Stat Chat: The home of the brave

Picture this. You’re an NBA player, exhausted in the fourth quarter of a long game at the end of a long road trip. The hotels were mediocre, your team’s performance has been mediocre and at this point, you just want to go home. But imagine the game goes down to the wire, and you end up at the free throw line in the last minutes of play. How demoralizing would it be, after all you’ve slogged through, to see out of the corner of your eyes fans wielding signs urging you to miss? Fans screaming at you? Even insulting your style of play?

At least for the portion of the season in the bubble, actual NBA players did not have to worry about this hypothetical. But how much did it really improve their performance at the charity stripe? Using official stats from NBA.com, I sought to answer this question. I examined the free throw percentages of the 22 teams who participated in the bubble before and after they arrived at Orlando. Because I had a before and after for each team, and the teams remained relatively the same across both conditions, I could perform what is called a paired samples t-test. These are usually conducted in a laboratory setting in which the same subjects are measured on some variable before and after a treatment is introduced. This way, any difference across measurements can be attributed to the effects of the treatment and not to differences across subjects. Considering the newfound absence of fans as the “treatment” in this scenario, I can assume that any difference in free throw percentage is due to the emptied arenas.

And there was, in fact, a significant (p < 0.01, df = 21) difference: on average, teams shot 1.4 percent better in Orlando than they did pre-bubble. And this wasn’t because they took fewer foul shots either, which might have meant better foul shooters were getting proportionally more looks. In fact, upon running another paired samples t-test, I found that teams actually attempted significantly (p < 0.001, df = 21) more free throws per game, by 2.13 on average.

Even though our sample size from the bubble was bolstered by teams shooting more free throws per game, we still have to take those results with a grain of salt because the bubble sample only included the eight regular season games that each of the 22 teams played. Meanwhile, the pre-bubble sample saw some teams with up to 70 games played. And the downside of using a paired samples test is that it weights each sample equally. So, to strengthen my case, I looked for more evidence from another high-pressure situation that has similarly been fundamentally altered by the changed in-person fanscape in sports: field goals and extra points in the NFL.

Using data from Pro Football Reference, I examined the differences in field goal and extra point success rates between this season and last. I again used paired samples t-tests; while the samples were still different sizes (teams have played five or six games so far this season, and played 16 last), the differences in the sizes were not as stark. I started by looking at field goals attempted 20 to 29 yards out from the goalposts—I skipped those taken from less than 19 yards because there have only been two such attempts this year, while all other categories have seen at least 65 attempts. Only two teams this year and one team last year did not take an attempt from 20 to 29 yards, allowing me to include 29 of the NFL’s 32 teams in the paired samples test. Teams have actually fared worse from this range this year by 3.36 percent on average. But, this was not a significant difference (p > 0.1, df = 28). Only three teams this year haven’t taken any attempts from 30 to 39 yards while all teams last year took at least one, so for this range I was again able to include 29 teams. From this range, teams have fared significantly (p < 0.1, df = 28) better this year to the tune of a 6.12 percent average improvement. The same was true from the 40 to 49 yard range, from which all teams this year and last have taken at least one attempt, faring significantly (p < 0.1, df =31) better by 11.03 percent on average. From 50 yards or more (p = 0.92, df = 28) and for extra points (p = 0.834, df = 31), the results were very insignificant.

What does this all mean? Interestingly, the two ranges (30 to 39 and 40 to 49) from which teams have fared better this year are the two from which the most field goal attempts have been taken. This suggests that with more data, the other two ranges might yield the same result. But, some in the NFL would disagree. Take Vikings’ kicker Dan Bailey, for instance, who thinks that silence can be just as distracting as crowd noise because, for one, crowd noise enables you to tune out your opponents’ trash talking. It’s worth noting that in the NBA, while the tradition is to make noise when opponents are at the stripe, it is customary for fans to remain silent when their own team is shooting free throws. Thus, the transition from 50 percent of free throws being taken in silence to 100 percent is a lot less jarring than the one NFL kickers have had to make: going from taking none of their field goal attempts in silence to nearly all. Although some teams in the NFL have allowed fans at limited capacity, the majority have not—even for those who have, the crowd noise has reached nothing near the routinely earth-shattering sounds of Seahawks fans.

Home court/field/arena advantage has effects on competitors as diverse across sports as the names for their respective venues. This is due in no small part to the expectations each sport has for fans’ behavior. Some, like tennis, require complete silence when the ball is in play. The NFL and MLB don’t have any such rules, and the NBA falls somewhere in the middle. In an attempt to isolate the effects of fans on pressure, I examined two high-pressure situations in the NFL and NBA. However, pressure seemed to improve performance in tennis, giving me data from sports with all three types of fan behavior. But there aren’t any discrete high-pressure situations in tennis matches that I could test for, and tennis is self-selecting in a way that requires players to perform well under pressure in order for them to play more matches, so naturally any dataset with a minimum match requirement will contain players who do well under pressure. While it remains to be seen whether pressure is truly beneficial for most tennis players, given the significance of the results for the NFL and NBA, I’d put my money on pressure being detrimental to athlete performance overall.

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