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Ilardi
Joined: 15 May 2008
Posts: 265
Location: Lawrence, KS
PostPosted: Sat Aug 08, 2009 5:14 pm Post subject: Adjusted Plus-Minus: Six-Season Averages Reply with quote
Hi All,
After a four-month hiatus to focus on book promotion and other writing commitments, I finally had a little time today to play around with adjusted plus-minus (APM) models.
My first little project: using the six-season full-lineup dataset I've compiled (from data provided by Aaron B. and Roland Beech) to run the offensive and defensive APM numbers based on a six-year average. In other words, each season from 2003-2004 to 2008-2009 was given completely equal weighting (while each year's playoffs were given double weighting to account for the heightened importance/significance of the league's "second season"). This multi-season approach has the advantage of reducing estimation errors, but the relative disadvantage of telling us only how each player has performed, on average, over a rather extended window of time. Still, on balance, I found the results interesting and informative.
Also, please note that I only modeled players who logged at least 400 minutes during the 08-09 season.
If interested, you can check out the results at: http://spreadsheets.google.com/ccc?key= ... nb0E&hl=en
Best wishes,
Steve
P.S. When time permits, I'd next like to look at time-trend data: i.e., changes in single-season APM for each player across the six-season window from 03-09.
Last edited by Ilardi on Sat Aug 08, 2009 5:54 pm; edited 1 time in total
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erivera7
Joined: 19 Jan 2009
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PostPosted: Sat Aug 08, 2009 5:22 pm Post subject: Reply with quote
This is valuable information. Thanks for taking the time to compile the data.
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DLew
Joined: 13 Nov 2006
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PostPosted: Sat Aug 08, 2009 5:23 pm Post subject: Reply with quote
It's worth noting that Garnett and Ginobili at and near to the top of the first list if they played enough minutes. I think it might be more useful to split the list by minutes over the whole sample. Also, I'm not sure why you only modeled players that played more than 400 minutes in 08-09. Because this is a list of best players on average over the six year period I think it would be nice to include all players who played enough minutes over that stretch even if they happen to be retired now. That said, thanks for posting this Steve, I always enjoy your stuff.
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Ilardi
Joined: 15 May 2008
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Location: Lawrence, KS
PostPosted: Sat Aug 08, 2009 5:30 pm Post subject: Reply with quote
DLew wrote:
It's worth noting that Garnett and Ginobili at and near to the top of the first list if they played enough minutes. I think it might be more useful to split the list by minutes over the whole sample. Also, I'm not sure why you only modeled players that played more than 400 minutes in 08-09. Because this is a list of best players on average over the six year period I think it would be nice to include all players who played enough minutes over that stretch even if they happen to be retired now. That said, thanks for posting this Steve, I always enjoy your stuff.
Thanks for the comments, Dave.
I agree that a split based on minutes-over-the-full-6-year-window would be more valuable, but I didn't have those aggregate 03-09 minutes handy (and time's still at a premium), so I figured I'd leave that task for another day. Better yet, maybe someone on APBRmetrics will take the time to re-do the split for us!!
As for including all players over the window (even if retired): today's little analysis was mostly a prelude to doing some year-by-year time-trend stuff to help predict player APM performance next year (and, to a lesser degree, to look at APM as a function of player age), so I was mostly just interested in guys who are still in the league. But it would certainly be of interest at some point to include all those retired players, as you suggest.
By the way, I assume you had something to do with the Cavs picking up Parker and Moon - two APM monsters - on the cheap this offseason? Most impressive! (When I was advising a certain team last season, I repeatedly pointed out Moon's off-the-chart APM performance and his likely post-season availability, but I guess I wasn't terribly persuasive.)
Last edited by Ilardi on Sat Aug 08, 2009 5:50 pm; edited 1 time in total
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Ilardi
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PostPosted: Sat Aug 08, 2009 5:49 pm Post subject: Reply with quote
erivera7 wrote:
This is valuable information. Thanks for taking the time to compile the data.
My pleasure.
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battaile
Joined: 27 Jul 2009
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PostPosted: Sat Aug 08, 2009 7:15 pm Post subject: Reply with quote
Thanks for posting the spreadsheet, this is great stuff. I'm surprised Dirk rated so well defensively.
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Ilardi
Joined: 15 May 2008
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Location: Lawrence, KS
PostPosted: Sat Aug 08, 2009 11:16 pm Post subject: Reply with quote
battaile wrote:
Thanks for posting the spreadsheet, this is great stuff. I'm surprised Dirk rated so well defensively.
Yeah, Dirk's somewhat above-average rating on D is a bit of a surprise, although I think he's helped there by his strong defensive rebounding.
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Crow
Joined: 20 Jan 2009
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PostPosted: Sun Aug 09, 2009 3:38 am Post subject: Reply with quote
Thanks.
So to mention a few highs and lows...
among guys over 2000 minutes
Mbah a Moute pulls the best estimate on defensive adjusted. Artest 3rd. 21 of top 24 at least 6'7 with Westbrook, Fisher and B Davis the only exceptions. Durant ranks 3rd weakest, Bargnani 8th, Andre Miller 15th.
Durant also gets 10th weakest on offensive adjusted. Rondo 4th lowest.
On overall adjusted Durant gets 2nd weakest, Bargnani 7th. Jason Thompson pulls 24th best and some other young guys weren't far behind showing it could be done.
Among those below 2000 minutes
Amir Johnson was the 6th best on defensive adjusted. A questionable project maybe, but a questionable giveaway too. Speights surprises me being that low with the 2nd worst defensive adjusted in the group. McGee I knew to expect in this range. Aaron Brooks 4th worst, Bayless 5th worst. Often criticized Bogut was 5th best.
On offensive adjusted Batum surprises with a 2nd best, Hibbert 3rd.
Overall, Gallinari, in very short minutes, 6th best. Brooks 17th worst, amongst this second tier.
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DSMok1
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PostPosted: Mon Aug 10, 2009 3:04 pm Post subject: Reply with quote
Perhaps the best way to look at this list is to look at the probability that each player is above average (on defense, offense, or overall). Remember, this is a 6-year average, not weighted. So this list tells us who was the best over the last 6 years.
That said, the probability that one player on the list is better than the next varies widely. The confidence that KG was the best defender (based on these stats) is actually very high (99.99%), and I show a 97% chance that Ben Wallace was second best... but the confidence that Ron Artest was 3rd best are only 42%.
To calculate the confidence that a player was above average, I used
Code:
normsdist(AdjPM/StdErr)
and to calculate the confidence that one was better than the next, I took the confidence that each player was above average and applied
Code:
(P1-P1*P2)/(P1+P2-2*P1*P2)
So here were the top 15 of each category:
Offensive Players:
Nash, Steve
Bryant, Kobe
James, LeBron
Wade, Dwayne
Jamison, Antawn
Garnett, Kevin
Pierce, Paul
Gasol, Pau
Allen, Ray
McGrady, Tracy
Ginobili, Manu
Paul, Chris
Billups, Chauncey
Davis, Baron
Redd, Michael
(There were about 40 players with confidence above 99% that they were above average offensively.)
Defensive Players:
Garnett, Kevin
Wallace, Ben
Artest, Ron
Collins, Jason
Hilario, Nene
Hayes, Chuck
Martin, Kenyon
Ming, Yao
Battier, Shane
Foster, Jeff
Duncan, Tim
Ratliff, Theo
Varejao, Anderson
Thomas, Kurt
Camby, Marcus
Overall
(The confidence that a player was above average, on average, over these six years. Twenty-five players listed.)
Garnett, Kevin
James, LeBron
Ginobili, Manu
Wade, Dwayne
Artest, Ron
Bryant, Kobe
Pierce, Paul
Davis, Baron
Duncan, Tim
Nash, Steve
O'Neal, Shaquille
Ming, Yao
Kirilenko, Andrei
Jamison, Antawn
Gasol, Pau
Foster, Jeff
Nowitzki, Dirk
Paul, Chris
Miller, Brad
McGrady, Tracy
Lewis, Rashard
Kidd, Jason
Battier, Shane
Wallace, Rasheed
Brand, Elton
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Crow
Joined: 20 Jan 2009
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PostPosted: Mon Aug 10, 2009 3:49 pm Post subject: Reply with quote
Hey DSMOK1. I see you've dived in quick and deep.
It is 6 year data but Foster might be the biggest surprise or least likely to be named by voice vote to the overall list- to many, but not all. Brad Miler is there too. Paid way more but probably somewhat overlooked / under-rated lately.
Care to compile % of above averages by position (or role, though that would be less universally accepted) or salary? Or plot the age distribution curve?
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DSMok1
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PostPosted: Mon Aug 10, 2009 4:29 pm Post subject: Reply with quote
Crow wrote:
Hey DSMOK1. I see you've dived in quick and deep.
It is 6 year data but Foster might be the biggest surprise or least likely to be named by voice vote to the overall list- to many, but not all. Brad Miler is there too. Paid way more but probably somewhat overlooked / under-rated lately.
Care to compile % of above averages by position (or role, though that would be less universally accepted) or salary? Or plot the age distribution curve?
Hello, Crow... I've been reading this forum off and on for years, but never posted. Now that the NBA is here in OKC, I'm finally getting around to it. (Besides, my statistical interest is not confined to basketball or even sports.)
I don't have any data besides what Ilardi posted actually on the spreadsheet... I don't think that an age-distribution curve on a set like this would be that informative. Salary could be interesting, but it will simply show the already-known biases I suspect.
I do note that the defensive players are dominated by post players... is that an artifact of the type of regression run (the stats available) to get the STAT part of the calculation? I suspect so. Once more data is put into that regression (it is broadened with more defensive data) I suspect there will be less pull to the post. I may be wrong, however...
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bchaikin
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PostPosted: Mon Aug 10, 2009 4:53 pm Post subject: Reply with quote
Brad Miler is there too. Paid way more but probably somewhat overlooked / under-rated lately.
this by chance the same brad miller that has been the starting C for sacramento the past 3 years (32 min/g and the 3rd most total minutes played on the team), 1 of the 5 worst teams defensively in the league since 06-07? the kings have ranked just 23rd (06-07), 25th (07-08 ), and 30th (dead last, 08-09) in least pts/poss allowed the last 3 seasons, and he was their key man in the middle during this time...
as for underrated lately miller was the starting C on a kings team that went just 9-34 when he played in 08-09, and they were by far the worst defensive team in the league (one of the very worst teams defensively over the last 30 years) in terms of points allowed per team defensive possession just prior to his being traded to the bulls...
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DLew
Joined: 13 Nov 2006
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PostPosted: Mon Aug 10, 2009 4:55 pm Post subject: Reply with quote
DSMok1,
I don't believe Steve used any box score statistics to generate these rankings, so the explanation for post players' superior defensive ratings must lie elsewhere...
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Crow
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PostPosted: Mon Aug 10, 2009 5:37 pm Post subject: Reply with quote
Alright thanks for the clarification of your path to here and now. I get the picture better now.
By salary (or at least future salary commitment) Bargnani is the only guy who will be making $10 million per season after tuning in worse than a -4 on 6 year unweighted adjusted. The closest comparison is Troy Murphy at -2.6 and a bit over $10 million. He may not be the last though. Depends if adjusted changes for Durant in year 3 or 4.
An age distribution would allow consideration of the career adjusted curve vs just peak individual stat performance. I assume the adjusted curve lags the stat performance curve early and might be elevated compared to just stats later and possibly strong longer. But I haven't seen it yet.
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DSMok1
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PostPosted: Mon Aug 10, 2009 5:43 pm Post subject: Reply with quote
DLew wrote:
DSMok1,
I don't believe Steve used any box score statistics to generate these rankings, so the explanation for post players' superior defensive ratings must lie elsewhere...
See: http://sonicscentral.com/apbrmetrics/vi ... php?t=2295
I think he is.
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Crow
Joined: 20 Jan 2009
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PostPosted: Mon Aug 10, 2009 5:47 pm Post subject: Reply with quote
Bob, right or wrong defensive adjusted has Miller as the 14th best defensive impact player on adjusted over the 6 year period for big minute guys and in strong contrast to some other main Kings. Hawes and Salmons in the bottom 20 for the group. Kevin Martin in the under 2000 minute group but 10th worst overall. Nocioni at almost -3 is a wash with Salmons.
Last edited by Crow on Mon Aug 10, 2009 6:26 pm; edited 1 time in total
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Ilardi
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PostPosted: Mon Aug 10, 2009 6:07 pm Post subject: Reply with quote
DSMok1 wrote:
DLew wrote:
DSMok1,
I don't believe Steve used any box score statistics to generate these rankings, so the explanation for post players' superior defensive ratings must lie elsewhere...
See: http://sonicscentral.com/apbrmetrics/vi ... php?t=2295
I think he is.
DSMok1,
Actually, DLew is correct: the ratings I posted are based only on raw lineup data (i.e., they're "pure" adjusted plus-minus). I inquired about statistical plus-minus on a separate thread because I'm interested in looking at how it might be used to bring the s.e. terms down even further, but I've never done any modeling with statistical plus-minus to date . . .
Sorry for the confusion!
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battaile
Joined: 27 Jul 2009
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PostPosted: Mon Aug 10, 2009 6:59 pm Post subject: Reply with quote
edit: never mind, realized my comment makes no sense given how these ratings were calculated
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DSMok1
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PostPosted: Mon Aug 10, 2009 8:20 pm Post subject: Reply with quote
Ilardi wrote:
DSMok1,
Actually, DLew is correct: the ratings I posted are based only on raw lineup data (i.e., they're "pure" adjusted plus-minus). I inquired about statistical plus-minus on a separate thread because I'm interested in looking at how it might be used to bring the s.e. terms down even further, but I've never done any modeling with statistical plus-minus to date . . .
Sorry for the confusion!
Ah! My error.
Perhaps, then, there really is that big a difference between the best bigs and the secondary tier of them--perhaps the fact that there is a more limited pool of good bigs yields this effect. Interesting indeed!
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Crow
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PostPosted: Mon Aug 10, 2009 9:41 pm Post subject: Reply with quote
I merged a demographic file with Steve's dataset and for 335 players found the following
(using a crude age determination since I lost the month and didn't want to recreate):
removed
to be replaced below
Last edited by Crow on Tue Aug 11, 2009 2:51 am; edited 4 times in total
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Ilardi
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PostPosted: Mon Aug 10, 2009 10:01 pm Post subject: Reply with quote
That's really interesting stuff, Crow. It's surprising to see APM peak in the 33-35 age window, since I recall an analysis by Ed Kupfer a while back that showed peak productivity on most boxscore metrics somewhere around age 27.
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Crow
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PostPosted: Mon Aug 10, 2009 10:09 pm Post subject: Reply with quote
I wanted to see what it would show.
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DLew
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PostPosted: Mon Aug 10, 2009 10:43 pm Post subject: Reply with quote
It's worth noting that because of selection bias it is possible that the peak age for any given player is 27, while the age with the highest average APM is 35.
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Crow
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PostPosted: Mon Aug 10, 2009 11:34 pm Post subject: Reply with quote
I was going to mention selection bias explicitly but instead I shifted a bit and just hinted at it by using the word "remaining".
A quick check of most contenders last season showed at least 2 30-something starters.
Except for slight misses by 2 of the championship versions of the Pistons that has been the case also for 20+ years of title winners.
Which contenders for the next title lack this?
Cavs is close if Moon starts but might miss officially unless Parker starts. Or they go big in the playoffs.
Joe Johnson is getting close to being the 2nd but isn't yet. Utah doesn't fit the pattern either but they have several close. Miami is close but doesn't have 2 fully 30 either. Miller would do it for Portland (assuming Joel P still starts) but Blake is close anyways.
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Kevin Pelton
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PostPosted: Tue Aug 11, 2009 12:57 am Post subject: Reply with quote
Correct me if I'm misunderstanding, but wouldn't the bigger factor here simply be that if we're looking at the entire six-year sample we're including many prime years of the 30-plus players and many development years of the players currently in their prime?
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BobboFitos
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PostPosted: Tue Aug 11, 2009 1:00 am Post subject: Reply with quote
Kevin Pelton wrote:
Correct me if I'm misunderstanding, but wouldn't the bigger factor here simply be that if we're looking at the entire six-year sample we're including many prime years of the 30-plus players and many development years of the players currently in their prime?
this was my thought as well
it would be more helpful to compare player x with his respective 23 yr season to 24 yr season and so on
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Crow
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PostPosted: Tue Aug 11, 2009 1:19 am Post subject: Reply with quote
Very good point.
I slept on that factor.
It would be better to use another flavor of adjusted. 2 year or the 6 year that is largely the most recent year.
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Kevin Pelton
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PostPosted: Tue Aug 11, 2009 1:33 am Post subject: Reply with quote
I do suspect, given some of DanR's early findings, that adjusted plus-minus will show a slightly older peak age than boxscore stats.
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Crow
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PostPosted: Tue Aug 11, 2009 2:15 am Post subject: Reply with quote
Using the 6 year adjusted that is mostly this past season
Age Off Def Total+/-
<23 -1.37 -0.68 -2.05
24-26 0.18 0.20 0.38
27-29 -0.01 -0.11 -0.11
30-32 0.56 -0.09 0.47
33-35 0.42 0.29 0.71
>36 0.49 0.56 1.04
Things are flatter, except for the 23 & under, with the mid and late 20 somethings doing better than the first dataset. But the remaining 30 somethings are better on offense on average and those are still around 33 & beyond are better on defense on average too.
The 6 year adjusted data input is largely the past season but the earlier seasons have some (distorting? from an age perspective) effect.
This may not be the ideal approach but it is what I could easily assemble.
Sorry for the problem with the earlier results.
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schtevie
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PostPosted: Tue Aug 11, 2009 9:45 am Post subject: Reply with quote
Perhaps, the most striking fact leaping from these APM tables has not been remarked upon because the 6 year average essentially repackages what are familiar facts from previous APM estimates spanning shorter durations. But I think it is worth pausing to appreciating the basketball greatness that is Kevin Garnett.
Taking LeBron James off the list - a phenomenon in his own right, but one of a different generation - KG has been 75% better than the next best player who can be described as his contemporary. And that is Tim Duncan. Tim Duncan! 75%!
A moment of silence, please.
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Ilardi
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PostPosted: Tue Aug 11, 2009 1:44 pm Post subject: Reply with quote
schtevie wrote:
Perhaps, the most striking fact leaping from these APM tables has not been remarked upon because the 6 year average essentially repackages what are familiar facts from previous APM estimates spanning shorter durations. But I think it is worth pausing to appreciating the basketball greatness that is Kevin Garnett.
Taking LeBron James off the list - a phenomenon in his own right, but one of a different generation - KG has been 75% better than the next best player who can be described as his contemporary. And that is Tim Duncan. Tim Duncan! 75%!
A moment of silence, please.
Seriously. Even knowing how dominant KG has been on the APM front for the past several seasons, I was stunned to see a gap of that magnitude.
And last year, despite 14 seasons on his odometer, he still wound up as the highest-rated defensive player in the league!
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erivera7
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PostPosted: Tue Aug 11, 2009 4:03 pm Post subject: Reply with quote
The fact Kevin Garnett has only garnered one Most Valuable Player award in his playing career is laughable.
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Mike G
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PostPosted: Tue Aug 11, 2009 6:02 pm Post subject: Reply with quote
Shaq, Olajuwon, and Robinson only got one.
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DSMok1
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PostPosted: Mon Sep 14, 2009 8:38 am Post subject: Reply with quote
Ilardi:
You said at the beginning of this thread that you compiled the APM data for 6 years, with help from Beech and Aaron B. Is that data available to the public? I've had a bit of trouble finding each year's data, complete with the standard error term (which is critical). Can you provide the data, or link to the sources where you got it?
Thanks!
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Ilardi
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PostPosted: Mon Sep 14, 2009 12:02 pm Post subject: Reply with quote
DSMok1 wrote:
Ilardi:
You said at the beginning of this thread that you compiled the APM data for 6 years, with help from Beech and Aaron B. Is that data available to the public? I've had a bit of trouble finding each year's data, complete with the standard error term (which is critical). Can you provide the data, or link to the sources where you got it?
Thanks!
I'm afraid I'm not able to provide the dataset (per the conditions under which parts of it were provided to me), but Aaron has made at least 3 years' worth of his raw lineup data available on his website: basketballvalue.com. So, that gets you at least half of the way there.
And, of course, no one can provide you with the standard error terms in any such dataset: that's something you have to estimate within the APM model itself.
P.S. Most people on the forum refer to me as Steve, although I suppose I'll answer to just about anything.
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DSMok1
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PostPosted: Mon Sep 14, 2009 12:43 pm Post subject: Reply with quote
Ilardi wrote:
I'm afraid I'm not able to provide the dataset (per the conditions under which parts of it were provided to me), but Aaron has made at least 3 years' worth of his raw lineup data available on his website: basketballvalue.com. So, that gets you at least half of the way there.
And, of course, no one can provide you with the standard error terms in any such dataset: that's something you have to estimate within the APM model itself.
P.S. Most people on the forum refer to me as Steve, although I suppose I'll answer to just about anything.
Thanks, Steve (I usually use each person's handle)!
I don't really need the original dataset--what I am looking for is the already-computed 1-year adjusted +/- ratings for as many years as possible. I am working on the projection system detailed elsewhere and I don't really want to use inter-correlated data (stabilized or 2-year values)--just 1-year versions, full of error though they may be. I know BasketballValue published the 1-year numbers for the last two seasons--are 1-year numbers available elsewhere?
You said you were working on your "stabilized" numbers for prior years--those also may work well in the model I'm working on, since they are so heavily weighted toward the current year. How is that coming? The school year started, so I suppose you're rather busy!
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Ilardi
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PostPosted: Mon Sep 14, 2009 9:34 pm Post subject: Reply with quote
Ah, right. I'm actually hoping to publish those numbers in article form some time in the next month or so . . . still have to run a few of the seasons and compile everything in a single spreadsheet. I'll keep you posted, though.
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Italian Stallion
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PostPosted: Wed Sep 16, 2009 7:06 pm Post subject: Reply with quote
First off, even though a 6 year study doesn't take yearly changes in form due to age/experience into account and also doesn't consider injury etc.... I think it does give a great look a most players that can them be subjectively altered to account for those things.
Thanks so much for posting this info.
I have one question.
Has anyone tried to take this information and then back into a system that would weight the various individual stats like scoring, rebounds, blocks, steals TS% etc.... and produce these +/- stats?
There are lots of debates about the proper weighting of various factors and this might be a great way of taking another look at it.
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DJE09
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PostPosted: Wed Sep 16, 2009 7:12 pm Post subject: Reply with quote
Do you mean a Statistical +/-?
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Crow
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PostPosted: Thu Sep 17, 2009 2:19 am Post subject: Reply with quote
Neil Paine has picked up the torch for keeping statistical +/- data available and improving it.
Check for posts here or at the blog at basketball-reference.com
I've occasionally made the pitch for keeping Dan Rosenbaum's overall +/- (combining adjusted and statistical) alive in some form. With Steve Ilardi's advancement in reducing noise I think adjusted could grow to being a relatively equal partner with statistical instead of the 15-20% weight tail that Dan made it in the original overall +/- immediately after producing pure adjusted. Or you can let it do the whole job if you want and are confident enough in it.
Off and on I've also pitched the related idea of giving the main actor or main 2 actors on a a play a good share of the credit or blame for offense and for defense (half to 2/3rds) directly using standard linear weights or statistical +/- regression derived weights and then dividing the rest of the credit equally among the non=main actors of the play to try to stay faithful to who actually had the most opportunity and responsibility for impact. But you could also perhaps restrict the direct credit operation to say half the value (or whatever share you want to give this direct credit operation) based on the last and generally "most important" action in the specific play and let adjusted "find" the split for the rest as it will from among everyone instead of letting it divide the full amount based on the season level data. But there doesn't seem to be much other interest in this general pursuit or this specific integrated approach.