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Stats: Why does no one look at variance?

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  • #16
    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.

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    • #17
      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.

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      • #18
        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.

        Code:
        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
        Code:
        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
        Code:
        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...
        Last edited by Marz; Fri Apr 26, 2013, 08:23 AM.

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        • #19
          Soft Euro wrote: View Post
          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.
          Last edited by Eric Akshinthala; Fri Apr 26, 2013, 10:00 AM.
          Attitude Is A Choice.

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          • #20
            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
            For still frame photograph of me reading the DeRozan thread please refer to my avatar

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            • #21
              Variance would likely correlate highly with win shares
              For still frame photograph of me reading the DeRozan thread please refer to my avatar

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              • #22
                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.

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                • #23
                  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.

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                  • #24
                    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.
                    "They're going to have to rename the whole conference after us: Toronto Raptors 2014-2015 Northern Conference Champions" ~ ezzbee Dec. 2014

                    "I guess I got a little carried away there" ~ ezzbee Apr. 2015

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