives, that might not be the case in competition, in which case they should modify their strategy and instigate the evolution of their sport in real time.

A few weeks ago, I wrote about how the psychological effects of normative and informational influence bias NBA players to try and “answer” their opponents’ successful shots by taking a similar shot themselves at the other end of the court. In our daily lives, these effects are helpful: when we are faced with an incomplete understanding of the world, we will reasonably look to others to fill in the gaps (informational influence), and even when we do have solid knowledge about our environment, we will justifiably still look to others to make sure that we fit in (normative influence). But are these effects beneficial in an NBA game?

NBA teams take significantly more two-point jumpers and three-pointers themselves directly after giving up a three-pointer on defense. Do these extra shots differ in success rate from when they’re taken otherwise? Alex Eisert/The Miscellany News.

To answer this question, I returned to my dataset from a few weeks ago, which contained play-by-play information from the 2018-2019 (the last full) NBA season. To recap, I found that after giving up a three-pointer, teams shot a three themselves 38.7 percent of the time, compared to 35.6 percent of the time otherwise (a significant difference with p < 1^-15). This is an example of informational influence; when players are not sure which type of shot to take, they look to what worked for their opponents. Did succumbing to the effects of informational influence benefit teams? It actually hurt them, but not significantly. Teams shot 35.0 percent from beyond the arc when answering a three and 35.6 percent otherwise (p = 0.32). 

Informational influence not only caused teams to shoot more threes, but it also caused them to shoot more two-point jump shots; I consider this to still count as informational influence because threes are jump shots too. After giving up a three, teams went with the two-point J 30.6 percent of the time, significantly more often than they did otherwise (26.4 percent; p < 1^-15). Did these shots fare worse than other two-point jumpers? Nope. Two-point jumpers in response to a made three scored 42.0 percent of the time, while two-point jumpers connected 41.4 percent of the time otherwise, an insignificant difference (p = 0.38).

I also established that, contrary to other types of shots, three-pointers exerted normative influence. This can be conceptualized as when a player is shown that a type of shot doesn’t work (i.e., our opponents miss with it) and then goes with it anyways. I found that when a team successfully defended a three, they took an attempt from beyond the arc at the other end of the court 37.6 percent of the time. Otherwise, they only went with the three-ball 35.6 percent of the time (a significant difference with p < 1^-9). Two-point jumpers were not significantly more likely after missed threes (26.5 to 26.7 percent; p = 0.36). 

Was it beneficial to yield to normative influence? Interestingly, it was slightly helpful, but not significantly: Three attempts after missed threes were successful 36.1 percent of the time, while all other three attempts were successful 35.4 percent of the time (p = 0.19). 

Okay, so informational and normative influence affect shot selection but not shot outcomes in response to three-point attempts. Since this is the case, teams can just allow these influences to run their course and keep everything the same, right? Not so fast. While it wouldn’t make sense yet to alter their shot selection on offense, teams can change their defense after they attempt a three-pointer themselves. Typically, it is a good bet to assume your opponents will take a jump shot; overall, they do so 62.6 percent of the time. However, it is an even better bet if you have just made a three. In these situations, as compared to all others, opponents will take a jump shot (be it for two or three points) 7.3 percent more often (69.3 to 62.0 percent). While offering less of an advantage (just a 2.0 percent difference), after missing a three, teams should still be aware that their opponents will be significantly more likely to shoot a three themselves. In conclusion, while social influences do not affect shot outcomes right now, if defenders catch on to their impact, they very well might in the future.

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