Stat Chat: The ‘Answer’

Juliette Pope/The Miscellany News
Figure 1. After giving up a basket, how often do NBA teams copy their opponents’ technique? “Answer Attempts” measures how often teams who have just given up a basket copy their opponents’ shot type for each particular type. “Other Attempts” illustrates how often teams opt for each type of shot otherwise (i.e., not after giving up a shot or after giving up a different kind of shot). Alex Eisert/The Miscellany News

What bearing does a player’s defense have on their offense? Ideally, players would be able to separate the two, for in a literal sense, they do not impact each other: Whether you give up seven errors in a half inning or make a spectacular diving play, you’ll still come up to bat regardless. Whether you give up a wide-open three-pointer after a defensive lapse or make an earth-shattering rejection off the backboard and get your own rebound, all the same, your next step will be to get the ball to the other end of the court and attempt to score. 

Practically, however, this is not the case. Obviously, the amount of runs you give up on the field or the amount of points you allow on defense will dictate the strategy coaches use at the other end. For example, if you are suddenly losing by a ton, the coach will bring in your mop-up reliever or your third-team subs. But beyond game plan, is there another manner in which defensive play can subtly impact offense? And can we measure it in a way that separates it from mere changes in strategy?

After running the numbers from Kaggle’s NBA play-by-play dataset for 2018-2019, I’ve concluded that the answers to the questions above are, respectively, yes and yes we can. I chose this dataset because, aside from it being the last full NBA season, in watching a lot of Knicks basketball these last few months (it’s hard not to, because they are actually good for the first time in seven years), I’ve noticed that teams seem more likely to shoot three-pointers immediately following the other team making one. The play-by-play nature of the dataset allowed me to isolate field goal attempts that came one after another. In other words, I could avoid shots that were separated by a timeout, foul, substitution or any other stoppage. Removing pairs of shots that were detached from each other in any of these ways also helped minimize the likelihood of any change in strategy; any shift in shot selection would thus be attributable to a more reflexive behavior in response to giving up a field goal on defense.

I theorized that of all the types of field goals, allowing a three-pointer would lead to the most significant behavioral change purely because threes are worth the most points. Giving up a three-ball might instill a sense of urgency in the defense as they transition to offense, a need to reclaim those lost points. At first glance, this seemed to be the case. There were 17,794 shots taken immediately after the other team scored a three; aside from these shots, there were 201,663 shots taken in the entire season. After giving up a three, teams shot a three themselves 38.7 percent of the time. Otherwise, they only shot a three 35.6 percent of the time, an extremely significant statistical difference given the large sample size (p < 1^-15). But one question remained: Do players have the same inclination to “answer,” say, two-point jumps shots, with one of their own, that they do with threes?

For two-point jumpers, the answer is a resounding yes (31.3 to 26.3 percent; p < 1^-15). Same goes for two-point hook shots (4.67 to 3.84 percent; p < 0.05). However, teams were significantly less likely to go for a layup when answering layups compared to going for a layup any other time (23.7 to 28.1 percent; p < 1^-15) and significantly less likely to answer dunks with dunks (4.90 to 5.83 percent; p < 0.0005; see Figure 1). But don’t dismiss the “answer” effect so fast; layups and dunks were probably less likely to be answered because they often happen on fastbreaks. A successful fastbreak is almost never immediately followed by another because the other team has to inbound the ball, providing the team coming off of the fastbreak with time to get back on defense. The answer effect would likely be present if we were to only look at layups and dunks that didn’t occur on fastbreaks; sadly, this data isn’t available on Kaggle.

Because of the lack of fastbreaks after a basket, one might argue that the answer effect I captured above for threes, two-point jumpers and hook shots is just a result of every other type of shot getting more play at the expense of layups and dunks. It turned out that teams responding to a made three were also far more likely to shoot a two-point jumper than they would be otherwise (30.6 to 26.4 percent; p < 1^-15), and the likelihood of answering a two-point jumper in kind was only slightly higher than the likelihood of answering a three with a two-point jumper (31.3 to 30.6 percent; p =  0.20). While the likelihood of answering a three in kind was significantly higher than the likelihood of answering a two-point jumper with a three (38.7 to 37.4 percent; p < 0.05), it is worth noting this effect is small relative to some of the miniscule p-values for two-point jumpers and threes above. 

In addition, teams were insignificantly more likely to opt for a hook (4.00 to 3.84 percent; p = 0.29) after a made three and for a three after a made hook (36.0 to 35.9 percent; p = 0.86). But, teams were significantly more likely to go with the hook after giving up a two-point jumper (4.40 to 3.81 percent; p < 0.001) and to go with a two-point jumper after giving up a hook (31.4 to 26.6 percent; p < 5^-7). 

This led me to a different conclusion: What we should be looking at is similarities across types of shots. Two-point jumpers and threes are both jumpshots, while two-point jumpers and hooks are both two-point shots. My theory was already in need of revising because the strong effects associated with answering two-point jumpers and hook shots in kind run contrary to the idea that trying to answer three-pointers leads to the largest behavioral change. Rather, it seems that players just try to emulate what they see working for their opponent, whether it is an exact emulation or just something similar—big men aren’t as adept at shooting jumpers, for example, so their way of emulating an opponent’s two-point jump shot might be with a hook. 

This result is in line with the social psychological theory of informational social influence, which states that when we don’t know all the facts, like which type of shot is best to take, we will look to others (in this case, opponents) to see if they know what works. We do this because we have a desire to be correct in our assessments of the world.

On the other hand, this phenomenon could also result from normative influence: Even when we do have good information, or an idea of which shot to take, our desire to fit in and conform might override that. In other words, even if an opponent’s two-point jumper isn’t falling, a player might still go for a two-point jumper themself just because they are being cued to conform. To test normative influence, I needed to see whether players were also more likely to answer a failed three-point shot, two-point jumper or hook shot attempt with one of their own. I excluded layups and dunks because of the fastbreak issue; although with a missed shot there is no inbounding, fastbreaks still happen more often on steals and blocks than defensive rebounds, and I selected only those missed shots that were immediately followed by defensive rebounds and a subsequent shot at the other end.

There were 26,812 shots taken right after the other team missed a three; aside from these shots, there were 192,645 shots taken the entire season. After thwarting a three-point attempt, teams shot threes themselves 37.6 percent of the time. Otherwise, they only shot a three 35.6 percent of the time, a very significant result (p < 1^-9), though slightly less so than when answering made threes. Interestingly, this effect went in the opposite direction for missed two-point jumpers (25.2 to 26.8 percent; p < 1^-5), and was not significant at all for hook shots (3.65 to 3.85 percent; p = 0.60). 

In sum, while we can’t speak for layups and dunks, all other shots likely activate informational influence cues when made, one subtle way that defense impacts offense in the NBA. But only successfully defending against threes appears to induce another subtle effect (while two-point jumpers might even deter it) on offense: normative influence. Perhaps there is something special about threes after all.

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