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APBRmetrics
The statistical revolution will not be televised.
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Ilardi
Joined: 15 May 2008
Posts: 262
Location: Lawrence, KS
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 Posted: Sun Jul 13, 2008 11:47 am Post subject: |
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Mountain,
Where are you getting the statistical plus-minus numbers you've cited (e.g., 1.6 for Posey)? Are they up online somewhere, or are you calculating them yourself?
Have you ever calculated the precise correlation between statistical plus-minus and the offensive/defensive breakdowns from adjusted plus-minus? (e.g., as posted recently by Eli W.)
If you (or anyone else) has time to check on that, I think it would prove highly enlightening. |
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Mountain
Joined: 13 Mar 2007
Posts: 1527
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Harold Almonte
Joined: 04 Aug 2006
Posts: 616
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| Posted: Sun Jul 13, 2008 1:02 pm Post subject: |
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I think that trying to change the weighting of players's inputs, giving more weight to play finishers and direct helpers than to non direct helpers, would convert the metric in almost a (formula type) linear metric. But, even upgrading the actual boxscore, to include more defensive stats, like defensive attempts and double teams defensive splits, etc, would be an easier job (and more reliable than trying with statistical +/-).
One of the problem of the metric is that blurry things of the game, like usage-efficiency tradeoff and diminishing/increasing returns, become more deceitful in plus-minus metric. In some way the metric suggests that the Moon, Hayes, ... players deceive more playing time than the Paul, Anthony,...etc.. It's debatable that the first group of players, being as (or more) unbalanced as the second, could really produce more positive outcomes, even in a teamed two way game like basketball. I don't know the adjusting process employed, but I think the players's off numbers should be adjusted different than the on-s, and with a different kind of weights. |
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Mountain
Joined: 13 Mar 2007
Posts: 1527
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| Posted: Sun Jul 13, 2008 2:00 pm Post subject: |
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Steve, I lined up 275 records and checked the correlation between statistical plus-minus and the offensive/defensive breakdowns from adjusted plus-minus and got .53 for adjusted offensive and statistical and only .07 for adjusted defensive and statistical. You were of course right that offensive was more highly correlated but it isn't that strong.
I might lineup offensive/defensive breakdowns from adjusted plus-minus with the same from statistical at some point in the future but will have to merge the databases.
Last edited by Mountain on Sun Jul 13, 2008 2:22 pm; edited 2 times in total |
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Kevin Pelton
Site Admin
Joined: 30 Dec 2004
Posts: 978
Location: Seattle
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| Posted: Sun Jul 13, 2008 2:12 pm Post subject: |
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| Ilardi wrote: | I believe it comes at a cost of introducing bias into the ensuing measure, since the boxscore stats pick up on offensive contribution much more than defensive contribution.
I think part of the appeal, though, is that statistical plus-minus has more "face validity" - inasmuch as virtually everybody has trouble believing that a guy with eye-popping boxscore stats and horrific defense is really as big a liability as adjusted plus-minus says he is (think: Al Jefferson, Carmelo Anthony, CP3, etc.) |
I have been thinking about this since looking at Jose Calderon's terrible adjusted plus-minus yesterday.
From a theoretical standpoint, it's my belief that an individual player has a greater impact on his team's offense than his defense. I'm also of the belief that coaches have more impact at the defensive end than the offensive end. If we had adjusted plus-minus broken down into its offensive and defensive components and used this to predict a team's offensive and defensive ratings based on the past performance of individuals on the team, I suspect it would tend to predict offense better than defense.
There's a connection here to the initial post of the thread. I think if you had followed the course I outlined, it would have said Boston would have one of the league's top offenses and a slightly weaker defense. Instead, the offense turned out to be good but not great while it was the defense that was historic in its excellence. How much of that had to do with the players and how much had to do with the coaching staff (particularly Tom Thibodeau) is something about which we can only speculate.
Adjusted plus-minus can't, by its nature, ascribe any value to coaching. It's my belief, then, that it somewhat overstates the difference between good defenders and bad defenders and this explains at least some of the discrepancy between conventional wisdom on players like Paul and Anthony and Calderon and their adjusted plus-minus ratings. Adjusted plus-minus still may reveal that their individual stats overrate them, but not to the extent apparent from their actual ratings.
Thoughts, Steve and others? |
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Harold Almonte
Joined: 04 Aug 2006
Posts: 616
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| Posted: Sun Jul 13, 2008 2:16 pm Post subject: |
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This is logical, given that the statistical +/- defense depends on boxscore defensive stats, although if the value of rebounds are regressed, then they aquire shot defense weights like in WP ( isn't high a correlation between WP and statistical +/-?). I think the compounded overall +/- created by DR with statistical and pure adjusted +/-, wich weights one system against the other, depending on errors (I think), should take account of these correlations to re-weight again.
| Quote: | | Steve, I might do more later but I lined up 200 records and checked the correlation between statistical plus-minus and the offensive/defensive breakdowns from adjusted plus-minus and got .52 for adjusted offensive and statistical and only .1 for adjusted defensive and statistical. |
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Mountain
Joined: 13 Mar 2007
Posts: 1527
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| Posted: Sun Jul 13, 2008 2:52 pm Post subject: |
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You can try to get to get coaching impact various ways. Not easy in Boston example but easier in some other situations where the players are relatively stable and the coaching changed.
I happened to see this comment again while at countthebasket:
#12
"the missing link in all of this is coaching. If you look at lineups, it matters if a coach has the right combination of players together. Put Chris Paul with the wrong 4 guys and he will look bad. Put him with the wrong guys, in the wrong situation, against a better matched unit, his numbers, no matter what the parameters will suffer relative to his ability.
if you want to start seeing some interesting information, take all the same information and formulas you have, and apply it to coaches. Look at what happens to the performance of players/teams and lineups before and after a coaching change."
Comment by mark cuban — May 30, 2008
I followed with some explorations of lineup usage in the Dallas situation.
Individuals may have more impact on offense than defense if you credit them for "making" plays and believe that players rely on a defensive system and its success or failure is more about scheme than individual great or poor shot defense. I am not necessarily disagreeing with Kevin's assertions as one player ultimately shoots while often several play important roles on the defense but I do have some caution about accepting them completely right now.
I aslo had some thoughts about possible changes to statistical +/-. |
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Harold Almonte
Joined: 04 Aug 2006
Posts: 616
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| Posted: Sun Jul 13, 2008 3:34 pm Post subject: |
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| Quote: | | Individuals may have more impact on offense than defense if you credit them for "making" plays and believe that players rely on a defensive system and its success or failure is more about scheme than individual great or poor shot defense. |
That's why I've allways though that defense is as much a "team system" as it is the offense. The only differences are that at offense you have delimited scoring options players, and at defense your desired defensive options players not necessarilly match with the opponent offensive options, even trying to force rotations; At defense two players can contest the same opponent shot, but two players can't touch the ball at the same time at offense, although a second offensive help player can make screen on a scoring defender, also scoring skills are more complex to develop (that's maybe why scorers's values and costs are view from a different economical point than just team wins), and distance from the ring is a help at defense, not necessarilly is that help at offense. Rotations are just like passes, how much of these defensive passes are "assists"? How many double team defensive attempts occur during a game? And that's why I've allways though that the set 80% from team defensive eff., in the DRTG compound, is a bit an exaggeration for some players.
Last edited by Harold Almonte on Sun Jul 13, 2008 4:18 pm; edited 1 time in total |
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Mountain
Joined: 13 Mar 2007
Posts: 1527
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| Posted: Sun Jul 13, 2008 4:14 pm Post subject: |
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"...that's why I've always though that the 80% from team defensive eff., in the DRTG compound, is a bit an exaggeration"
This part I agree with Harold. |
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Mountain
Joined: 13 Mar 2007
Posts: 1527
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| Posted: Sun Jul 13, 2008 4:49 pm Post subject: |
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Running correlation of adjusted and statistical +/- for a modest sample for the offensive parts I get .54. For the defensive parts .36. Overall .44 (pretty close to Eli's figure of .49).
Not sure what all to make of it but using either measure alone doesn't seem wise or representative of all of what happens and yet using both it isn't clear either.
In the future hopefully a better integration of local and global impacts can be achieved.
Maybe the hybrid input adjusted method I described or team specific statistical would help. And more work with lineups and individual to lineup crosswalks. etc.
Still then the mysteries are vexing. |
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Ilardi
Joined: 15 May 2008
Posts: 262
Location: Lawrence, KS
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| Posted: Sun Jul 13, 2008 8:31 pm Post subject: |
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| Kevin Pelton wrote: | | Ilardi wrote: | I believe it comes at a cost of introducing bias into the ensuing measure, since the boxscore stats pick up on offensive contribution much more than defensive contribution.
I think part of the appeal, though, is that statistical plus-minus has more "face validity" - inasmuch as virtually everybody has trouble believing that a guy with eye-popping boxscore stats and horrific defense is really as big a liability as adjusted plus-minus says he is (think: Al Jefferson, Carmelo Anthony, CP3, etc.) |
I have been thinking about this since looking at Jose Calderon's terrible adjusted plus-minus yesterday.
From a theoretical standpoint, it's my belief that an individual player has a greater impact on his team's offense than his defense. I'm also of the belief that coaches have more impact at the defensive end than the offensive end. If we had adjusted plus-minus broken down into its offensive and defensive components and used this to predict a team's offensive and defensive ratings based on the past performance of individuals on the team, I suspect it would tend to predict offense better than defense.
There's a connection here to the initial post of the thread. I think if you had followed the course I outlined, it would have said Boston would have one of the league's top offenses and a slightly weaker defense. Instead, the offense turned out to be good but not great while it was the defense that was historic in its excellence. How much of that had to do with the players and how much had to do with the coaching staff (particularly Tom Thibodeau) is something about which we can only speculate.
Adjusted plus-minus can't, by its nature, ascribe any value to coaching. It's my belief, then, that it somewhat overstates the difference between good defenders and bad defenders and this explains at least some of the discrepancy between conventional wisdom on players like Paul and Anthony and Calderon and their adjusted plus-minus ratings. Adjusted plus-minus still may reveal that their individual stats overrate them, but not to the extent apparent from their actual ratings.
Thoughts, Steve and others? |
Kevin,
I can understand why you think adjusted plus-minus might overstate the value of the defensive contribution of individual players, but I don't believe it does. Take the case of the Boston Celtics, as you suggested. They became an elite defensive team this past season in large part due to the addition of KG - something that could have been predicted a priori based on the knowledge of KG's extraordinary defensive adjusted plus-minus value (the highest in the league at +9.8 pts/100 possessions, and similarly high in past seasons at Minnesota, even under Saunders).
It's just one example (albeit the one you raised), but it demonstrates that a player can have as large an impact with defense as with offense, and that adjusted plus-minus can capture this. Likewise, if you only looked at the offensive side of things with a player like Calderon, you'd think you were seeing an emerging All Star . . . that's why adjusted plus-minus is so potentially valuable - by unmasking the fact that players like Calderon and Carmelo and Al Jefferson and Richard Jefferson and Amare Stoudemire don't have nearly the positive impact that people think they do, because they give away on defense much of what they add on offense (if not more, in some cases).
This is not to disagree with your point that coaching matters for defense (and I certainly give Thibodeau at least a bit of credit for Boston's staggering defensive efficiency last year), although one could make the argument that coaching has just as big an impact on offense (e.g., D'Antoni's system in Phoenix).
Finally, you say that "adj +/- can't, by its nature, ascribe any value to coaching" . . . but it can. All it requires is using multiple seasons (probably at least 4) and adding the league's coaches into the model as additional independent variables. Trust me - if there's an effect of coaching (above and beyond that of players), it will show up. If I weren't working to a book deadline this month, I'd get right on it . . . but I promise I'll look at it in a month or two and report back to you. (If someone on here doesn't beat me to it first.)
Last edited by Ilardi on Sun Jul 13, 2008 8:49 pm; edited 1 time in total |
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Ilardi
Joined: 15 May 2008
Posts: 262
Location: Lawrence, KS
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| Posted: Sun Jul 13, 2008 8:40 pm Post subject: |
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| Mountain wrote: | Steve, I lined up 275 records and checked the correlation between statistical plus-minus and the offensive/defensive breakdowns from adjusted plus-minus and got .53 for adjusted offensive and statistical and only .07 for adjusted defensive and statistical. You were of course right that offensive was more highly correlated but it isn't that strong.
I might lineup offensive/defensive breakdowns from adjusted plus-minus with the same from statistical at some point in the future but will have to merge the databases. |
Thanks for running this. What it tells me is that defensive adjusted plus-minus is probably the single most valuable stat we have right now, since it picks up on something no other stat is capturing.
As I read it, all the boxscore-derived stats - PER, win shares, statistical plus-minus, etc. - largely reflect contributions on the offensive side of the ball, as indicated by their relatively high intercorrelations with one another (and their weak respective correlations with defensive plus-minus). Agreed? |
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DLew
Joined: 13 Nov 2006
Posts: 224
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| Posted: Sun Jul 13, 2008 8:53 pm Post subject: |
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Some limited thoughts, as I would like to say more but can't:
Box score statistics better measure offense than defense, keep this in mind when thinking about when to use adjusted plus-minus and when to use statistical plus-minus...
Statistical plus-minus is better than one year adjusted plus-minus because it is not noisy, however there are now several years of adjusted plus-minus available, and while averaging them is not as good as running a regression with multiple years, it pretty much works...
Adjusted plus-minus only measures how a played has performed in the context of his role and team, player effectiveness can change when role changes...
Adjusted plus-minus suffers from diminishing returns like virtually everything else in the world, if you had a team of the five best players in the league they wouldn't average a 30 point margin of victory even if they 'should'... |
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Ilardi
Joined: 15 May 2008
Posts: 262
Location: Lawrence, KS
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| Posted: Sun Jul 13, 2008 9:09 pm Post subject: |
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| Mountain wrote: | Running correlation of adjusted and statistical +/- for a modest sample for the offensive parts I get .54. For the defensive parts .36. Overall .44 (pretty close to Eli's figure of .49).
Not sure what all to make of it but using either measure alone doesn't seem wise or representative of all of what happens and yet using both it isn't clear either. |
That's great info. Out of curiosity - what were the stats that went into the defensive part? I assume at least steals, blocks, and defensive rebounds . . . what about fouls? Anything else? |
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Ilardi
Joined: 15 May 2008
Posts: 262
Location: Lawrence, KS
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| Posted: Sun Jul 13, 2008 9:16 pm Post subject: |
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| DLew wrote: | Some limited thoughts, as I would like to say more but can't:
Box score statistics better measure offense than defense, keep this in mind when thinking about when to use adjusted plus-minus and when to use statistical plus-minus...
Statistical plus-minus is better than one year adjusted plus-minus because it is not noisy, however there are now several years of adjusted plus-minus available, and while averaging them is not as good as running a regression with multiple years, it pretty much works...
Adjusted plus-minus only measures how a played has performed in the context of his role and team, player effectiveness can change when role changes...
Adjusted plus-minus suffers from diminishing returns like virtually everything else in the world, if you had a team of the five best players in the league they wouldn't average a 30 point margin of victory even if they 'should'... |
Dave,
Thanks for weighing in on this. In response to a couple of your points above:
1) Any player stat will vary based on team context and role - that's not unique to adjusted plus-minus.
2) The "diminishing returns" phenomenon you've raised is simply a special case of an interaction effect (i.e., the statistical phenomenon where the linear effect of Player A depends on the presence or absence of Players B, C, D, E, etc.) - and such interaction effects can be estimated, in principle, in an adjusted plus-minus model.
3) Glad we're agreed on the fact that boxscore-based stats don't do nearly as good a job at capturing defensive contributions: that's my main argument, in fact, for the unique value of adjusted plus-minus.[/i] |
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