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APBRmetrics
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Ilardi
Joined: 15 May 2008
Posts: 265
Location: Lawrence, KS
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 Posted: Sun Aug 09, 2009 6:30 pm Post subject: 2008-2009 Adjusted Plus-Minus Ratings (Low-Noise Version) |
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I've now had a chance to generate 2008-2009 APM ratings, using a full six-year (03-09) lineup dataset to greatly reduce estimation error.
Specifically, I've given each prior season a fractional weighting of the form:
weight = 1/(2^(YearsAgo +1)
This generates the following season-by-season weighting scheme:
2008-2009 = 1
2007-2008 = 1/4
2006-2007 = 1/8
2005-2006 = 1/16
2004-2005 = 1/32
2003-2004 = 1/64
Note that the resulting model still accords nearly 70% of the overall weight to the 2008-2009 season, with much of the rest of the weight coming from the preceding season (and all weightings tapering off exponentially as a function of time).
Obviously, the ideal is an APM model based 100% on the target 08-09 season, but (as we've seen in the past - and as posted at bv.com), such a model yields estimation errors so high as to render the estimates of only limited value. By including prior seasons' data in the model (at reduced weight), we're able to dramatically reduce estimation error, and still allow the results to primarily reflect the target season.
If interested, you can find the latest APM estimates posted at: http://spreadsheets.google.com/ccc?key=0AnGzTFTtSPx_dFVrZXdHNlNZQUJadllKUm1Ld294WkE&hl=en
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Ryan J. Parker
Joined: 23 Mar 2007
Posts: 711
Location: Raleigh, NC
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| Posted: Sun Aug 09, 2009 6:38 pm Post subject: |
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Here's a top 20 list:
| Code: | Wade, Dwayne 13.61
Garnett, Kevin 13.21
James, LeBron 13.19
Paul, Chris 12.71
Nash, Steve 8.83
Odom, Lamar 8.81
Iguodala, Andre 8.61
Lewis, Rashard 8.11
Ming, Yao 7.29
Kidd, Jason 6.66
Gasol, Pau 6.64
Nowitzki, Dirk 6.5
Young, Thaddeus 6.37
Bosh, Chris 6.19
Johnson, Amir 6.18
Artest, Ron 5.83
Parker, Tony 5.77
Bryant, Kobe 5.63
Jamison, Antawn 5.58
Duncan, Tim 5.4
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Ilardi
Joined: 15 May 2008
Posts: 265
Location: Lawrence, KS
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| Posted: Sun Aug 09, 2009 6:42 pm Post subject: |
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| Ryan J. Parker wrote: | Here's a top 20 list:
| Code: | Wade, Dwayne 13.61
Garnett, Kevin 13.21
James, LeBron 13.19
Paul, Chris 12.71
Nash, Steve 8.83
Odom, Lamar 8.81
Iguodala, Andre 8.61
Lewis, Rashard 8.11
Ming, Yao 7.29
Kidd, Jason 6.66
Gasol, Pau 6.64
Nowitzki, Dirk 6.5
Young, Thaddeus 6.37
Bosh, Chris 6.19
Johnson, Amir 6.18
Artest, Ron 5.83
Parker, Tony 5.77
Bryant, Kobe 5.63
Jamison, Antawn 5.58
Duncan, Tim 5.4
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Face validity? |
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Ryan J. Parker
Joined: 23 Mar 2007
Posts: 711
Location: Raleigh, NC
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| Posted: Sun Aug 09, 2009 6:48 pm Post subject: |
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Steve, you mentioned making predictions before, and I wanted to know what you think is the most important to predict. In the coming year, what would you want to predict? Individual player APM ratings, actual lineup efficiency, etc?
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Ilardi
Joined: 15 May 2008
Posts: 265
Location: Lawrence, KS
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| Posted: Sun Aug 09, 2009 9:20 pm Post subject: |
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| Ryan J. Parker wrote: | | Steve, you mentioned making predictions before, and I wanted to know what you think is the most important to predict. In the coming year, what would you want to predict? Individual player APM ratings, actual lineup efficiency, etc? |
I guess I'm mostly interested in predicting:
(a) individual APM as a function of player history and age
(b) team W-L records/efficiency (especially for teams with major personnel change from preceding season) |
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Ryan J. Parker
Joined: 23 Mar 2007
Posts: 711
Location: Raleigh, NC
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| Posted: Sun Aug 09, 2009 10:23 pm Post subject: |
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Cool. I'm interested in predicting team offensive and defensive efficiency, so I want to set a baseline for how a very basic model, like adjusted plus/minus or similar variant, predicts these team measures. Then the fun is figuring out how to improve on those predictions, and figuring out what models do and do not predict well.
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DSMok1
Joined: 05 Aug 2009
Posts: 611
Location: Where the wind comes sweeping down the plains
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| Posted: Mon Aug 10, 2009 8:40 am Post subject: |
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I just looked over the numbers... what I can see is that out of 341 players, there are 75 players that we can say with 95% confidence are above league average. (That is 2 StdDev, or the player's mean - 2*stderr still being above 0.) Is that interpretation correct? And there are 107 that we can say with 95% confidence are below league average (or 0 +/-). There are 9 players that are 95% likely above 5.0 APM, and 3 above 10 APM (Wade, Garnett, James).
And there are 158 players that we cannot say are below or above average with 95% certainty. |
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Ryan J. Parker
Joined: 23 Mar 2007
Posts: 711
Location: Raleigh, NC
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| Posted: Mon Aug 10, 2009 9:12 am Post subject: |
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I think the only change I would make is:
| DSMok1 wrote: | | And there are 158 players that we cannot say are below or above average with 95% confidence. |
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Ilardi
Joined: 15 May 2008
Posts: 265
Location: Lawrence, KS
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| Posted: Mon Aug 10, 2009 9:23 am Post subject: |
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| DSMok1 wrote: | I just looked over the numbers... what I can see is that out of 341 players, there are 75 players that we can say with 95% confidence are above league average. (That is 2 StdDev, or the player's mean - 2*stderr still being above 0.) Is that interpretation correct? And there are 107 that we can say with 95% confidence are below league average (or 0 +/-). There are 9 players that are 95% likely above 5.0 APM, and 3 above 10 APM (Wade, Garnett, James).
And there are 158 players that we cannot say are below or above average with 95% certainty. |
Yes, that interpretive stance is basically correct, although probably a bit too conservative, as it's based on a "two-tailed" test (which yields a 95% interval of +/- 1.96 se) for all coefficient estimates: it's permissible instead to use one-tailed tests (95% at 1.65 se) when we're only interested in testing directional hypotheses (e.g., "I've observed a player's estimate at +1.70 with an se of 1.0, and want to know if he's truly above-average"), as opposed to constructing a two-tailed confidence interval each time.
It actually gets a little more complicated than that, though, because the se's I've provided apply only to the offensive and defensive APM components. To make a long story short, there are two different ways we can come up with the full set of Offensive, Defensive, and Total APM estimates, either: (a) directly estimate Total APM together with an offense-defense adjustment/offset parameter (OffDiff), and then derive Offensive and Defensive APMs based on linear combinations of the aforementioned (Rosenbaum's approach); or (b) directly estimate Offensive and Defensive APM, and then add them together to derive Total APM estimates (my approach*).
In Dan Rosenbaum's approach, you wind up with larger se's for the Offensive and Defensive APM components (since they're not directly estimated in the model, but derived indirectly from other estimates - a process that involves adding se terms), whereas with my approach you wind up with lower se's for Offensive and Defensive APM but a higher se for the Total APM estimate (for the same reason). My approach/model does, however, have the advantage of adjusting each offensive lineup to account for the defensive efficiency of each opposing lineup, and vice versa, which is the main reason I prefer it.
Now, how much higher is the se for the Total APM in my model? It's equal to roughly 1.41 (square root of 2) times the se for the offensive/defensive APM estimates. (And, yes, for technical reasons, the se for each player's offensive APM is always nearly identical to the se for his defensive APM).
If enough people are interested, I could always go back and do a direct estimate for Total APM in order to bring down those se's . . . though the resulting APM estimates would, of course, be very close to those already provided.
*developed in collaboration with Aaron Barzilai (who also came up with the same basic idea at roughly the same time).
Last edited by Ilardi on Mon Aug 10, 2009 9:30 am; edited 1 time in total |
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Ryan J. Parker
Joined: 23 Mar 2007
Posts: 711
Location: Raleigh, NC
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| Posted: Mon Aug 10, 2009 9:30 am Post subject: |
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Good catch Steve. One tailed tests FTW.
This part confused me though:
| Quote: | | Now, how much higher is the se for the Total APM in my model? It's equal to roughly 1.41 (square root of 2) times the se for the offensive/defensive APM estimates. (And, yes, the se for each player's offensive APM is always identical to the se for his defensive APM). |
Why is the SE for each player's offensive APM always identical to the SE for his defensive APM?
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Ilardi
Joined: 15 May 2008
Posts: 265
Location: Lawrence, KS
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| Posted: Mon Aug 10, 2009 9:36 am Post subject: |
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| Ryan J. Parker wrote: | Good catch Steve. One tailed tests FTW.
This part confused me though:
| Quote: | | Now, how much higher is the se for the Total APM in my model? It's equal to roughly 1.41 (square root of 2) times the se for the offensive/defensive APM estimates. (And, yes, the se for each player's offensive APM is always identical to the se for his defensive APM). |
Why is the SE for each player's offensive APM always identical to the SE for his defensive APM? |
Yeah, that puzzled me at first, too. It seems to be based on the fact that se's in APM modeling are driven by the intercorrelatedness of player oncourt minutes - a phenomenon which will be virtually identical for any given set of players whether on offense or defense. (For example, if Duncan shares 71% of his oncourt offensive minutes with Parker, he will also share almost exactly 71% of his oncourt defensive minutes with him, as well.) |
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DSMok1
Joined: 05 Aug 2009
Posts: 611
Location: Where the wind comes sweeping down the plains
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| Posted: Mon Aug 10, 2009 9:58 am Post subject: |
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| Quote: | | If enough people are interested, I could always go back and do a direct estimate for Total APM in order to bring down those se's . . . though the resulting APM estimates would, of course, be very close to those already provided. |
That could be interesting--how hard would it be to have both shown next to each other...your current and then this elaboration?
Thank you very much for your discussion of two-tailed vs. one-tailed confidence intervals... For some reason I missed that, though it should have been obvious!
EDIT:
So now there are, at 95% confidence, 60 above-average offensive players, 79 above-average defensive players, and (because of the 1.41*stderr) 65 above-average overall players. |
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Ilardi
Joined: 15 May 2008
Posts: 265
Location: Lawrence, KS
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| Posted: Mon Aug 10, 2009 1:29 pm Post subject: |
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| Quote: | EDIT:
So now there are, at 95% confidence, 60 above-average offensive players, 79 above-average defensive players, and (because of the 1.41*stderr) 65 above-average overall players. |
That certainly sounds plausible . . . Also, if you go back and look at the 6-year average ratings I posted yesterday, you'll find even lower se terms, leading to an even larger number of players about whom you can derive inferences regarding above-average and below average performance at a 95% confidence level. |
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DSMok1
Joined: 05 Aug 2009
Posts: 611
Location: Where the wind comes sweeping down the plains
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| Posted: Mon Aug 10, 2009 1:50 pm Post subject: |
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| Ilardi wrote: | | Quote: |
So now there are, at 95% confidence, 60 above-average offensive players, 79 above-average defensive players, and (because of the 1.41*stderr) 65 above-average overall players. |
That certainly sounds plausible . . . Also, if you go back and look at the 6-year average ratings I posted yesterday, you'll find even lower se terms, leading to an even larger number of players about whom you can derive inferences regarding above-average and below average performance at a 95% confidence level. |
Oddly enough, no, that is not the case. Perhaps due to regression to the mean over that period (fewer players being good over the WHOLE six years) the number above average (95% confidence) in each of the 3 categories is between 57 and 59. |
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Ilardi
Joined: 15 May 2008
Posts: 265
Location: Lawrence, KS
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| Posted: Mon Aug 10, 2009 1:52 pm Post subject: |
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| Fascinating. Thanks for the clarification! |
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