The statistics behind fouling Ben Simmons on literally every possible possession
It was hilarious watching the Wizards foul Simmons every time in the latter half of the fourth quarter in Game 4 of their 2021 NBA Playoffs first round series against the 76'ers… but it had me wondering, what’s the threshold below which it would be statistically preferential for the Wizards to foul the 76’ers on every possible play for the rest of the series?
The 76’ers averaged 103.5 possessions and 113.6 points per game take in the regular season. Now, although the 76’ers have been averaging 122.75 in the postseason so far against the Wizards, to maintain parallelism with the possessions stat, we’ll use 113.6ppg in our calculations for now. We also take into account the ‘Hack-a-Shaq’ rule imposed some years back, in which teams cannot conduct such behavior in the final two minutes of every quarter.
So, if there are 103.5 possessions for Philadelphia and Washington is restricted from fouling Simmons 1/6 (2 mins of every 12 min quarter) of the game, there are on average 86.25 possessions where they can foul. Although teams are permitted to foul four times every regulation period without additional penalties, we can neglect this because there is no free throws and thus subsequent change of possession. The Wizards can burn all four of their team fouls in one 76’ers ‘possession,’ be in the bonus, and send Simmons to the line thereafter.
Assuming points are uniformly distributed over the duration of the game, the 76’ers will score ~18.93 points in the non-fouling minutes. Thus, to make up the ~94.67 point deficit, Simmons will have to score at least that across 86.25 trips to the free throw line. That translates to 168.5 opportunities to convert 94.67 buckets, or in other words, a free throw percentage of 56.18%. Now, although he still had the lowest free throw percentage in the league, in the regular season, Simmons made 61.3% of his free throws, but that figure has since plummeted to 25% in the post-season, albeit with a smaller sample size.
Still, given the situation, I’d foul Simmons on every possible possession in Game 5 [and try to keep a straight face in doing so].
Now I’ll admit this analysis was rather cursory and ladled with many assumptions that might not reign true, beyond just the fact that the 76’ers have been scoring a prolific 122.75ppg in the last four games against the Wizards. Other than that, consider that if possessions were truly uniformly distributed, that would mean the 76’ers have ~2.15 possessions per minute, or a possession every 27.83 seconds. We know that in the final thirty seconds or so of a quarter, teams may try to heave a rushed shot for a change at a 2-for-1. Again, this estimation is rather rudimentary, but this might result in on average 1.5 possessions in the final 30 seconds of every quarter, or 4.5 possessions across 1.5 minutes of every game, neglecting the fourth quarter. Although this discrepancy may seem trivial, consider that a 3 possession differential is the difference between the 9th and 25th-ranked team in average possessions per game.
An even more glaring issue with the above approximations is that by fouling every possession, the entire dynamic of the game is altered, and not just trivially in the sense that it might be less enjoyable to watch for some fans. By prohibiting the 76’ers from playing basketball 5/6 of the game, the Wizards will effectively have an additional 5/6 * 103.5 = 86.25 possessions that otherwise would have belonged to the 76’ers. Pacing will invariably be altered, and who knows how many possessions the 76’ers will actually have for the Wizards to foul.
Perhaps some wisdom can be gleaned in the numbers from the Spurs vs Magic series some years back, where Coach Popovich pushed his team to continually foul Shaq. I’ll leave that for the internet to figure out.
In the meantime, I’ll sit back, relax, and hope that in Game 5, the Wizards do what’s statistically superior and break the game of NBA basketball.
