I have been doing these rankings since 2008 - at least in the blogosphere. I have tinkered with the formula a lot. But I think I've found something I am happy with the last few years. Here are some of the basics:
The engine is a Bradley-Terry based model. This is basically a giant logistic regression using the results to determine team ratings. Thank god for R.
Now instead of using straight win-loss, I use a formula of 0.8 for a win, and up to 0.2 based on margin of victory. The margin of victory is lognormal, so there are diminishing returns for blowouts. The model can be stumped by winless and unbeaten teams so this helps that out.
The ratings that come out of this end up being log-odds relative to a base team. Since I entered the teams in alphabetical order, the base team is Air Force. So if Air Force's rating is 100, a rating of 2000 for a team means a team would win 20 times against Air Force for each Air Force victory.
Using these ratings (and their variance), I ran a Monte Carlo Simulation over 10,000 trials where every team plays the other. This results in a Round Robin winning percentage.
Then I borrowed a concept from how the NCAA ranks hockey teams - a pairwise comparison. Each team is compared against each other team on A) round robin win pct, B) record v common opponents, C) head to head. The team with the most number of pairwins is #1. Now, as a practical matter, round robin win % is the driving factor - but doing this means that teams that do well in conference or in a head to head result can potentially leapfrog a position or two here and there.
Whew. So with all of that, 4 games in is a good time to put the first rankings out. There is some decent strength of schedule record. Now, each week with rankings like these - the teams move but we also learn more about the season at large. One thing I have included is the 20th and 80th percentile win % numbers, so you can see the confidence of the model.
Ultimately, no ranking is a be-all and end-all. I think stuff like this is more like a "better RPI/NET" which can guide discussions for a committee seeding model. To that end, this space will also do a 12-team playoff based on these rankings.
Obviously, this does not match the AP poll. But remember that the model only knows what has happened this year. There are no priors about the teams. Georgia's #26 rating is driven entirely by who they haven't played. These rankings will change as more data comes in!
For a 12-team bracketology, it'd work something like this. While there are some highly rated 1-loss teams, that one loss is a loss to a team above them in the rankings. The error bars are big enough to defer to unbeatens for now where possible.
Conference Champions:
ACC: Miami-FL (1)
Big 12: Texas (2)
Pac 12: Oregon (3)
Big Ten: Penn State (5)
SEC: Missouri (12)
MAC: Miami-OH (27)
MWC: Air Force (42)
Sun Belt: Georgia State (35)
American: Memphis (38)
CUSA: Liberty (59)
At Large:
Washington State (4)
Ohio State (6)
Washington (7)
Michigan (8)
Oklahoma (11)
Utah (13)
Just off the bubble
Duke (14)
Maryland (18)
Florida State (19)
Bracket - moving first round matches as needed to avoid intraconference 1st rounds
(1) Miami-FL
(8) Michigan v (9) Oklahoma
(4) Penn State
(5) Washington State v (12) Miami-OH
(2) Texas
(7) Washington (10) v Missouri
(3) Oregon
(6) Ohio State (11) v Utah
コメント