Better to go 6 for 12 in 2 games or 0 for 12 and 12 for 12?

[EvanZ]

Does that make sense? The question is whether variance in shooting from game-to-game actually matters, in terms of winning. I'm having a discussion on another forum about Reggie Williams, who I think is a very efficient scorer. He shot 58.5 TS%. Ranked 7th in the league in spot-up shooting. The counter-argument from this guy is that Reggie goes 0 for 5 in some games and then will "go off" for 9/10 in another game. My question to him is, so what? Over the course of a season, it's not clear to me why that would make any difference, whether a player gets points in bunches or not. And this doesn't even take into account the lack of evidence of a "hot hand" in the first place. Any thoughts?

[mtamada]

If the hot games and cold games are random, i.e. not correlated with the performance of his teammates or opponents, then we can simply apply DeanO's Bell Curve model, i.e. basic probability. A team that is on average inferior to its opponents will want to have a high standard deviation, because e.g. if it has incredibly consistent play resulting in 99 points every game and 101 for its opponents, it will go 0-82. But if it has huge swings, it can win close to 50% of its games.

The opposite is true for teams which are on average superior; they like to see low standard deviations.

[EvanZ]

Great point. Yeah, that makes sense that we might be able to extend the team-level observation down to the player level. And on a team like the Warriors, who depend on 3 point shooting more or less, Reggie's "hot and coldness" now actually becomes a strength, right?

[EvanZ]

As a followup, I calculated the TS% game-to-game for Reggie Williams, Dorell Wright, Monta Ellis, Stephen Curry. Here are the standard deviations (given as %):

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Reggie: 13.63%
Monta: 13.63%
Dorell: 18.52%
Curry: 19.51%

So, it turns out that Reggie is actually not wildly variant at all, and that Curry's variation is actually the largest.

[Crow]

Somebody published an article recently (I forget where) suggesting that the role / level of usage of a player affected how their FG% variance would impact wins. I think they found it is was in general better or safer for secondary players to be high variance than lead guys. But it will depend on team specifics. The full set of offensive and defensive strengths and variances and which opponents specific players and the team as a whole tend to vary from average against and in which direction.

[Mike G]

... it is ... in general better or safer for secondary players to be high variance than lead guys. ..

This makes sense, and it often seems as though it actually determines who starts and who comes off the bench.

Arron Afflalo isn't really 'better' than JR Smith, but he may be more consistent. Tyrus Thomas' averages may be better than Boris Diaw's, and Nazr better than Kwame; but they don't start...

A consistent starting unit is less likely to get way behind in the early going, to a superior opponent; more likely to build a lead vs a lesser opponent. Then the reinforcements have a more predictable environment to enter, just as the starters began at 0-0.

A player's defense is surely more consistent than his offense, and so all else being equal, a reliable defensive player often starts, while a mercurial offensive 'maybe' comes off the bench.

[bchaikin]

A player's defense is surely more consistent than his offense...

after looking at the Synergy data of the past 5 years, i certainly would not make this assumption. i've seen just as much variance in individual player defensive data as their offensive data...

[Mike G]

Well, we know that a player can get in a groove and make a lot of shots, or conversely he cannot hit the side of a barn, on a given night.
What could possibly be that variable in defensive play?

[bchaikin]

What could possibly be that variable in defensive play?

a player's PPP (points per possession) allowed on defense varying by as much as 20%, and their FG% or eFG% allowed on defense by as much as 9%-10%, from one season to the next. if there can be that much variance from season to season, i can imagine how much more variance there might be from game to game...

[Mike G]

I guess I did not know an individual could be assigned a defensive shooting%.
Game to game, an opponent's offense can be expected to vary a lot, and how would one be able to tell what part of that is due to the defender(s)?

Certainly, on a team level, we see PPG and OppPPG varying in a similar distribution. And of course the offensive or defensive strength of the opponent can be anticipated, and the final score can be gauged relative to the opponent's averages.

Does an individual's D, when adjusted to the O of the opponent, still vary as much as his offense does, from game to game?
How do you measure individual defense?

[EvanZ]

One big difference is that offensive usage is much more variable than defensive usage. Also, I believe the variance in ORAPM is much greater than DRAPM, but I should probably check to be sure.

[bbstats]

If we assume (perhaps incorrectly) that each missed shot lowers the efficiency margin by:

=Average PPP * (1-average OR%)
=(1.073) * (1- .264)

Where the average made field goal is worth 2.173. We get the following changes:

12 for 12: +26.1 points, or +28.3 points per 100
6 for 12: +14.7 points, or +16 points per 100
0 for 12: +3.4 points, or +3.7 points per 100


Plugging these in to the pythagorean expectation formula (exp of 16.5), using an average defense & baseline offense of 107.3, the following delta Win% occurs (ExpWin% - 0.5):

12 for 12: +47.9%
6 for 12: +40.8%
0 for 12: +13.6%

in which case going 0 & 12 nets you +1.23 wins and going 6 & 6 nets you +1.63 wins

These numbers are clearly exagerrated a bit as they are without good context, but it appears that consistency helps here.

[EvanZ]

Haha. Nice! I didn't even remember having asked this question (although oddly enough, I thought about it again recently).

[bbstats]

This gives us some good theory for an ORTG-style SPM.

Based on the 10-year stuff from Jerry (offensive rAPM):

EDIT: The per-100 stuff is all estimates, and the cutoff is random, but this is so very intuitive.

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Multiple R		0.821504809
R Square		0.674870152
Adjusted R Square	0.668685617
Standard Error		1.107620346
Observations		376

Code: Select all

		Coefficients	Standard Error	t Stat		P-value
Intercept	-5.00068565	0.376933848	-13.26674607	4.22841E-33
eFG%*FGA100	 0.979512431	0.067093861	14.59913635	2.10661E-38
FGmiss100	-0.428279943	0.062343531	-6.869677329	2.75607E-11
FTM100		 0.444260583	0.049599337	8.956986251	1.68786E-17
FTmiss100	-0.357553321	0.124693571	-2.867455938	0.004376092
AST100		 0.470896085	0.03550695	13.26208222	4.41017E-33
ORB%		 0.120914891	0.028032396	4.313398355	2.0678E-05
TOV100		-1.229082483	0.128371471	-9.574420828	1.54962E-19