First Attempt at Hockey Pythagorean Theorem

Some really good stuff here.

The problem here is that the first sum varies within very small range near 1 while the 3*5v5 is much larger and therefore the difference in the result comes primarily from 3*5v5. What about 5v5 +(PK-PP)? For instance, this makes SJS 2.032, CHI 1.916, WSH 2.021 and, at the bottom, EDM 1.379, CAR 1.39, TOR 1.49, CBJ 1.324.

The first thing I thought when I saw this is well then what would the new ranks be. So:

1. WSH 5.501
2. SJS 5.204
3. VAN 5.179
4. CHI 4.876
5. COL 4.483
6. PIT 4.441
7. PHX 4.412
8. NJD 4.376
9. BUF 4.324
10. PHI 4.208
11. NYR 4.032
12. LAK 3.972
13. NSH 3.965
14. CGY 3.961
15. ANA 3.904
16. STL 3.889
17. ATL 3.882
18. FLA 3.829
19. MIN 3.816
20. TOR 3.742
21. DET 3.719
22. BOS 3.718
23. DAL 3.704
24. OTT 3.69
25. MTL 3.55
26. NYI 3.528
27. TBL 3.509
28. EDM 3.423
29. CAR 3.306
30. CBJ 3.156

What this really calls for is a regression analysis.

And with that comment, I’ve exhausted my expertise on how to actually, you know, do it.

Great Stuff!! Thanks.

The anomoly that sticks out to me is Vancouver. 12 points behind SJ, but only .025 behind based upon your theorem. My first thought is that Vancouver gives up bunches of goals and defensively are not as good as SJ. I do not know if it means anything, but based upon the theorem itself Vancouver should be #3 in the overall standings. Why aren’t they?

Nice work. I messed around with shot differentials last night to see if I could get something to work, and nothing ended up patterning nicely. I used last year’s results, to have a full year’s worth of data.

I also am working at stripping out OT points and going back to the W/L/T point distribution, just so there’s only 2 points awarded in a game.

I think this is a great start.

I like stuff like this; I will help you when I get time. There definitely needs to be some regression analysis run against other standard forms of this theorem and compared to years past (since the lockout, in reality) before we can declare any sort of progress. I like the concept of including PP and PK, though.

I agree with all the comments that regression is necessary.

I will say though, that I think the PP% and PK% need to be adjusted for number of penalties. Some teams cause a lot and take very few (Devils, anyone?), so even if their special teams combined percentage isn’t that high, their weighted percentage would be and I think that should be taken into account in an explanatory model.

One more thought: Baseball’s Pythag is based solely on runs scored and runs allowed. Could we do a hockey pythag based only on goals scored and goals allowed?

The one issue I have with all these special teams indices is that by using PP/PK% you’re not accounting for the frequency of the PP or PK for each team. Some teams will be on the PK or PP more often (and in this case might be worth a < 3x multiplier to 5v5).

I would think a better measure would be net special teams goals (PP+SHG-PPA-SHGA) in some fashion, as that measures what you’re looking for instead of a rate.

Also, the simple James’ pythag I just ran compared favorably to current at R^2 of .9.

-d