# Team Rankings with Strength of Schedule and Home Ice included

I have put together a spreadsheet which compares all teams league wide.
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1. ### MNNumbersRegistered User

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EDIT TO ADD: The original article was written last spring. Current rankings for this year (2018-19) are in post #15.

For statisticians....

I have put together a spread sheet which compares all teams league wide with a Bradley-Terry comparison model. Details of the model can be found here:

http://sites.stat.psu.edu/~drh20/papers/bt.pdf
or, less mathematical rigor on either USCHO or Collegehockeynews.com, where the model is called KRACH, and some math is explained on the site.

Basically, it works like this:
Assume every team has a Power#. We will this P(1) - P(31) for all the teams. These number are such that the odds of Team(1) beating Team(2) on neutral ice are found by:
P(1)/(P(1) + P(2)).
If it were possible to find such numbers, then one could simply replay the entire year's schedule using these number, and add up all those odds for every game, and one would get the current standings.

There are 2 problems with applying this to NHL:
1- The OT system
2- Home ice.

In the first link, above, there is a mathematical discussion of extending the model to home-ice, which I have done. And, about the OT system, my technique in dealing with this matter is to normalize each teams point total so that the sum of standings points over the whole league equals 2 pts/game.

Results (as of games played 2/26)
 WEST EAST VGK 160.75 TBL 162.78 NAS 156.83 BOS 141.25 WPG 142.55 TOR 129.27 MINN 120.26 PHL 112.62 SJS 107.25 WAS 110.96 DAL 107.01 PIT 110.58 LAK 103.98 NJD 96.3 ANA 103.11 CMB 89.25 CGY 102.86 FLO 85.52 STL 101.21 NYI 81.66 COL 99.89 CAR 79.76 CHI 75.48 DET 72.9 EDM 69.31 NYR 67.82 VAN 62.96 MTL 61.21 ARZ 48.29 OTT 57.75 BUF 49.68

In one way, there is not much new information here this late in the season. The west shows teams 5-11 covered by a very small margin.

One thing that jumps at you is Philly's lower ranking. They have a brutal schedule left, with lots of BOS games, VEG and WPG as well, etc.

The interesting part of this analysis is the home-ice number. Something like 20%. As an example of what this means.....
If 2 absolutely equal teams played on neutral ice, the odds would be 50/50. Play on someone's home ice, and the odds move to: 1.20*50/(1.20*50 + 50). or 60/110 or....55/45. I found it interesting to find a model to quantify that. Obviously, this method is not perfect in its rankings. Hockey players are very streaky, there are injuries, etc. But I do think the Home-ice advantage portion would squash out correctly over time.

Last edited: Nov 4, 2018
2. ### morehockeystatsUnusual hockey stats

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3. ### MNNumbersRegistered User

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I appreciate the input. However, when using Bradley-Terry, the strength of schedule component integrates itself naturally, without needing to use any Co efficient. That's what makes it a great tool for this.

You should read about it. It's fascinating in the way it works.

4. ### morehockeystatsUnusual hockey stats

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It's fascinating, but I'll stick with my Elo and Buchholz.

Regarding the home ice advantage, it's interesting that in chess statistics and chess Elo predictions the color is not being taken into account, although the advantage for W is higher than home ice (~58%).

5. ### MNNumbersRegistered User

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I was just wondering about that for Elo and chess yesterday. Does that mean that Elo predictions are good for a series of play, but not a single game?

6. ### MNNumbersRegistered User

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And, Elo calculations don't use W or B? That would seem to be a defect, no?

7. ### morehockeystatsUnusual hockey stats

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They don't. It's not a defect, it's a feature. I researched this issue, it was not significant; it could be significant in a specific environment like team chess with replacement.

The point is that the color balance is the key constraint of any individual chess tournament, so if the number of games you play with black in a tournament is B, and with white - W, abs(B-W) must be p>

8. ### morehockeystatsUnusual hockey stats

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It's actually more delicate specifically in chess.

You can do probability of outcome based on rating delta and then apply the 0.58-0.42 adjustment. However, some chess players have styles that wildly favor them with White, and some have styles that are near ambivalent.

Semyon Furman used to have a nickname "World Champion when playing White" in the Soviet Union. This is a highly striking nickname, because overall Furman was never really considered even in the top ten within the USSR.

I did various adjustments to Elo ratings: colors, after win/loss, after a successful/bad tournament, after N games in N days and so on. Beyond the team applications, everything else turned out to be evening itself out.

And then, any prediction, chess or hockey, should be better over a span. I.e. your prediction's precision should improve from outcome of a single game to number of point scored in a 5-9 games span.

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Strength of schedule. Explain how each option accounts for the three games in four nights effect and the /sitting at home waiting/ phenomena.

10. ### MNNumbersRegistered User

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You mean, the difference in the amount of rest one team has before a game compared to another?

The analysis I am doing, while technically very complete, uses only game results to calculate its numbers. The numbers which come out of the calculations do NOT factor order of games, player injuries, etc at all.

In order do accommodate 'restedness', the algorithm would have to be made much more complex. I am not sure I have the mathematical ability to do that. Sorry.

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Team on the road playing a well rested team =sitting at home waiting.

3 games in 4 nights. In the RS Team A has X strings of 3 games in 4 nights, Team B has (X+A) such strings while Team C has (X-A) such strings. Which team A,B or C has the tougher schedule if any.

12. ### Doctor NoRegistered User

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I've got a SRS variation that considers rest days and travel (both of which started in an attempt to reduce the residual).

Will post more about it if I ever catch up on my goaltender game logs.

13. ### MNNumbersRegistered User

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To do this purely mathematically, so that you don't introduce "well, I guess that such a restedness factor means 20%...." which is just a guess, and to let the math break out the factor itself, one would need to do the following:

Introduce not only a 'home-ice advantage factor', but also a restedness factor (3 games in 4 night when the opponent does not have that), which would be called "alpha" or something. Then, on the occasions when such a thing happens you record it through the schedule, which teams were the unlucky ones with that in their schedule. Then, the differentiation and the equations become much more complicated, and you end up, hopefully, with 3 things:
1- the Rankings for the teams (these would take into account all the factors in all the games)
3- Restedness factor

But, my rudimentary spreadsheet would become very complicated, and I have no way of scraping a schedule to see where this applies, and I fear I would make many copying mistakes. Plus, I'm not sure I could figure out how to handle the math.

And, the point of my exercise is that I am only interested in the situation where I don't have to guess at the numerical value of anything - that is, that the values come out of the equations.

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Definitely something to look forward to.

15. ### MNNumbersRegistered User

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See the OP for the idea behind this Ranking System.

Current Rankings for this year - calculated on Nov1 at 8:00 AM

 WEST EAST NAS 221 PIT 196 MINN 154 TBL 194 EDM 149 BOS 137 COL 137 TOR 123 CGY 133 WAS 122 VAN 123 NJD 120 WPG 106 MTL 116 SJS 97 NYI 105 CHI 89 CAR 90 ARZ 83 BUF 86 DAL 68 CMB 64 VGK 67 OTT 57 STL 61 PHI 49 ANA 51 NYR 47 LAK 32 FLO 43 DET 33