2016 Ratings Field

July 17, 2016

The primary purpose of this site is just to analyze sports ratings. Like the NSA's, the analysis depends upon meta-data, since for most of the ratings the algorithms are either not public or not easily reproduced. Even if they were I wouldn't waste programming or processor time re-running algorithms that have already been run when Dr. Massey has already collected the results expressed in team rankings.

To assist in the analysis I do calculate and publish a few ratings. Boyd Nation's ISR and my ISOV variation of the ISR are very basic implementations of retrodictive and predictive algorithms. I can use them to divide the advanced ratings in Dr. Massey's list into the two categories based upon which of the two have the higher correlation coefficient to any of the ratings he includes.

There is nothing special about these choices. Several ratings Dr. Massey includes come in retrodictive and predictive variaties and any of the pairs could serve the purpose. The main value provided by using the ones I calculate is that ratings explicitly labeled retro or pre can be used to validate the determination by correlation coefficient.
One could even use the correlations to assign ratings a value that characterizes them by most to least predictive using some linear combination of the correlations to "standard" retrodictive/predictive "baselines" with the choice of "baseline pair" being arbitrary. The only requirement is that you can't choose for instance, Dolphin for the retrodictive one and Sagarin's Predictor for the predictive one. I use ISR/ISOV. SAG/SP or DOL/DP would work as well, but the other reason I use the ones I calculate is that I know when they are available.

Schedule Topology and Advanced Ratings

In case anyone wonders why I post my annual rant about D1A schedules, it is because the "D1A team hosting D1AA team" (it is never the other way around) games present a problem for any rating of D1A teams. The analyst has a number of choices, and in general we do not know what choices were made to form the ranking of D1A teams.
Ignore games vs non-1A teams
Back in the "good old days" teams could count a win vs a 1AA patsy only once every four years, so on average only 25 per cent of 1A teams played such a game. Ignoring those games didn't change anything significantly. As soon as the FBS rule (remember, even though the NCAA governs FCS, FBS can do whatever it wants) was changed so that games against 1AA teams could count for bowl eligibility almost all teams starting scheduling easy wins and the number of games became too large to ignore.

Include all division 1 teams
There are good reasons to do this especially if the rating ranks FCS teams, but there are complications. Including FCS vs FCS games where neither team has an FBS opponent or opponent's opponent extend the calculation without adding a lot of value. Reporting is problematic for rating value comparison purposes - nearly all of the FBS teams wind up with a rating value greater than the average even though that's only half of this field. There are ways around this but they all seem somewhat artificial to me.

Aggregate the non-FBS contributors
Treating all FCS teams in the FBS gameset as the same team was actually a fairly good idea when there weren't as many of them as there are now. Colley uses a more sophisticated approach by making multiple "virtual teams" that have played about the same number of games against FBS opponents as the average FBS team. This improves convergence of his algorithm without unduly increasing the impact of the games involved. I have not tried this mainly because I'm too lazy to analyze the impact of different aggregations.

Define a relevant subset of D1
What I chose to do is include all games between teams with more than half of their games where the opponent is a 1A team or a 1AA team with a 1A opponent. This shortens the diameter of the games graph by a full step by leaving out the games that contribute the least to "connecting" the field. This year my field includes all 128 FBS teams and 92 of the 125 FCS teams. No team in the Ivy, Northeast, Patriot or Pioneer conferences meets the criterion, so the field consists of teams from these conferences:
FBS: ACC(14 teams) B10(14) B12(10) ND P12(12) SEC(14) AAC(12) CUSA(13) Ind(2) MAC(13) MW(12) SBC(11)
FCS: BSky(13) BigS(6) CAAF(12) IndFCS(2) MEAC(11) MVC(10) OVC(9) SoCon(8) SLC(11) SWAC(10)
The 2016 field sorted by team contribution to connectivity is 2016 Field for Iterative Ratings ISR and ISOV.

The ratings I calculate do not converge until the games graph consisting of these teams is connected. With the field as defined above, that will occur after the third week of games, so I'll start publishing them on 19 September. The first version will probably make no sense, as some of the team-pairs will be 15 steps apart. By September 26 none will be farther than seven steps apart. Although I will publish the results, I won't pay much attention to them until October at least.

By the end of the season all 220 teams will be connected by a path no longer than five steps long. You can see that the longer path lengths all involve FCS teams. This graph shows the pathlength between all 24,090 team-pairs (twice.) Conferences can be identified as the squares along the diagonal, and are in the same sequence as the lists above.

Iterative field pathlengths

All of FBS would be connected by a games graph with diameter four, but it takes five steps to connect the 220-team field. That's better than the six it would take were we to include all of D1, but there's still a consequence. That extra step contributes a large number of paths to pairs that were already connected at a shorter pathlength. It is pretty much impossible to figure out how that impacts advanced algorithms but all such do a better job when there is not such a large disparity in the number of connecting paths.

Everything begins with the pairs of teams that play a game. The 1236 games are plotted here (twice, since each team shows up in both the vertical and horizontal axes.) The number of paths is equal to the number of games, since no pair of teams has scheduled two games this year.

Pairs connected at pathlength 1

When we look at the number of paths connecting teams that are at least opponents' opponents, we find that no team is connected to half the field.

Paths connecting teams at pathlength 2

You can see how the number of paths multiply for teams connected at two steps from the path counts for three and four steps:

Paths connecting teams at pathlength 3
Paths connecting teams at pathlength 4

There's an order of magnitude difference in the number of ways an advanced rating can compare each team's results to every other team - after the regular season is done the number of connections between teams looks like this:

Paths connecting teams at pathlength 5

© Copyright 2016, Paul Kislanko