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THWilson
Joined: 19 Jul 2005
Posts: 164
Location: phoenix
PostPosted: Tue Mar 24, 2009 2:48 pm Post subject: Re: Statistical +/-, 2K9 Reply with quote
Ilardi wrote:
I'm planning to spend some time in the weeks ahead developing a revised statistical plus-minus (SPM) model - probably in collaboration with Aaron B. (though I won't presume to speak for him, as we haven't yet firmed up plans).
In any case, I'll be sure to post all details of this revised SPM model here in the public domain.
Well that is great news. Looking at Dan's model there is clearly room for improvement. A few thoughts:
Is there a need to use the same explanatory variables on offense and defense? I would think that it would make more sense to build these models without regard for each other.
Wingspan is often cited as useful for defense. I believe draftexpress has published wingspan info for a number of years now.
Number of years of college ball could be interesting.
As could more stylistic measures, FTA/TSA, AST/Usage, VI etc.
I imagine personal fouls have a polynomial relationship where a moderate amount is good, few and lots are bad. Giving that variable the opportunity to vary in that way may be fruitful.
Per possesion would be better than per minute, but I know that can be tough.
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YaoPau
Joined: 28 Jan 2009
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PostPosted: Tue Mar 24, 2009 3:13 pm Post subject: Statistical APM with TS% Reply with quote
I created a Statistical Offensive APM which uses TS% along with OREB%, AST%, TOV%, USG% which I regressed against Aaron's '07-'08 numbers. I posted the results at
http://www.3hoopsfans.com/2009/03/expected-opm/ . My excel is available for download there at both the middle and bottom of the page.
Edit: If you don't feel like combing through my lengthy post for the download link, here's the spreadsheet:
http://spreadsheets.google.com/ccc?key= ... 0HlWipWiUg
Last edited by YaoPau on Tue Mar 24, 2009 3:30 pm; edited 2 times in total
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YaoPau
Joined: 28 Jan 2009
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PostPosted: Tue Mar 24, 2009 3:21 pm Post subject: Reply with quote
Quote:
Wingspan is often cited as useful for defense. I believe draftexpress has published wingspan info for a number of years now.
I flirted with that idea too - I tried creating a Defensive Statistical APM using DREB%, STL%, BLK%, usual position, height relative to positional average, vertical jump, and difference between wingspan and height. The average error between my overall umbers an Aaron's defensive APM numbers were good, but it still left the usual Bruce Bowen / Jason Collins errors.
I saw basically no correlation between wingspan and defensive ability among players with eligible minutes. For every crappy defender with short arms (Troy Murphy (-2.11), Michael Redd (-4.47), Chris Paul (-4.54)) there was an equally crappy defender with long arms (Marvin Williams (-3.03), Kevin Durant (-4.11), Al Thornton (-4.55)). I wouldn't doubt there'd be a correlation between short arms and poor defense with bench players though. Just looking briefly at the list - Steve Novak (-10.1Cool, JJ Redick (-8.54)...
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Carlos
Joined: 21 Jan 2005
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Location: Montevideo, Uruguay
PostPosted: Tue Mar 24, 2009 4:50 pm Post subject: Reply with quote
Interesting work. It would be good to check how does it correlate teamwise with teams's Off. Eff. as compared with other linear weights ratings (for example, Offensive PER).
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mtamada
Joined: 28 Jan 2005
Posts: 375
PostPosted: Wed Mar 25, 2009 3:04 am Post subject: Re: Statistical +/-, 2K9 Reply with quote
THWilson wrote:
I imagine personal fouls have a polynomial relationship where a moderate amount is good, few and lots are bad. Giving that variable the opportunity to vary in that way may be fruitful.
I was giong to suggest the same. I'm not sure that low PFs will show up with any sort of statistical effect, but theory and common sense tell us that someone who fouls excessively if nothing else is putting the other team into the bonus more quickly ... has anyone looked at the impact of being in the bonus on offensive efficiency?
Anyway, either a polynomial, or a spline (slope dummy) with the threshold at ... I don't know more than maybe 5 or 6 PFs/48 minutes.
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Mountain
Joined: 13 Mar 2007
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PostPosted: Wed Mar 25, 2009 3:05 am Post subject: Reply with quote
Is Ariza a defensive specialist? Maybe not clearly a specialist by the numbers against al opponents but the Lakers have him playing one on tv.
Defense specialist + passing + 3 point game. Bowen, Battier Bell have that 3rd ingredient. Ariza takes the shot too and is at least average. 11% assist% basically ties him for the lead for your set of current names.
A steal for what they paid for him.
Walton and Odom are different mixes on these 3 variables but I have no doubt the Lakers are looking to get some impact from each on these 3 and getting some of all 3 was a factor in them being there over others who might be less 3 dimensional even if they were better on one.
Artest would seem to be one the leading candidates for being like a Michael Cooper type or beyond. I hadn't really given him or Houston's staff enough credit for climbing back to 41% FG on 3 pointers. Turkoglu and Ginobili are high on the criteria too. They are too good for inclusion on your defensive specialist list but I mention them anyways.
Offensive APM - EOPM essentially is non-boxscore offensive impact and Offensive APM error. How much is each, hard to say but it is certainly not all error. Each case is a different mix but on average are they similar sized?
Maybe you get some better results for wingspan in combo with draft combine agility score and possibly vertical leap even though quickness of jumping would be a better indicator?
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Ilardi
Joined: 15 May 2008
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Location: Lawrence, KS
PostPosted: Wed Mar 25, 2009 10:18 am Post subject: Re: Statistical APM with TS% Reply with quote
YaoPau wrote:
I created a Statistical Offensive APM which uses TS% along with OREB%, AST%, TOV%, USG% which I regressed against Aaron's '07-'08 numbers. I posted the results at
http://www.3hoopsfans.com/2009/03/expected-opm/ . My excel is available for download there at both the middle and bottom of the page.
Edit: If you don't feel like combing through my lengthy post for the download link, here's the spreadsheet:
http://spreadsheets.google.com/ccc?key= ... 0HlWipWiUg
Great stuff, thanks. What was the R^2 for your Statistical Offensive APM model? I'm curious to see how it compared with Dan's model (which was about 0.57).
Also, what were the standard errors and p-values for each coefficient in the model? (In other words, were all 5 independent variables making significant contributions?)
Finally, just to be clear . . . You said you regressed "against Aaron's 07-08 numbers", but it looked to me like you used the Ilardi/Barzilai numbers from 82games rather than Aaron's numbers from basketballvalue.com, correct?
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YaoPau
Joined: 28 Jan 2009
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PostPosted: Wed Mar 25, 2009 12:49 pm Post subject: Re: Statistical APM with TS% Reply with quote
Ilardi wrote:
Great stuff, thanks. What was the R^2 for your Statistical Offensive APM model? I'm curious to see how it compared with Dan's model (which was about 0.57).
0.5218. For a five-variable system I expected it to come up short of Dan's model accuracy-wise; its benefits are logical variables and simplicity.
Ilardi wrote:
Also, what were the standard errors and p-values for each coefficient in the model? (In other words, were all 5 independent variables making significant contributions?)
Variable, Coefficient, Standard Error
TS%, 30.2201, 5.105298
OREB%, .128564, .070669
AST%, .183697, .028898
TOV%, -0.31078, .075418
USG%, 0.136568, .045257
I don't know how to calculate p-values, but there's a table on my post (
http://www.3hoopsfans.com/2009/03/expected-opm/) titled "Which rates impact EOPM the most" that attempts to answer your question. The short of it is AST% means more than TS% TOV% USG% which mean more than OREB%.
Ilardi wrote:
Finally, just to be clear . . . You said you regressed "against Aaron's 07-08 numbers", but it looked to me like you used the Ilardi/Barzilai numbers from 82games rather than Aaron's numbers from basketballvalue.com, correct?
Yep, both names are in the post. I was the one who emailed you a couple weeks back asking if you planned to split your bv ratings into Offense and Defense. Hopefully you're releasing the split numbers again after this season, I'd love to see how the coefficients hold from year to year.
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YaoPau
Joined: 28 Jan 2009
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PostPosted: Wed Mar 25, 2009 1:01 pm Post subject: Reply with quote
Mountain wrote:
Is Ariza a defensive specialist? Maybe not clearly a specialist by the numbers against al opponents but the Lakers have him playing one on tv.
Defensive specialist + passing + 3 point game. Bowen, Battier Bell have that 3rd ingredient. Ariza takes the shot too and is at least average. 11% assist% basically ties him for the lead for your set of current names.
I didn't include Ariza or Artest because I figured they were too well-rounded to be labeled defensive specialists. You're right about Artest's passing ability though, I watched him play three seasons on the Bulls and never thought of him as a good passer, but the stats say he's one of the best passing forwards in the league. Despite his horrific TS%, he's got a career EOPM of +0.15 (+0.67 this season). I heard Morey took some heat at Sloan Sports for acquiring Artest this offseason, but the numbers back it up.
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fundamentallysound
Joined: 18 Jul 2008
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Location: VA
PostPosted: Fri Oct 16, 2009 1:00 am Post subject: Resurrecting this thread Reply with quote
Hi all, just wanted to see if I couldn't resurrect this thread, because I was playing around with YaoPau's EOPM, and had a thought about how it might be improved, and how we might use what we know about the Four Factors to use relatively simple rate statistics to create a better EOPM and EDPM.
First, I'd like to say that I really like YaoPau's work here and don't mean for this to come off as disparaging at all. However, there's some interesting stuff that comes as a conclusion from his findings on the importance of AST% in estimating offensive adjusted plus minus. It seemed to be suggested (and I seem to remember some of his comments on Blog-a-Bull hinting at this as well) that being a good passer is a heavy component of being a positive offensive player by adjusted plus minus. I would like to challenge that notion for a couple of reasons.
First, AST% is more of a measure of a player's role within an offense than his intrinsic passing ability. For instance, Tyrus Thomas had AST percentages of 6.6% and 11.0% in his first two years in the league, under Scott Skiles's offense. Then, in the isolation heavy Del Negro offense of last year, he managed a paltry 5.5% AST%. Does that mean that Tyrus was suddenly a worse passer? Hardly. The same phenomenon happened to John Salmons coming over from the Kings to the Bulls. Salmons went from having an AST% of 17.3% to dropping all the way to 8.8% in the same year all because the offense that he was working within called for more isos from him and less passing opportunities that would result in scores. It stands to reason, though, that a player that's being asked to shoulder a heavy load in the offense (by way of a high AST%) would probably be pretty offensively talented and very likely to have a positive OAPM. But, this effect is already captured by Usage or preferably, DeanO's Possessions Used.
Second, assists are a pretty subjective stat and they aren't correlated at all to winning via the Four Factors. Great offenses can be primarily isolation heavy or they can be focused on ball movement and finding the open man. There are all sorts of ways to achieve success, so I find it rather dubious that at the individual level that AST% is really as useful as the correlation might be indicating to us. Correlation, of course, does not always equal causation and I think this is a case of that. I believe the causation, as I mentioned above, is just that the same players that are offensively talented enough to post high OAPMs are also very often called upon to be distributors on their team.
For those two reasons, I would eliminate AST% from his EOPM a re-run the regression. Similarly, I would use FTM/FGA and eFG% instead of TS%, because it's relatively simple to use those two aspects of the Four Factors rather than the slightly simpler, but less accurate version of them, TS%. Finally, and perhaps most radically, I would use raw +/- as part of the regression to figure out the correlation between raw +/- and adjusted +/-, when OReb%, eFG%, FTM/FGA, TOV% and USG% are accounted for. Unfortunately, I am not educated enough in the ways of excel, R, or otherwise to run such a regression, but I figure that the raw data is all available, and it would be relatively easy for those of you who are so inclined to run this regression on the 6-year noise reduced 2008-09 apm figures that have been provided elsewhere in this forum.
On the other side of the ball, I would like to see a regression done with DReb%, BLK%, STL%, Personal Fouls per 100 possessions (maybe), and raw defensive +/- (from 82games). Those figures seem to be the best proxies for Four Factors on the defensive side on the individual level that we have, so I think coming up with an EDPM or Statistical +/- (whatever you want to call it) based on them would be useful.
I think running these two regressions would likely give us very good statistical estimates of offensive and defensive adjusted plus minus, which would be useful in reducing the noise of single year APM.
Anyone that is capable and willing to do this work, please do. I'd really like to see the results.
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Mike G
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PostPosted: Fri Oct 16, 2009 6:42 am Post subject: Re: Resurrecting this thread Reply with quote
fundamentallysound wrote:
... assists are a pretty subjective stat and they aren't correlated at all to winning ...
I would eliminate AST% from his EOPM a re-run the regression.
.
Neither Ast% nor Blk% correlate much with winning. Part of this is because the made FG and the opponent's missed FG are already 'counted', and the arbitrary grant of an additional stat doesn't change the scoreboard any further.
The other part of the reason is that there's great variability in how liberally these 'awarded' stats are accrued, between franchises. If one uses 'adjusted' Ast% and Blk% (scaled to home/away differences), there is probably a better correlation with winning, as well as greater consistency when a player's context is changed.
I'd hesitate to call these 'true Ast%' or TBlk%, because they're just estimates. TS% is also an estimate, is almost never 'true', but is fairly close.
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YaoPau
Joined: 28 Jan 2009
Posts: 28
PostPosted: Fri Oct 16, 2009 10:40 am Post subject: Reply with quote
FS, thanks for the interest in EOPM and bringing up some legitimate concerns. I'm glad to know somebody's still looking at that old site Smile
You questioned whether AST% should be component of statistical APM because it can vary wildly from year to year based on a player's role in an offense. But APM only rates how effective a player was in his role, that season. Tyrus Thomas's AST% dropping doesn't mean he's less skilled at passing now than in 2008, it means he didn't pass as much, and thus wasn't contributing as much to the Bulls via his passing. It's not his fault, that's just what happened in VDN's system, and all we can do is estimate Tyrus's effect within that system.
Passing, as the data suggests, has a HUGE correlation with offensive APM, and I don't think it makes sense to toss it out considering the importance of passing. It's backed up, I think, by this article from 82games which shows a strong correlation between touches per second and offensive rating (scroll down a quarter way).
Are assists subjective? Somewhat. But no stat is perfect. Rebounds are dependent on who's on the floor with you, USG% as well. The point is to get an estimation of what the player is doing, and it looks like assists do a decent job of accounting for passing.
As for your suggestion that: "the same players that are offensively talented enough to post high OAPMs are also very often called upon to be distributors on their team." In many cases, that's not true. Look at the offensive APMs for Kevin Martin, Kevin Durant, Amare Stoudemire compared to Brad Miller, Kevin Garnett, Pau Gasol. High USG% doesn't necessarily correlate with high AST% (our own Ben Gordon is a great example), but AST% reigns in its correlation with APM.
As for statisticals in general, I tried a defensive statistical using the categories you listed and got around a .4 correlation. Doesn't work. I'm mining some other data right now to try to improve on it.
But I have improved EOPM by a metric shitload. I ran 4 year APMs, accounted for garbage time, and left each year unweighed so I could use them directly in a regression. Then I regressed them against TS%, OREB%, DREB%, AST%, STL%, BLK%, TOV%, USG% and got a .699 correlation. Will post soon.
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fundamentallysound
Joined: 18 Jul 2008
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PostPosted: Fri Oct 16, 2009 12:10 pm Post subject: Reply with quote
YaoPau wrote:
As for statisticals in general, I tried a defensive statistical using the categories you listed and got around a .4 correlation. Doesn't work. I'm mining some other data right now to try to improve on it.
But I have improved EOPM by a metric shitload. I ran 4 year APMs, accounted for garbage time, and left each year unweighed so I could use them directly in a regression. Then I regressed them against TS%, OREB%, DREB%, AST%, STL%, BLK%, TOV%, USG% and got a .699 correlation. Will post soon.
So with DRb%, Blk%, Stl%, PF per 100 poss. AND raw +/- you still get just a .4 correlation? Wowza. I would have guessed that the inclusion of raw +/- would have greatly increased the correlation. Shows what I know.
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YaoPau
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PostPosted: Fri Oct 16, 2009 12:25 pm Post subject: Reply with quote
My fault, I didn't see the raw +/- part. I had run a regression a couple months back with DREB%, BLK%, STL%, PF/40 and position played and got .4.
I agree raw +/- could help, but I don't love the idea of using an input that's so dependent on teammates. Hinrich was +6.4 raw defensively last year. Stick him behind Iguodala instead of Gordon and he's probably negative.
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fundamentallysound
Joined: 18 Jul 2008
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PostPosted: Fri Oct 23, 2009 4:58 pm Post subject: Reply with quote
YaoPau wrote:
My fault, I didn't see the raw +/- part. I had run a regression a couple months back with DREB%, BLK%, STL%, PF/40 and position played and got .4.
I agree raw +/- could help, but I don't love the idea of using an input that's so dependent on teammates. Hinrich was +6.4 raw defensively last year. Stick him behind Iguodala instead of Gordon and he's probably negative.
What are the possible categories to include in a EDPM outside of those DReb, Blk, Stl, and Fouls? People always suggest age and wingspan, but the data for those is not always readily available, particularly wingspan.
Would you plug in the offensive categories to get at EDPM as well? It seems that you've used the defensive categories (DReb, Stls, Blks) in your new .699 correlation for the offensive side? Have you tried the inverse with the defensive side of the ball?