Comments on: Championship Probability Added II

By: Scott

Scott — Fri, 04 Dec 2009 03:20:53 +0000

I did some more work on this a while ago. The main variable that could change from year to year (and are difficult to predict) is win distribution (the probability of team X finishing with Y wins). If we expect the 2nd best team to win about 60-65 games, a 70 win team would be far less likely to win a championship than if we expect the 2nd best team to win 50 games.

There is also the issue that a player worth 10 wins on a 50 win team is more valuable than a player worth 25 wins on a 30 win team since the second team is not going to make the playoffs and has no chance of winning a championship. Also a the same player isn't expected to use as many possessions or play as many minutes on a better team (or play as many minutes on a terrible team). I took all of these factors into account, just to find how the impact on championships differ from the impact on wins. (For this purpose a simple statistical plus minus sufficed.) What I preferred to use was an average expected championships added above replacement based on the weighted expected distribution on wins for the NBA. In the end, it was a pretty involve set of formulas. Some discussion is in the following post:

http://sonicscentral.com/apbrmetrics/viewtopic.php?t=1864&postdays=0&postorder=asc&start=0

In the end, I came up with a table using rounded statistical pm based on SPM, Usg and MPG. I am sure you could do the same thing with wins added. This needs to be done for every season in order to see the effect. The end result would be that the best seasons weighs far more heavily. This would shoot Lebron James way ahead of Cliff Robinson. Keep in mind this assumes playoff performance can be asserted based on regular season performance. (No playoff statistics were used beyond determining championship distributions.)

Here is my table for mean expected championships added to mean expected wins added. (Note that wins added is wins above replacement, not to be confused with replacement player. I assume that a starter's minutes are basically replaced by a reserve, whose minutes are replaced by a scrup, whose are replaced by an NBDL player.)

MEWA MECA
-5 -0.01882
-4 -0.01704
-3 -0.01481
-2 -0.01238
-1 -0.00963
0 -0.006
1 -0.00037
2 0.001511
3 0.004367
4 0.00811
5 0.013328
6 0.017616
7 0.023498
8 0.029744
9 0.035451
10 0.043908
11 0.052041
12 0.063664
13 0.073888
14 0.087118
15 0.101152
16 0.119303
17 0.138155
18 0.157056
19 0.177604
20 0.1988
21 0.222828
22 0.248568
23 0.275004
24 0.303676
25 0.334224
26 0.366949
27 0.398595
28 0.433916
29 0.469887
30 0.502555

Let me know if you want to discuss

By: David Lewin

David Lewin — Thu, 03 Dec 2009 23:44:34 +0000

Neil,

I wouldn't be too discouraged with this, it looks pretty good. My one question is, did you properly account for differing number of playoff games across years?

By: Neil Paine

Neil Paine — Thu, 03 Dec 2009 18:59:16 +0000

No, I didn't even initially adjust for different league sizes, because I figured a championship is a championship. However, guys from the early days of the league were showing up obscenely high on the list. I'm not thrilled with the idea of a kludge like multiplying by x/30, but you have to admit that this list "looks" a heck of a lot better than the one yesterday. This whole idea is a lot better on paper than in execution, and it's my fault, but I'll come back to it and clean up the method someday. 85 was the total number of playoff wins in the NBA in 2009, btw.

By: Jason J

Jason J — Thu, 03 Dec 2009 18:54:37 +0000

I'd like the peak season info you had on the last post added here. I think the two together gave a more comprehensive view.

By: AnacondaHL

AnacondaHL — Thu, 03 Dec 2009 18:23:57 +0000

In your calculations, did you adjust for years that didn't have 82 games, or 1230 league wins, in the season? Or for shorter playoffs? You only explicitly mentioned adjusting for having more or less teams in the league. And what was the 85 in "0.508 / 85 = 0.0063 CPA per playoff win in 2009"?

By: Mike G

Mike G — Thu, 03 Dec 2009 17:51:36 +0000

You shouldn't ding playoff WS in earlier eras, should you? Or at least, not at the same proportion as RS games? Each PO win was 1/8 of the way to a title, in Russell's day. If a title is worth (9/30) .30 as much as now, but an PO win is 2.0 times, then a 1960 PO WS might be worth .60 as much as in 2010?

By: David Lewin

David Lewin — Thu, 03 Dec 2009 17:39:25 +0000

Looks like a pretty good list though. I thought it might be too harsh on old timers, but it looks about right.

By: Neil Paine

Neil Paine — Thu, 03 Dec 2009 17:28:02 +0000

Yes, that and the fact that I dinged players pretty harshly for playing at a time when the league had <30 teams.

By: Mike G

Mike G — Thu, 03 Dec 2009 17:07:37 +0000

"we can multiply RS Win Shares by .0004 and playoff Win Shares by .0063" Does this mean a PO WS is worth 16 times a RS WS? That may explain how Robert Horry added more 'championship probability' than Oscar Robertson.

By: DSMok1

DSMok1 — Thu, 03 Dec 2009 17:03:52 +0000

That list looks absolutely excellent, Neil. Great work.