College Football Ranking

Welcome to my College Football Ranker! This ranks football teams using a general ranking algorithm I designed, but with some options you can choose. Select from the options below and then click on the button to generate the rankings. Warning: when you click on that button, many browsers will freeze up for a bit! (Chrome will just freeze this tab.) The page must calculate the rankings based on the options you chose. Depending on your computer, this can take a LONG TIME! Recommendation: open this page in a different browser (not just a different window) so you can keep doing stuff while the code runs.

Ranking Properties

I'm pretty opinionated about how rankings should be determined. I really don't trust humans to rank teams. You may disagree with that, or with some of these:

Order of the games doesn't matter: I don't see why this should matter. A team's performance throughout the entire season matters, a loss at the beginning of the season is just as important as a loss at the end. Yes, the teams are more consistent later, but that's true for all teams.
Margin of victory matters: A three-point win is evidence that the two teams are pretty evenly matched; a lopsided result means the opposite. However, the first point is the most important. A ten-point win is more than half as good as a twenty-point win.
Overtime matters: A 7-point overtime win is the result of a closer game than a 3-point win. Currently, my ranker does not take into account whether a game went to overtime. (If you know a good online source that includes the possiblity of overtimes and has at least as many teams as I have here, please let me know: paithanq@gmail.com.)
Other stats are irrelevant. Or worse, they may contribute to confirmation bias. I just stick to the scores.
All teams should be ranked. Unfortunately, it's hard to get stats on all the NAIA games, etc. Their results can make differences on the ratings for even the top teams.

How does it work?

I'll add more details here later. Here's the brief version: all teams start with a rating of .5. Then it looks at all the games for each team and applies the score factor function to each margin of victory, multiplies that with the opponent's rating and sums those products. Once this sum has been determined for each team, those become the new ratings. We repeat the evaluation until all ratings converge; the order of those final ratings determines the ranking.

Evaluating the Ranking

Given a ranking, you can determine which games were actually upsets. From there you can evaluate the soundness of the ranking by some statistics based on the upsets. This page calculates those and reports them based on the ranking your options generate.

The percentage of games that are upsets: a ranking that minimizes these is good.
The percentage of total margin of victory points from upsets. Again, a ranking should seek to minimize this.
Got any other good metrics I could use? I'd love to hear about them and maybe add them here!

I expect that actually finding the ranking that minizes either of these is NP-hard. (If you know of that result, I'd love to link to it from here.) That would mean there's no efficient algorithm that can devise the ranking that minimizes these percentages.

Select Season

Season: (Future: add some old seasons.)

Season Stats

(Choose a season above.)

Ranking Options

Once you've picked a season, choose the parameters here to customize your ranker.

Which Weeks

How much of the season do you want to analyze?

Max Margin of Victory

This is the maximum margin of victory that "counts". If a team beats another team by more than this value, then it's the same as if they'd beaten them by the max.

1100
35

Score Factor Function

This determines how strong a win is. A loss by the same amount is a reflection through the line y = .5. Hover over the graph to see the actual function. (All graphs generated at fooplot.)

Linear Function

y =.5 + x / (2*max-margin)

Logarithmic Function

y = .5 + ln(((e - 1) * x / max-margin)+1)/2

Square Root Function

y = .5 + sqrt(x / max-margin)/2

Quarter-Circle Function

y = .5 + sqrt(1 - (1 - (x / max-margin))^2)/2

Constant Function (Margin of victory doesn't matter)

y = 1

<-- Wait! In case you didn't read above, clicking this will probably freeze your browser (or tab, for Chrome users) for a while. MOBILE USERS: do not click the button!

Ranking and Ratings

Ranking Stats

(Populates after you generate the rankings.)