One of the most basic calculations a person can do with NBA stats is the average. Yes, it’s something a kid should be able to handle, and it’s intelligible even to the most math-adverse among us. But there are a surprising number of situations where the wrong average is applied. These are counter-intuitive calculations, and it’s tough to know when exactly different averages should be used. But when you know what to look for, even someone without a background in math can pick up on when the wrong average is used and how it can distort our view of the world.
I’m always on the lookout for interesting, bizarre little trends that go against conventional wisdom, but there was one recently I saw that caught my eye and I haven’t been able to sweep it under the deeper recesses of my brain. A 538 article recently stated that the Rockets have had issues with shooting fewer 3-pointers in the postseason compared to the regular season, and then pointed out that this is even stranger because 3-point rates usually increase in the playoffs. While we can all wax poetic on the failure of the Rockets and what it means for such an extreme style, but I’m skeptical that teams take substantially fewer 3-pointers in the postseason.
Let’s start with something unconventional that should illustrate the point here. What’s the average age in the regular season versus the playoffs? For 2017, using Basketball-Reference’s listed ages and weighing by minutes played, the average age was 26.6. However, for the playoffs it’s 27.6. Excusing the presence of a black hole, it’s not possible for everyone to age a year in a smaller time span, and actually given how age is calculated on Basketball-Reference — it’s your age on Feb. 1 of that season — there shouldn’t be any discrepancy. But it’s obvious what’s going on: there are a different set of players in the post-season, and on average they’re older. The same phenomenon is occurring with team 3-point rates.
Since the playoffs are filled with the best teams, and better teams tend to shoot more 3-pointers, the average rate increases in the playoffs. But you can’t see this with a typical average; you have to take an average of the differences. This is also analogous to Simpson’s paradox. In fact, using some linear regression, there’s nearly a one-to-one correlation between a team’s regular season rate and their post-season rate (the coefficient was 1.01, meaning there’s a slight increase in the 3-point rate from the regular season to the post-season). This is true when you define the rate as 3PTA/(FGA +.44*FTA) and without free throws. This is actually surprising because these teams are facing better defenses and opponents have more time to scout and plan — teams are still shooting from as often behind the arc as they normally do.
We can look at different patterns too. For instance, the ratio of free throws to field goals slightly increases in the playoffs, generally, but as you can see from the graph below the relationship is pretty chaotic. Some teams see huge reductions in the post-season, but I should offer this disclaimer: I plotted everything with a transparency value where the lighter points are teams with fewer post-season games (Weighing by minutes played didn’t change the overall results substantially, however. It mainly helped in reducing the standard error). Even so, you can see that the trend isn’t as tight as it was with 3-pointers.
Most other team stats have similar trends to the ones above, like assist percentage, which is pretty consistent. Then there’s blocks per foul, which reduces by about 14 percent when the playoffs hit — blocks decrease in the playoffs, weirdly, while fouls increase. Strangely, one of the more consistent team stats is true-shooting percentage. You may theorize that shooting percentages drop in the playoffs, but remember that both better defenses and offenses are present; thus, the net effect is that there’s only a slight decrease, if anything.
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While at the beginning of the month the Rockets were taking significantly fewer 3-pointers than they had during the regular season, they have since evened out, as they unleashed a barrage during their unsuccessful series against the Spurs. Their postseason and regular season rates ended up being fairly similar, and as we’ve seen that’s to be expected for playoff teams. You can use an average to see this — just make sure it’s the right average.