Projected Wins Adjusted to Match the NBA’s Zero Sum Reality

I mentioned before that my initial run through of the projected wins for each team overestimated wins, due to the xRAPM projections combined with my minutes projections projecting league average xRAPM to be +1.11 per game, which is impossible. The average total xRAPM per team across the league must, by definition, equal zero. Any team’s positive xRAPM- because it is a plus-minus statistic- comes at the expense of its opponents’ xRAPM, so across the 30 teams, things must sum to 0. In order to account for this, I adjusted the net rating of each team to reflect the +1.11 initial average and reset the league average to 0. This also results in team wins summing properly to the 1230 available in any given year. Below is a chart with the adjusted net ratings and win totals. After that, those win totals are placed into the context of each conference, so you can see which teams project to be in the playoffs.

Projected Eastern Conference Standings

1. Miami — 57–25

2. Brooklyn — 55–27

3. Chicago — 53–29

4. Indiana — 49–33

5. New York — 44–38

6. Atlanta — 43–39

7. Toronto — 39–43

8. Detroit — 39–43

— — — — — — — — — — — — — — — — — — — — — — — — — — —

9. Cleveland — 38–44

10. Washington — 36–46

11. Milwaukee — 33–49

12. Philadelphia — 32–50

13. Charlotte — 32–50

14. Boston — 27–55

15. Orlando — 25–57


Projected Western Conference Standings

1. Oklahoma City — 57–25

2. Houston — 56–26

3. Los Angeles Clippers — 53–29

4. Memphis — 51–31

5. Spurs — 50–32

6. Golden State — 47–35

7. Minnesota — 42–40

8. Dallas — 42–40

— — — — — — — — — — — — — — — — — — — — — — — — — — —

9. New Orleans — 39–43

10. Denver — 38–44

11. Portland — 37–45

12. Utah — 33–49

13. Sacramento — 32–50

14. Los Angeles Lakers — 28–54

15. Phoenix — 26–56


I think these results pass the smell test, with the notable exception of Philadelphia inexplicably projecting to win 32 games. Let me know what you think. I’ll be continuing to post team breakdowns, with the unadjusted numbers (all of my graphics showing the numbers are already done and it would be a pain to redo them all), though I’ll be sure to make note of the need to adjust the numbers to account for the +1.11 average in those future posts.

Image from Keith Allison via Flickr.

Addressing a problem with the xWARP projections

In calculating the xWARP projections I’ve been doing, I noticed a worrying problem. The total number of wins projected for each team appeared to be roughly 7% too high. There are only 1230 games, and thus, 1230 wins available for the 30 teams in the NBA to win. In doing my xWARP projections, I had just been posting the win totals as I did each team.

Last night, I finally got around to running the numbers on all of the remaining teams I’d yet to post and summed up team wins for the whole league. Unfortunately, total team wins summed to roughly 1318 wins, which is obviously way too many. There are a number of ways to deal with this problem. The lazy, easy way would be to simply multiply the win totals of each team by 1230/1318 or roughly .933. The top teams then have 55 projected wins and the bottom dwellers would be in the mid to high 20s in wins. This solves the problem, but it doesn’t seem that consistent with reality, so I’ve decided to go another way.

I’ve hinted at wanting to do this before, but my current plan is to go through each and every game on the schedule and utilizing the projected MOV for each team (in the spreadsheets it’s the total Contribution / Game) plus Evan Zamir’s ridge regression work on homecourt advantage, I plan to figure out the win probabilities of each of the 1230 regular season games and then use those probabilities to determine total team win totals. I will then post the updated results. I will be updating the posts that already exist to reflect changes in team win totals after this is all done, and I will also do a master post with the full league projections.

I’m bummed out that the math didn’t work out as well as I’d hoped, but I’m excited to go through the schedule in such detail. The other good thing is that doing things this way acts as a built in strength of schedule adjustment for teams with more or less difficult schedules. Thanks for reading and for your patience while I work out the kinks of all this.

Image from gammaman via Flickr.