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PostPosted: Sun Dec 02, 2012 7:26 pm 
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Usage is a commonly discussed issue so I decided to do a quick and dirty analysis by tracking true shooting attempts per 48 and points per 48 for players from 2002 through to the end of last season using exponential smoothing, then I used predicted numbers for each player given their minutes in games to compare the expected points per TSA of a lineup to its actual points per TSA in that game. The linear regression is: (Points per TSA - E(Points per TSA)) on (TSA - E(TSA)), here's the resulting graph taking bins at each one TSA step of (TSA - E(TSA)) with the threshold for inclusion being 50 samples in that bin.
Image


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PostPosted: Mon Dec 03, 2012 2:51 am 
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What's a typical expected number of TSA for a line-up?


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PostPosted: Mon Dec 03, 2012 3:06 am 
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Roughly 91, suggesting that each expected TSA over actual TSA in the lineup is worth about 0.27 points.

EDIT: I should mention that I am abusing the term 'lineup', as I don't mean a five man unit, I mean a full team for a full game.


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PostPosted: Mon Dec 03, 2012 1:01 pm 
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On the face of it this would appear to imply a quadratic tradeoff with the number of points to be added to the player's contribution looking like this:

points added = team tsa * (player tsa - average teammate tsa)*0.003, which assumes the player plays a full game.

To put numbers on this, taking team tsa as a constant at 91 and hence varying teammate usage to make up the numbers we get:

Code:
player tsa usage   player effect
0   -4.97
1   -4.70
2   -4.42
3   -4.15
4   -3.88
5   -3.60
6   -3.33
7   -3.06
8   -2.78
9   -2.51
10   -2.24
11   -1.97
12   -1.69
13   -1.42
14   -1.15
15   -0.87
16   -0.60
17   -0.33
18   -0.05
19   0.22
20   0.49
21   0.76
22   1.04
23   1.31
24   1.58
25   1.86
26   2.13
27   2.40
28   2.68
29   2.95
30   3.22


Please forgive the ugly table, I was in a rush...


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PostPosted: Mon Dec 03, 2012 8:02 pm 
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Thanks for posting; interesting.


v-zero wrote:
EDIT: I should mention that I am abusing the term 'lineup', as I don't mean a five man unit, I mean a full team for a full game.


So this has nothing to do with lineup performance. Oh well, that is another interesting issue though that has had some prior work by Ben Falk and maybe others.



I would want to compare your findings to Jerry's findings of factor level RAPM for own team eFG% impact, to see how consistent your impact findings for different usage levels are with his eFG% impact findings for those same usage levels and to see how much of the total eFG% impact findings are correlated with the asserted usage impacts and how much is left for other types of eFG% impacts besides usage directly and solely.


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PostPosted: Mon Dec 03, 2012 8:29 pm 
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Crow wrote:
Thanks for posting; interesting.


v-zero wrote:
EDIT: I should mention that I am abusing the term 'lineup', as I don't mean a five man unit, I mean a full team for a full game.


So this has nothing to do with lineup performance. Oh well, that is another interesting issue though that has had some prior work by Ben Falk and maybe others.



I would want to compare your findings to Jerry's findings of factor level RAPM for own team eFG% impact, to see how consistent your impact findings for different usage levels are with his eFG% impact findings for those same usage levels and to see how much of the total eFG% impact findings are correlated with the asserted usage impacts and how much is left for other types of eFG% impacts besides usage directly and solely.

It still uses minute allocations, so it shouldn't really differ much from lineup considerations. In fact, when I use TSA + TOV (what I consider player opportunity usage) I get the same 0.25 point per 100 that Ben found, but my dataset is much larger so there is confidence (tiny p-value) in the numbers even without binning. I could also run this just considering the FGA component for eFG% if anybody is interested?


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PostPosted: Mon Dec 03, 2012 9:25 pm 
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"It still uses minute allocations, so it shouldn't really differ much from lineup considerations."

I hope I am understanding what you are doing correctly.

The whole point of doing a lineup based test would be to see if on average the sum of average usage levels of players in actual lineups affected the performance of that particular lineup favorably or unfavorably and by more or less than expected by a static arithmetic approach. There was a lineup usage study done and discussed here years ago but I can't immediately recall where or how much the actual lineup performance varied from the expected.



J.E., have you ever done a multi-variate regression analysis of your eFG% RAPM factor with a player's personal eFG% and say usage, assist rate, 3PF FGA rate (or 3pt threat as a combination of 3pt FGA rate and 3pt FG%) and maybe a proxy for pick-setting (height)? Is your database set up so that this could be done easily on the old eFG% RAPM factor data or on your new xRAPM data? I might be able to assemble it from scratch but not sure if / when I'd get to it.


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PostPosted: Mon Dec 03, 2012 10:17 pm 
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Indeed, I understand why doing it with lineup data would be better from a theoretical point of view. What I'm doing is essentially treating it as if all the guys are on court at once (in one sense). I am using their expected tsa and expected points rather than their straight ts%, and that is how usage comes into it, because I then calculate a ts% for that number and compare it to the actual ts% for the game, and then I also compare the number of tsa to the expected number. For instance imagine a 5 man unit with these per 48 numbers on average:

1. 10 points, 10 tsa
2. 20 points, 17 tsa
3. 15 points, 20 tsa
4. 12 points, 10 tsa
5. 22 points, 23 tsa

Then here the expected points would be 79, expected tsa would be 80, but let's say they all play the whole game together and end up taking 95 tsa, then we might expect them to get (79/80)*95 = 93.8 points, but what I have found is that in such situations they would actually get around (79/80)*95 - 0.3*(95-80) = 89.3 points on average.


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PostPosted: Tue Dec 04, 2012 4:19 pm 
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v-zero, I am wondering how your impact estimates match up to the implicit impact of usage on Hollinger's PER. Might be interesting to check some examples.


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PostPosted: Tue Dec 04, 2012 4:31 pm 
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Crow wrote:
v-zero, I am wondering how your impact estimates match up to the implicit impact of usage on Hollinger's PER. Might be interesting to check some examples.

If somebody could provide those examples/explain how PER reacts to usage (as I don't have any material on PER and looking at Wikipedia the formulation is opaque) that would be interesting.


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PostPosted: Tue Dec 04, 2012 4:38 pm 
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v-zero wrote:
Crow wrote:
v-zero, I am wondering how your impact estimates match up to the implicit impact of usage on Hollinger's PER. Might be interesting to check some examples.

If somebody could provide those examples/explain how PER reacts to usage (as I don't have any material on PER and looking at Wikipedia the formulation is opaque) that would be interesting.


http://www.basketball-reference.com/about/per.html

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PostPosted: Tue Dec 04, 2012 4:49 pm 
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DSMok1 wrote:
http://www.basketball-reference.com/about/per.html

Thanks, I'll try to wade into that and decipher what it says about usage at some point.


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PostPosted: Tue Dec 04, 2012 5:57 pm 
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Doing a small scale, quick and crude test, I get about a 2.5 pt increase in PER for every 5 %pts of usage increase. Converting that to points still needs to be done. Using the formula for Hollinger's "Value Added", it appears that would be worth a bit less than 1 point per game. Your table suggest 5 %pts of usage increase is worth about 1.5 pts. Reasonably similar.


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