NBA: More Four Factors

[Latrinsorm]

The four factors are shooting, turnovers, rebounding, and free throws. Suppose you took every playoff series from the past 10 years (150 total), looked at only one factor at a time, and predicted a win based on even the slightest margin (out to the thousandths place, because that's how far basketball-reference lists and it produces few ties):

shooting - 125 and 21: 85.6% ± 5.8%
turnovers - 76 and 74: 50.7% ± 8.2%
rebounding - 86 and 62: 58.1% ± 8.1%
free throws - 93 and 56: 62.4% ± 7.9%

Shooting obviously dominates (and for the record is fifteen standard deviations clear of 42%). Neither turnovers nor rebounding are statistically distinguishable from chance. Free throws surprisingly are, all the way past 3 standard deviations. If you're going to win something, you want it to be shooting.

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In the last thread I observed that defensive rebounding made defense worse, and to a greater degree than offensive rebounding made offense better. It follows that a team that wins shooting and loses rebounding should do better than a team that wins both, but:

e&r - 68 and 4: 94.4% ± 5.4%
e~r - 56 and 16: 77.8% ± 9.8%

These values are distinguishable; just barely so, but still.

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Of course, a trinary win/loss/tie evaluation loses a lot of information that might not average out in a mere 150 samples. For one thing, each factor has a very different standard deviation:

e - 3.72%
t - 1.91%
r - 4.35%
f - 5.13%

This could also explain why free throws (which have the least impact on ratings) end up being significant predictors of success: margin for margin they are behind turnovers, but because their margins are 2.5x as big turnovers can't catch up...?

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I'm going to perform the same analysis out to 1981 just to be sure, then I'm going to be more subtle. Still, I'm glad the basic point has been reiterated: shooting matters way more than everything else, to the point where even if you lose all three of the other factors you're in good shape (11 and 2: 84.6% ± 20.0%).

[Latrinsorm]

It turns out full box scores were only kept for every series starting after 1984 (thanks a lot Jobs) so that's as far as I could go. Let's go through the coarse grained findings: the only thing that matters is that a team wins the series and the factor, margin (for both terms) is irrelevant and every other factor is irrelevant. (I also checked for best of 5 vs. best of 7, but there were no differences.)

shooting - 350 and 79, 81.6% ± 3.7%
turnovers - 198 and 233, 45.9%(!!!) ± 4.8%
rebounding - 253 and 178, 58.7% ± 4.7%
free throws - 258 and 176, 59.7% ± 4.7%

The turnovers one is just barely within range of pure chance, but still, wow! And still, shooting is by far and away the deciding factor. Combos:

win ET - 179 and 61, 74.6% ± 5.6%
win ER - 190 and 17, 91.8% ± 3.8%
win EF - 209 and 35, 85.7% ± 4.5%
win E and lose R - 158 and 60, 72.5% ± 6.0%
win E and lose TRF - 37 and 11, 77.1% ± 12.1%
win ET and lose RF - 29 and 18, 61.7% ± 14.2%

win all - 70 and 4, 94.6% ± 5.3%
win ERF and lose T - 46 and 0(!!!), 100.0% ± undef

Rebounding is definitely the second thing you want to win, but it definitely can't make up for losing shooting. Turnovers are weird, more on this in a second.

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Are these reasonable?

1. Shooting trumps everything.
I think this is reasonable. You can't rebound a shot that doesn't miss, and if you always miss you can rebound all you like but it won't make a difference. Similar story with turnovers: although they precede the shot and a literal 100% vs. 100% scenario would therefore result in a draw, in practice turnovers are nowhere near common enough relative to shots.

Free throws are a lot more nuanced. Good eFG% can be generated by excellent 3 point shooting or excellent finishing at the rim. The former always comes from jump shooting, the fouling of which is taboo, and on top of that is usually associated with good to great free throw shooting. The latter is famously targeted for fouling (no layups, Jordan Rules, etc.), and on top of that many elite eFG% rim guys are notoriously poor free throw shooters: Shaq and Dwight are in the top 5 all time in eFG%, for instance. There's no direct box score way to measure contesting a shot, but clearly you're a lot more likely to foul when contesting than not. There's a lot going on, but like turnovers, free throws are dramatically less frequent than field goal attempts (and are growing even less so).

2. Causing net turnovers is bad.
Strictly speaking, winning the turnover battle is statistically indistinguishable from having no effect whatsoever, but it's darn close to having a negative impact on winning. This is hard to believe. A forced turnover ends the opponent's possession and in some (many?) cases offers a transition opportunity, which results in uncontested shots at the rim or from 3 or fouls to prevent doing so (including delicious clear path fouls) or a secondary transition opportunity against a mismatched defense. Causing a turnover is really good, having a turnover is really bad...

...but what about all the times you try to cause a turnover and fail? That is, gamble? As a perimeter player you give the opposition a 5 on 4, as a post player you give your man a layup. Those are really bad. What if NBA players are mediocre (on average) at deciding when to gamble and when to play straight up, and therefore the turnovers they generate are outweighed by the (invisible to the box score) costs when they gamble and lose?

What makes this even more interesting is that in the regular season turnovers are very nicely correlated with ORtg and DRtg, which are in turn nicely correlated with winning and losing. I can think of two explanations for why the NBA player's internal calculus gets thrown off in the playoffs: national TV leads to highlight-seeking, or more probably after 82 games NBA players are tired, and tired people's decision-making is biased towards the easy path.

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Next I will look at the margins for shooting rather than crude win/loss and see if anything interesting emerges.

[Latrinsorm]

So I messed up the turnovers part. I c/ped the "which value is higher?" function across all four categories, but winning the turnover battle means having less. Thus, it is when teams win all four factors that they go 46 and 0, which makes more sense. Turnovers join rebounds and free throws as slightly significant factors that are much, much, much less significant than shooting.

As for shooting, looking at gap in eFG% quantitatively gives us:


delE W L pct ±
0.01 45 25 64.3% 11.5%
0.02 40 22 64.5% 12.2%
0.03 55 15 78.6% 9.8%
0.04 40 9 81.6% 11.1%
0.05 42 5 89.4% 9.0%
0.06 24 1 96.0% 7.8%
0.07 40 1 97.6% 4.8%
0.08 16 1 94.1% 11.4%
0.09 16 0 100.0% 0.0%
0.1 6 0 100.0% 0.0%
0.11 7 0 100.0% 0.0%
0.12 7 0 100.0% 0.0%
0.13 4 0 100.0% 0.0%
0.14 7 0 100.0% 0.0%
0.22 1 0 100.0% 0.0%
Which I think falls neatly into the following bins:


delE W L pct ±
0.02 85 47 64.4% 8.3%
0.04 95 24 79.8% 7.4%
0.06 66 6 91.7% 6.5%
inf 104 2 98.1% 2.6%
The two outliers are:
Pistons over Magic in 5 games in the 2008 ECS (dominated turnovers, narrowly lost rebounding, dominated free throws)
76ers over Bucks in 7 games in the 2001 ECF (narrowly won turnovers, won rebounding, dominated free throws)

So shooting is the road to winning, and the more you win it by the better your chances are. Next we shall see how the teams that win shooting in the regular season do in the playoffs.