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DJE09
Joined: 05 May 2009
Posts: 148
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 Posted: Tue Aug 11, 2009 11:45 pm Post subject: |
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from the Spreadsheet: | Quote: | | Playoffs for each season are accorded double the regular-season weighting |
I am not sure I like this misxing when you are scoring relative to zero. All 16 teams in the playoffs are average or above. But the teams that loose in the playoffs will be accorded a net negative weighting in terms of +-?
How about the teams / players that don't make the playoffs - you score them nothing i.e. Zero for their playoff contribution, i.e. they are better than the players playing...but then their team didn't make the playoffs.
Now I understand you are controlling for the line-up people play in and face, but I don't understand why you can compare people who didn't play in the playoffs against players who had to go 7 games against the Lakers eg. Houston
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Mike G
Joined: 14 Jan 2005
Posts: 3617
Location: Hendersonville, NC
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| Posted: Wed Aug 12, 2009 4:57 am Post subject: |
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| DJE09 wrote: |
Now I understand you are controlling for the line-up people play in and face, but I don't understand why you can compare people who didn't play in the playoffs against players who had to go 7 games against the Lakers eg. |
Unless you fail to 'cover the spread' vs your opposition, you can still have a net positive, I would think. If the Lakers have beaten average opposition by 7 Pts/48, and you lose by 4, you shouldn't net a negative.
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Ilardi
Joined: 15 May 2008
Posts: 265
Location: Lawrence, KS
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| Posted: Wed Aug 12, 2009 8:27 am Post subject: |
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| DJE09 wrote: | from the Spreadsheet: | Quote: | | Playoffs for each season are accorded double the regular-season weighting |
I am not sure I like this misxing when you are scoring relative to zero. All 16 teams in the playoffs are average or above. But the teams that loose in the playoffs will be accorded a net negative weighting in terms of +-?
How about the teams / players that don't make the playoffs - you score them nothing i.e. Zero for their playoff contribution, i.e. they are better than the players playing...but then their team didn't make the playoffs.
Now I understand you are controlling for the line-up people play in and face, but I don't understand why you can compare people who didn't play in the playoffs against players who had to go 7 games against the Lakers eg. Houston |
I believe your concerns are based on a misunderstanding (or partial understanding) of the APM model:
1) Because the model explicitly controls for the strength of each player's teammates and opponents during each possession, there is no risk of unfairly penalizing playoff losers for having been outperformed by stronger teams. In fact, it is quite possible for a player's APM rating to increase when playing on a losing team.
2) Those who play for teams that miss the playoffs are not penalized in the APM model - at least not in the sense of lowering their APM ratings. The only detriment for them is the mere fact of having fewer observations (data points) available to derive their APM estimates, with the result that the standard errors for their respective ratings will be slightly higher.
The basic premise of APM modeling is to use all data at our disposal to derive estimates of each player's impact on the game's bottom line; thus, we certainly want to incorporate the valuable information inherent in playoff performance. |
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DJE09
Joined: 05 May 2009
Posts: 148
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| Posted: Wed Aug 12, 2009 7:19 pm Post subject: |
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| Ilardi wrote: | 1) ... In fact, it is quite possible for a player's APM rating to increase when playing on a losing team.
2) Those who play for teams that miss the playoffs are not penalized in the APM model - at least not in the sense of lowering their APM ratings. The only detriment for them is the mere fact of having fewer observations (data points) available to derive their APM estimates, with the result that the standard errors for their respective ratings will be slightly higher.
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I am certain I don't properly understand how APM is obtained, but I was working from the assumption that
| Quote: | | Adjusted +/- ratings indicate how many additional points are contributed to a team's scoring margin by a given player in comparison to the league-average player over the span of a typical game (100 offensive and defensive possessions). |
I appreciate that an individual players APM can increase, but I can't see how, for all players on a TEAM their APM can increase when they loose a 7 game series.
OK, I am making this assumption:
The Minute Weighted Sum of a Team's Members APM is an approximation of their expected margin of victory over a "League-average" team.
So for teams like Orlando and Cleveland we should expect generally for their players to have positive APM (I know some can be negative, it just means others are more positive).
I can't see how adding in a series of games against tough opposition, where your team's margin of vistory is less (even negative) is not penalising their APM score relative to the teams who don't play those games (and so get the proxy zero return).
Example time, from http://basketballvalue.com we have for Orlando in 1 year APM (P=Playoff, RS=Regular Season):
| Code: |
Player Min P+/- SE RS+/- SE Delta
Lewis 986 9.7 4.2 10.2 4.8 -0.5
Turkoglu 934 3.5 3.9 3.2 4.5 0.3
Howard 903 -0.3 5.6 1.0 6.1 -1.3
Alston 740 -8.3 4.2 -4.3 4.7 -4.1
Pietrus 618 -1.2 4.0 -4.7 4.9 3.5
C. Lee 550 -1.3 3.9 -1.2 4.6 -0.2
Redick 327 -3.3 4.3 -1.3 5.0 -2.0
Johnson 280 -9.3 5.0 -3.1 5.8 -6.2
Gortat 271 -1.0 6.0 -8.1 6.7 7.1
Battie 128 -2.8 4.5 0.7 4.9 -3.5
Nelson 90 -1.0 5.7 6.7 6.3 -7.6
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As I understand this, the Playoff value is calculated from the same regular season data, plus doubly weighted playoff data. So based on their regular season data, Orlando as a team were +8, but when you include 2* the Playoff data they are about 4 points Worse as a team? for the team that managed to make the NBA finals?
I am sure I am not understanding something, but can't help but feel that it is due to the fact that they had 18 games against the three top teams (I readily conceed that they didn't spank Philly in first round when they should've, and Boston was playing without Garnett).
Please help me understand. |
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Ilardi
Joined: 15 May 2008
Posts: 265
Location: Lawrence, KS
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| Posted: Thu Aug 13, 2009 10:01 am Post subject: |
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DJE,
Perhaps an apt analogy will help make things clearer . . .
Think about how team "power ratings" (e.g., Sagarin) are generated: in essence, such ratings derive an estimate of each team's "strength" based on its performance (scoring margin) vis-a-vis each opponent - adjusting statistically for the strength of each opponent.
Thus, if Team A has a power rating of 90 and Team B has a rating of 100 (i.e., Team B would be expected to beat Team A by 10 pts on a neutral court), and Team A then loses to Team B by only 2 points, this better-than-expected performance by Team A will actually increase the team's overall rating, despite the fact that Team A lost.
Similar considerations apply to APM estimates . . . |
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DJE09
Joined: 05 May 2009
Posts: 148
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| Posted: Thu Aug 13, 2009 7:23 pm Post subject: |
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I get how you can lose and improve your rating, what I don't get is how strength is generated.
I thought you were using a weighted regression model over all instances of a player appearing in a 10-man unit. Once the model has run, the B_x represents Player X's contribution to the team's winning margin. Perhaps that is a big over simplification at I am missing something important.
I guess what I am thinking is that when we incorporate playoff data, and we re-run the model, we seem to get different values for the player's APM for the players who played in the playoffs, but not for the other players in the league who didn't?
So we seem to have re-evaluated the relative strength of Orlando based on their playoff perfomance, and we have excellent opportunity to evaluate them against top opposition (9-9 against top-3). Given the 'net' winning margin of ORL was less, I would expect the 'best estimate' to decrease, BUT we haven't had the same opportunity to further evaluate a team like, say the Nets, so their 'best estimate' stays the same ie. 0 contribution from playoffs, or a net gain over teams that exhibit a higher loosing margin than expected in the playoffs.
Concrete question: Does Kevin Garnett's APM change when we include Boston's playoff data? |
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Ilardi
Joined: 15 May 2008
Posts: 265
Location: Lawrence, KS
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| Posted: Thu Aug 13, 2009 9:10 pm Post subject: |
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| DJE09 wrote: | I get how you can lose and improve your rating, what I don't get is how strength is generated.
I thought you were using a weighted regression model over all instances of a player appearing in a 10-man unit. Once the model has run, the B_x represents Player X's contribution to the team's winning margin. Perhaps that is a big over simplification at I am missing something important.
I guess what I am thinking is that when we incorporate playoff data, and we re-run the model, we seem to get different values for the player's APM for the players who played in the playoffs, but not for the other players in the league who didn't?
So we seem to have re-evaluated the relative strength of Orlando based on their playoff perfomance, and we have excellent opportunity to evaluate them against top opposition (9-9 against top-3). Given the 'net' winning margin of ORL was less, I would expect the 'best estimate' to decrease, BUT we haven't had the same opportunity to further evaluate a team like, say the Nets, so their 'best estimate' stays the same ie. 0 contribution from playoffs, or a net gain over teams that exhibit a higher loosing margin than expected in the playoffs.
Concrete question: Does Kevin Garnett's APM change when we include Boston's playoff data? |
Every player's APM values will change somewhat by virtue of incorporating playoff data into the model (whether or not any given player actually appeared in the playoffs), inasmuch as the playoffs simply represent additional data points (lineups) that help the model reduce noise (i.e., lowering estimation error) by further disentangling the effects of heavily intercorrelated players - a process that affects every parameter in the model.
Does that help? |
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DJE09
Joined: 05 May 2009
Posts: 148
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| Posted: Thu Aug 13, 2009 10:24 pm Post subject: |
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Don't teams go to more concentrated lineups in the playoffs, so the player intercorrelations are more strongtly represented?
I think I understand what you are saying is the APM calculations are done for the whole season, and playoff games, OK.
Now I look at the Boston page I can see a recalculated APM post playoffs, where KG's APM changes (increases by 2!) based on 0 playoff minutes - but I can't just go and see the GSW APM post-playoffs (presumably since they weren't in playoffs) ... I guess this is what has made me assume the the recalculation was only done for playoff teams.
So I need to interpret the changes as a "re-evaluation" of the previously noisy figure in light of new evidence. For some of the players, eg. Ray Allen, Peja (negative), Chuck Hayes and Carl Landry (positive) the magnitude of the change (Poff - RS) is greater than the standard error.
What should I understand that to show (I want to say something about role in team, but I'm not sure I understand it properly yet).
Given Playoffs are such a small sample compared to the regular season, about 80 games, I am suprised at how much it reduces the SE. |
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Crow
Joined: 20 Jan 2009
Posts: 825
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| Posted: Mon Sep 14, 2009 11:56 pm Post subject: Re: 2008-2009 Adjusted Plus-Minus Ratings (Low-Noise Version |
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| Ilardi wrote: |
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).
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Choices have to made and I am not sure any is the perfect one but this weighting translates to
2008-9 67.4%
2007-8 16.8%
2006-7 8.4%
2005-6 4.2%
2004-5 2.1%
2003-4 1.1%
I like it pretty well but in another thread I suggested perhaps at least considering a blend of 2/3rds 1 year stabilized and 1/3 6 year average.
That would translate to
2008-9 50.5%
2007-8 16.8%
2006-7 11.2%
2005-6 8.4%
2004-5 7.0%
2003-4 6.3%
Which is "better" or preferable?
Probably a matter of taste.
The blend isn't that different but it does put year 4, 5 and 6 on closer to the same footing and much closer to year 3. That makes some sense to me.
I'll check it the actual blended results later
but if you have any feedback I'd be interested in hearing it Steve.
Even halfway between my proposed blend and your original weight set might be worth considering if you feel mine goes too far away from year 1.
2008-9 58.9%
2007-8 16.8%
2006-7 9.8%
2005-6 6.3%
2004-5 4.5%
2003-4 3.7%
It could an alternate roll-up column on your spreadsheet. Or I can just add it my copy if I am the only one interested in it. |
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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: Tue Sep 15, 2009 8:42 am Post subject: |
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It is not too hard to create a "correct" weighting for best estimate of true talent level at the end of last season. The primary issue is that the "correct" weighting would vary for each player, depending on the minutes played. See Toward and Adjusted +/- Projection System; the forth post there details the Bayesian statistics necessary to generate the correct values.
Essentially, if one knows the variances for each player-year (based on minutes played, or more accurately possessions played), and the transformation curve from one year to the next is known (based on propagation of uncertainty--additive form) then calculating the precise weights is not very hard.
I intend to do that fairly soon. |
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Ilardi
Joined: 15 May 2008
Posts: 265
Location: Lawrence, KS
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| Posted: Tue Sep 15, 2009 9:05 am Post subject: |
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| DSMok1 wrote: | It is not too hard to create a "correct" weighting for best estimate of true talent level at the end of last season. The primary issue is that the "correct" weighting would vary for each player, depending on the minutes played. See Toward and Adjusted +/- Projection System; the forth post there details the Bayesian statistics necessary to generate the correct values.
Essentially, if one knows the variances for each player-year (based on minutes played, or more accurately possessions played), and the transformation curve from one year to the next is known (based on propagation of uncertainty--additive form) then calculating the precise weights is not very hard.
I intend to do that fairly soon. |
What makes this tricky is the fact that 'weight' within my APM model is assigned to each lineup as a complete unit: i.e., all 10 players on the court receive the same weight based on the number of possessions each given lineup appears for. I know of no way to parse apart a lineup within the model to assign differential weighting to each individual player. |
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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: Tue Sep 15, 2009 9:28 am Post subject: |
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| Ilardi wrote: |
What makes this tricky is the fact that 'weight' within my APM model is assigned to each lineup as a complete unit: i.e., all 10 players on the court receive the same weight based on the number of possessions each given lineup appears for. I know of no way to parse apart a lineup within the model to assign differential weighting to each individual player. |
Ah yes, good point.
I was thinking in terms of Bayesian Statistics, where we use a "transformation" function to bring data up to the current year (age adjustment or just propagation of error), while your model combines all years directly. It is weighted by the number of possessions played each year... I think that I could derive an appropriate weighting per year.
Time to break out MathCAD... |
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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: Tue Sep 15, 2009 11:30 am Post subject: |
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| Ilardi wrote: | | DSMok1 wrote: | It is not too hard to create a "correct" weighting for best estimate of true talent level at the end of last season. The primary issue is that the "correct" weighting would vary for each player, depending on the minutes played. See Toward and Adjusted +/- Projection System; the forth post there details the Bayesian statistics necessary to generate the correct values.
Essentially, if one knows the variances for each player-year (based on minutes played, or more accurately possessions played), and the transformation curve from one year to the next is known (based on propagation of uncertainty--additive form) then calculating the precise weights is not very hard.
I intend to do that fairly soon. |
What makes this tricky is the fact that 'weight' within my APM model is assigned to each lineup as a complete unit: i.e., all 10 players on the court receive the same weight based on the number of possessions each given lineup appears for. I know of no way to parse apart a lineup within the model to assign differential weighting to each individual player. |
Okay, Steve, here we go:
I don't have the full adjusted +/- 1 year ratings, but here is the process and my approximate results.
First, an approximate distribution of NBA players is generated (average, stdev) for their 1 year APM ratings. (I got 0, stdev ~ 5.6)
Next, each year's data is regressed to the mean according to the standard error of the player (using Bayesian system--see my other thread for the formulas).
Using player pairs from year to year, each player's change (+ or -) was calculated, using the regressed numbers to damp the error.
Using players with low standard error for both the year and year+1, a normal distribution curve of year-to-year change was created. This is the key to the model. I used (Year+1)-(Year), or an additive change, rather than multiplicative, since this distribution is centered around (and our data points are as well, which would yield spurious results with multiplicative change). The result: Year-to-year change ~0, standard deviation of change = 3.4. This means that 68% of players changed between -3.4 and 3.4 from one year to the next.
Next, I calculated an approximate weighted average for the average player's 1 year APM standard error: 4.4
Finally, I used the Propagation of Error theorems to calculate the average player's standard error for Year, Year-1, Year-2, etc. The result: 4.4, 5.56, 6.5, 7.4, etc....
The weighting is equal to 1/(stderr)^2. I then normalized that so Year=1. The weighting becomes:
1.000
0.626
0.456
0.358
0.295
0.251
0.218
0.193
0.173
0.157
I didn't run the actual derivation (it's recursive and I'm rusty), but an approximate best-fit line is:
| Code: |
1.156
------------------- - .156
(YearsAgo+1)^.578 |
A note: this derivation did not account for aging effects. However, the spread in it's YtY transformation did implicitly...
Comments? |
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Crow
Joined: 20 Jan 2009
Posts: 825
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| Posted: Tue Sep 15, 2009 12:02 pm Post subject: |
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If I understand it right, if you used a 6 year data set these weights would work out as
33.5% say 2008-9
21.0% then 2007-8
15.3% 2006-7
12.0% 2005-6
9.9% 2004-5
8.4% 2003-4
Different from what I first suggested above, which neither of you choose to respond to. Would have appreciated some feedback then or now, if you wish.
But if you flip to 1/3rd 1 stabilized and 2/3rds 6 year average you get
33.6%
16.7%
13.9%
12.5%
11.8%
11.5%
That would be pretty darn close to the set above it. And at least provides one way of understanding DSMok1's weights in relation to what Steve had provided in his 2 previous sets.
Last edited by Crow on Wed Sep 16, 2009 2:26 am; edited 1 time in total |
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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: Tue Sep 15, 2009 12:20 pm Post subject: |
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| Crow wrote: | If I understand it right, if you used a 6 year data set these weights would work out as
33.5%
21.0%
15.3%
12.0%
9.9%
8.4%
Different from what I first suggested above, which neither of you choose to respond to. Would have appreciated some feedback then or now, if you wish.
But if you flip to 1/3rd 1 stabilized and 2/3rds 6 year average you get
33.6%
16.7%
13.9%
12.5%
11.8%
11.5%
That would be pretty darn close to the set above it. And at least provides one way of understanding DSMok1's weights in relation to what Steve had provided in his 2 previous sets. |
Yep, that looks right. I will note, though, that my numbers were approximate because I didn't compile the full APM 1-year for the last few years to do it completely.
I still wish there were a way to include aging effects explicitly in the model... that looks difficult.
Hmmmm..... If I know the aging curve, and I know the weights accorded to each year, and I know the minutes each player played in each year, I think an adjustment factor could be applied! I must ponder. |
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