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. MNNumbers

    MNNumbers Registered 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)
    WESTEAST
    VGK160.75TBL162.78
    NAS156.83BOS141.25
    WPG142.55TOR129.27
    MINN120.26PHL112.62
    SJS107.25WAS110.96
    DAL107.01PIT110.58
    LAK103.98NJD96.3
    ANA103.11CMB89.25
    CGY102.86FLO85.52
    STL101.21NYI81.66
    COL99.89CAR79.76
    CHI75.48DET72.9
    EDM69.31NYR67.82
    VAN62.96MTL61.21
    ARZ48.29OTT57.75
    BUF49.68
    Home ice advantage = 1.21

    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. morehockeystats

    morehockeystats Unusual hockey stats

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  3. MNNumbers

    MNNumbers Registered 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. morehockeystats

    morehockeystats Unusual 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. MNNumbers

    MNNumbers Registered 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. MNNumbers

    MNNumbers Registered User

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

    morehockeystats Unusual 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. morehockeystats

    morehockeystats Unusual 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.
     
  9. Canadiens1958

    Canadiens1958 Registered User

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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. MNNumbers

    MNNumbers Registered 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.
     
  11. Canadiens1958

    Canadiens1958 Registered User

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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 No

    Doctor No Registered 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. :D
     
  13. MNNumbers

    MNNumbers Registered 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)
    2- Home Ice advantage factor
    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.
     
  14. Canadiens1958

    Canadiens1958 Registered User

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    Definitely something to look forward to.
     
  15. MNNumbers

    MNNumbers Registered 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

    WESTEAST
    NAS221PIT196
    MINN154TBL194
    EDM149BOS137
    COL137TOR123
    CGY133WAS122
    VAN123NJD120
    WPG106MTL116
    SJS97NYI105
    CHI89CAR90
    ARZ83BUF86
    DAL68CMB64
    VGK67OTT57
    STL61PHI49
    ANA51NYR47
    LAK32FLO43
    DET33

    Home Ice Advantage: 1.133

    It's very early in the season, but in one way, that's when this system may be best. As the season wears on, the unbalanced schedule balances out, and this becomes less necessary.

    It was suggested to find a way to find a home ice advantage for each individual team, rather than league wide. Under this calculation, that would essentially require finding 2 Power Rankings for each team, one home and one away. That would mean trying to tease twice as much information out of the same data, which may not be feasible, especially this early.

    And, it would be more work than I really want to do, because it would necessitate a labor intensive rewrite of my spreadsheet to do so.
     

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