Ratings Scope

August 29, 2015

At some point instead of ranting about the poor scheduling practices in Division 1A we just threw up our hands and started trying to figure out how to take into account all the games those play against D 1AA now that there's no penalty for playing them. Different ratings systems handled that various ways, but I've spent a bit of time analyzing the consequences and I'm not sure there's a good way.

Originally we just ignored games against non-1A opponents. When the penalties for playing 1-AA teams were relaxed and a majority of teams did so every year, it was thought that those games ought to count somehow (especially when 1AA teams won.) Some systems just rank all Division 1 teams and include all the 1AA vs 1AA games as well as 1A vs 1A and 1A vs 1AA.

For the iterative methods I use to calculate ratings, including all of the division one games did not appeal to me. Knowing that the 1AA field diameter was two steps longer than 1A's I suspected the major contribution of the "extra" team-pairs would be to exaggerate the rating values at the extremes. I wanted to take into account the 1A-1AA games in some way so I defined the D1* field to be all D1 teams who either played a 1A team or played a team that played a 1A team.

That field for 2015 is indicated by the D1* column in the table to the left. I have always been a bit uneasy about that definition (and when I came up with it Boyd opined that it "didn't seem right") but didn't really analyze that field until I re-wrote my presentation for this year. When I did, i noticed what should have been an obvious flaw. There are some teams who's rating (and contribution to opponent ratings) depends entirely on one or two games.

So for 2015 I have modified the field definition: D1** consists of all the teams who play at least half their games against 1A teams or 1AA teams with at least one 1A opponent. This eliminates six of the teams that would have been included as a part of D1*.

The table below shows the effect of the change and gives a good indication of why including all of D1 is not a good idea.



I've always published the ISR and ISOV ratings along with poorly-named meta-ratings ASOS(rating) and PASOS(rating). These characterize results against teams' schedules and support some qualitative analysis of relative performance. I have found histogram-based characterizations to be more useful, so for 2015 I am changing the report format.

The new format is:

ISR (Average=98.42 Standard Deviation=15.44)
29 Aug 2015 10:40:19
Through games of 12 Jan 2015

RankISRNormTeamConfSOSRank    WSOS(W)    LSOS(L)
11133.252.256Ohio StateB10112.08131314112.361108.18
33130.702.091Florida StateACC109.81313113108.151131.30
22119.011.333North Dakota StateMVC98.041031297.521104.34
2322118.981.332Kansas StateB12109.7532329103.124124.65
19764.26-2.213Delaware StateMEAC78.76197267.66881.53
19861.51-2.391Savannah StateMEAC85.5118700.001085.51

RankTwo ranks are listed, the overall relative position in the field and for 1A teams the relative position if 1AA teams are not considered.
ratingThe rating name - ISR or ISOV.
NormThe rating expressed as number of standard deviations above or below the mean rating value.
TeamTeam name (1AA team names are italicized)
ConfConference affiliation
SOSAverage of opponents' rating values.
RankRelative position in the overall and 1A lists sorted by descending SOS values.
WNumber of wins against teams in the field.
SOS(W)Average opponents' values in team's wins.
LNumber of losses to teams in the field.
SOS(L)Average opponents' values in team's losses.

Links are provided to switch between the ratings-order and SOS-order.

© Copyright 2015, Paul Kislanko