Stats: Why does no one look at variance?

[ezz_bee]

I dislike any analysis based on averages alone, I find median (the middle number) and mode (the number that most often) to give you a far superior understanding of the data, as it gives you some insight into outliers.

For instance player A averages 22 pts /game but has a median of 10 points per game and a mode of 28 points per game
player B also averages 22pts/game but has a median of 20 points/game and a mode of 21 pts per game.

It's easy to see that player B is more consistent.

Any argument that averages work out over times also works out when including median and mode. I would love to see all stats broken down into average/median/mode for every category, and would tell you more about a player than just average alone.

[Hugmenot]

I have incorporated year-to-year variance as a predictor of the future norm of a player. See posts 85 and 92 of the link below to see why I argued Nicolas Batum was a better target than Wilson Chandler in my opinion.

http://www.raptorsrepublic.com/forum...ighlight=Batum

I am sure many teams are looking at variance in much more details and have much more sophisticated predictive models. It's not something I expect to see published until teams acknowledge their base model no longer gives them an advantage over the competition.

[Ajar]

You need to make sure to weight for minutes somehow, since minutes are one of the biggest factors in per-game stats. Basketball Reference provides per 36 numbers, which would be a simple way to control for that, or you could just work out the average minutes played for each player and then scale their per-game stats to that value. That way you account for outlier games where the guy who normally plays 15-20 mpg ends up playing 40 minutes, but only scores 20% more points than his ppg average.

[thead]

Variance would likely correlate highly with win shares

[thead]

the more I read into this the more I think you are on to something.

to put this in the simplest of terms. Is it better to have a guy that averages 15 pts a game but does it by scoring 10 one game and 20 the next at 45% clip. Or a guy that scores 14 - 16 a game at a 45% clip. One is consistent and one can shoot you either in to or out of a game

[Eric Akshinthala]

Ok, I get it, but I don't particularly agree that you'll find out who's more consistent that way. It would be nice if someone could give an example of just a comparison between two players.

Here's an example. I'm using Demar Derozan and Rudy Gay as examples. I'm comparing their points over a 5 game stretch. I hope it helps.

DEMAR:

GAME PTS. SHOOTING FG%

1 20 8/17 47%
2 16 7/16 44%
3 15 6/13 46%
4 20 8/16 50%
5 12 5/15 33%


RUDY:

1 30 12/30 39%
2 22 8/22 36%
3 20 8/14 57%
4 25 11/28 39%
5 30 12/22 54.5%


Demar averages 16.6 PPG at a FG% of 44%.

Rudy averages 25.4 PPG at a FG% of 44%.

Even though Rudy has more PPG and their overall FG% are identical, Demar is the more consistent scorer based on his game to game FG%. Rudy had excellent shooting in two games but poor shooting in three whereas Demar had one poor game but four good games which makes him the more consistent scorer.

[Marz]

I'm not very good with Excel, and I don't have much time, but here's some raw data. All from basketball-reference game logs for the 2012-2013 season. Feel free to draw your own conclusions.

DeMar DeRozan

Metric	FG	FGA	FG%	3P	3PA	3P%	FT	FTA	FT%	ORB	DRB	TRB	AST	STL	BLK	TOV	PF	PTS

Average	6.68	15.01	0.44	0.41	1.46	0.22	4.33	5.21	0.81	0.59	3.32	3.90	2.49	0.93	0.29	1.84	2.11	18.11

STDEV	2.76	4.47	0.12	0.75	1.31	0.31	3.14	3.41	0.20	0.73	1.70	1.94	2.09	0.97	0.59	1.32	1.19	6.87

Alan Anderson

Metric	FG	FGA	FG%	3P	3PA	3P%	FT	FTA	FT%	ORB	DRB	TRB	AST	STL	BLK	TOV	PF	PTS

Average	3.63	9.48	0.34	1.46	4.38	0.27	1.94	2.26	0.85	0.52	1.75	2.28	1.58	0.74	0.11	1.23	2.02	10.66

STDEV	2.77	4.57	0.19	1.60	2.76	0.26	2.10	2.34	0.22	0.73	1.38	1.61	1.32	0.93	0.31	1.13	1.54	7.85

Amir Johnson

Metric	FG	FGA	FG%	3P	3PA	3P%	FT	FTA	FT%	ORB	DRB	TRB	AST	STL	BLK	TOV	PF	PTS

Average	4.15	7.48	0.54	0.06	0.16	0.40	1.68	2.31	0.73	2.80	4.74	7.54	1.51	1.00	1.36	1.44	3.72	10.04

STDEV	2.62	3.90	0.22	0.24	0.46	0.44	1.58	1.95	0.30	2.05	2.62	4.03	1.32	0.97	1.29	1.21	1.42	5.99

Not sure how to include an attachment on this forum, but I can share the full excel file (it has other stats and information in it).

EDIT: Bleh, don't know how to disable word-wrap...

[Bouncepass]

I agree that looking at variance is an interesting concept, and consistent with statistical principles used in many other fields.

Alan Anderson seems like a "high variance" kind of guy.

[Marz]

I'm not saying using variance is the be-all end-all indicator of consistency. I was just interested as to why it's never considered when discussing stats, at least from what I've read. In statistics, an average with a standard deviation of 3 vs. one with a standard deviation of 20 is different. I'd assume this would be important information to consider when looking at aggregate stats of a player.

Whether or not variance tells us a player is consistent or not is still an open question, but I believe it would be a good metric to look at.

[Soft Euro]

While other factors are considered, the most common stats that determine a players offensive consistency are PPG and FG%. As Mars who started this thread states as example, if player A shoots 40% one night and 50% another as opposed to player B who shoots 45% on both nights, player B is more consistent, This can be determined when 'variance' is considered. Hence a more accurate indication of consistency.

Ok, I get it, but I don't particularly agree that you'll find out who's more consistent that way. It would be nice if someone could give an example of just a comparison between two players.

[Primer]

Another interesting stat to look at would be on/off +/-. If there is a large variation in that from night to night, it shows how that players inconsistency is affecting the team as a whole. Even for someone like DD, who currently has a higher off court +/- than on court, the game by game analysis would at least show when he is doing worse and better, not necessarily good and bad since you could argue its always bad when the +/- favors you being off the court. If DD has lots of nights with a +6 on court, followed by lots of nights with a -5 on court, then you know his inconsistency is causing the team to lose games, and they'd be better with a player who consistently gets +1 On court every night, or even +0 On court every night, as those -5 On court games probably equal losses. Maybe every player is wildly inconsistent in those stats, I'm not sure. That's why the analysis would be cool to see.

[Eric Akshinthala]

What do you mean by a "more accurate indication". More accurate than what? And why would it be accurate at all? Too much noise.

While other factors are considered, the most common stats that determine a players offensive consistency are PPG and FG%. As Mars who started this thread states as example, if player A shoots 40% one night and 50% another as opposed to player B who shoots 45% on both nights, player B is more consistent, This can be determined when 'variance' is considered. Hence a more accurate indication of consistency.

[Soft Euro]

The simple solution to this is compare 'variance' as per positions. For example, compare a PF to a PF, a SF to a SF and so on. Even though 'variance' provides a more accurate indication of a players consistency, it's OBVIOUSLY not been considered important enough to be used. Nothing to prove this but in this day and age, it's highly unlikely that the idea has not been explored.

That only solves a small part of the problems. I could add tons of other examples about context influencing a players production, especially if we focus on points.

What do you mean by a "more accurate indication". More accurate than what? And why would it be accurate at all? Too much noise.

[Eric Akshinthala]

For example, if it's a big who's getting a lot of his points from PnR situations, his points will be influence by the way the opposing team defends the PnR. The same holds true, of course, for the ball handler.

It's also highly depended on the role a player has on the team, just as it's depended on the game plan. If there are favorable matchups on the floor, a coach will try to exploit those. That doesn't mean anything for the consisticy of that player and some coaches try to make more use of this than others.

The simple solution to this is compare 'variance' as per positions. For example, compare a PF to a PF, a SF to a SF and so on. Even though 'variance' provides a more accurate indication of a players consistency, it's OBVIOUSLY not been considered important enough to be used. Nothing to prove this but in this day and age, it's highly unlikely that the idea has not been explored.

[Soft Euro]

A problem is that there are so many reasons for variance undependent of a players consistency.

For example, if it's a big who's getting a lot of his points from PnR situations, his points will be influence by the way the opposing team defends the PnR. The same holds true, of course, for the ball handler.

It's also highly depended on the role a player has on the team, just as it's depended on the game plan. If there are favorable matchups on the floor, a coach will try to exploit those. That doesn't mean anything for the consisticy of that player and some coaches try to make more use of this than others.

If we take DeRozan as an example, his variance is also related to the way he is being defended (and the quality of that defender). In fact, I think that's one of the most important factors in his case. Does that mean that this makes him inconsistent? No, the explanation for that part of his variance stems from the variance in defenders.

And I think there are countless other examples to show other influences besides consistency for a stat like this.

All in all, I think there are too many other factors besides a player's consistency causing noise in a stat like this.