My First Rankings Data
All right, it is still rough, but I’ve analyzed data from Boise State and Alabama last year to see who really deserved the national title. I found some interesting points. To recap this rankings methodology, here it is in a nutshell. After 6 games have been played, you take every teams average points per game scored and average points per game allowed. You then look at the averages of any given team vs. the averages of their opponents. Look at the actual scores of the games. Then each team gets another set of averages- how many more points do they score on their opponents than their opponents allow, and how many fewer points they allow than their opponents score on average. Still with me?
We then say, according to the data, this next game Team A should beat Team B by this score. Those are our expected values. We then watch the game and input the observed values- the actual score of the game. We look for significant differences, whether in doing better than expected or worse than expected. A Chi-Square test tells us if these differences between what we expected and what we observed are statistically significant. By averaging out the negative significance (performing worse than expected) and positive significance (performing better than expected), we give a score to each team. Obviously if this score is positive, great. If it is negative, not great. If it is around 0, you play exactly as you were expected to…probably a good thing if you won a lot of games.
I did this test on the data from Alabama and Boise State last year. Here’s what I got:
1. Boise State had some great games. They were expected to beat Bowling Green 37-18 but won 49-14. They should have beaten Hawaii 41-15 but won 54-9. Their best win was TCU, where they were expected to lose 26-19 but instead won 17-10. However, they blew it against Louisiana Tech and Tulsa, who they should have beaten 36-16 and 43-18, respectively. Instead they won 45-35 and 28-21. They also gave up way too many points to Fresno State and didn’t score enough on New Mexico State. Their positive variance was 58.05, but their negative variance was 74.89. The Boise State Broncos were under performers last year. They won, but not the way they should have given the schedule.
2. Alabama blew away some expectations against good competition. Florida was only supposed to be a 14-13 win, but they beat them 32-13. Ole Miss was going to be a 17-16 win, but they beat them 22-3. Tennessee and Auburn were big let downs though. However, they really helped themselves against Texas, who they should have beaten 23-14 but beat 37-21 instead. It was close with them, but in the end their positive (68.84) outweighed their negative (64.73). So did other teams play above their expectations more often? Yes, but in the end there were two undefeated teams, so it was only a matter of comparing those two.
So you can see these rankings can be a good model. If we put filters in place like major penalties for losing games you were supposed to win and not being able to be ranked ahead of teams who have a lot more wins or something…this could be a good system. What I’ve seen so far is that Alabama played their schedule better than Boise State. By that I mean these numbers say that if I plugged Alabama’s numbers into Boise State’s schedule, then the expected scores for Alabama would be better than what Boise State actually did. And vice versa. If you put Boise State’s numbers into Alabama’s schedule, then the expected scores for Boise State would in fact be worse, or closer games, than what Alabama actually did.
Hopefully that helps to explain these numbers a bit. It will be tough to try for a whole season, but I’ll do my best to give it a shot and see where it goes.
Comments
Sloppy, I like your attempt to qualify one team’s opponents against another’s opponents where they are completely different from each other.
However, what I don’t like about your system is that one team has the opportunity to artificially inflate their numbers by running up the score. Instead of putting in their 3rd stringers late in the game, they may instead choose to keep piling on the points to improve their ranking.
My two cents…
Dane
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My thoughts are that this is probably the best formula out there. Obviously I’d need to know more specifics about it to formulate an educated opinion, but for right now I think you’re on the right track.
However, no formula is perfect. There are some situations that would throw the formula off, which is why you still need a human component (e.g. polls), albeit as unbiased as possible. I’ve thought of a couple situations that might throw it off: 1) Team A, a half-decent team, beats up on patsies for every game. These patsies only play other patsies for the rest of their games. Team A will probably have the best score out there just because it did better against these patsies than all the other patsies they played. However, Team A may not be the best team out there. 2) Team B beats up on patsies for the first 6 games of the year (these patsies only play other patsies besides their games against Team B). But then, once you start measuring actual vs. expected, Team B starts playing good teams that have only played other good teams up to that point. Because Team B’s spread is so much higher than the teams that they’re playing, Team B is expected to whallop them. So even if Team B beats all of them, they most likely won’t beat them by as much as is expected by the formula, and thus won’t have a high ranking, even though they might be the best team out there.
I recognize that these situations are only hypothetical, but as I said before, this is why you need a human component as well. It’s still a great idea.