## Championship Probability Added II

Posted by Neil Paine on December 3, 2009

Yesterday I rolled out a very primitive idea for evaluating players by logically weighting their regular-season and postseason production. In case you missed it, I put everything in terms of the typical team's championship probability, and weighted regular-season and playoff Win Shares based on how much each type of win added to the probability of winning a title. I still think the core idea is terrific, but when the smoke cleared yesterday we came out with a list that saw old-school NBAers and ABA stars dominate over modern players -- I mean, Cliff Hagan ranked ahead of Michael Jordan, for goodness' sake! What in the name of Max Zaslofsky is going on here?

David Lewin suggested we fix the problem of overvaluing the pre-expansion NBA by discounting stats from leagues with fewer teams than the modern NBA with a multiplier of *x*/30 (where *x* = the # of teams in the league that year). I liked that plan, and I also decided to throw out the ABA stats entirely; I don't have a great rationale for this, except that I'm not sure what kind of prestige the ABA's championship had next to the NBA's (that and the fact that ABA players were clearly overvalued by CPA and I didn't want to deal with them at the moment). So with that in mind, here's an amended list that looks at who added the most adjusted championship probability in NBA history:

December 3rd, 2009 at 12:47 pm

It's interesting that two of the top 11 (and three of the top 15) never even won a championship.

December 3rd, 2009 at 12:58 pm

That's probably because Miller, Stockton, and Malone often played the team that had the guy at the top of the list. Lol

December 3rd, 2009 at 1:03 pm

That list looks absolutely excellent, Neil. Great work.

December 3rd, 2009 at 1:07 pm

"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.

December 3rd, 2009 at 1:28 pm

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

December 3rd, 2009 at 1:39 pm

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

December 3rd, 2009 at 1:51 pm

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?

December 3rd, 2009 at 2:23 pm

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"?

December 3rd, 2009 at 2:54 pm

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.

December 3rd, 2009 at 2:59 pm

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.

December 3rd, 2009 at 7:44 pm

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?

December 3rd, 2009 at 11:20 pm

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