Is this objective college football ranking formula statistically sound?

[SeekerOfTruth007]

I might have discussed this in the past. The formula I concocted is this:

Power = Win Percent * Scoring Percent * Yardage Percent * Opponent's Win Percent (To determine Strength of Schedule)

Team with highest Power becomes ranked number 1, and every other team falls in order.

With this system, there would be no voting and no political bias, just raw stats telling us who the real best teams are. This is much better than simply having a biased poll about who the top 12 teams are in football.

Explanation:

Yardage Percent is determined by the total of returned yards on special teams plus offense plus any defensive yards gained, not just offensive yards. It is based on the percent of total yards earned by both teams in each game. so LSU vs Auburn, let's say they have 1000 yards in the game and LSU scores 600 of the yards, that would be 60% of the yards for that game.

Scoring Percent is more useful than Scoring Margin, because it is expressed as a fraction of the number 1.

We use both scoring percent and yardage percent because it smooths out any anomalies that either metric alone would tell. I realize turnovers matter too, but turnovers are sort of already baked into scoring percent and yardage percent.

this ranking ignores preseason rankings, and works only on your BODY OF WORK and Objective numbers, not opinions and hyperbole.

What do you think of this? I have used this system with some success in predicting past championship teams based on regular season results. It's as good or better than the computer models or the polls anyway.

[AI Opinion]

Your idea is creative and way better than pure polls, but statistically it has some issues.

Multiplying all those percentages punishes teams heavily for one bad area and makes the metric very sensitive to small-sample noise early in the season. Strength of schedule as just opponents’ win percent is also crude and recursive.

You’d want normalization, weighting, and maybe regression testing against past seasons 📊.

[SeekerOfTruth007]

The biggest flaw I find with my own system is it may under-rank the best team in the strongest conference, simply because the best teams int he strongest conference are going to "beat one another up" and lose some games no matter what. So the SEC and Big 10 might both be under-rated by this system, even though they consistently beat all the other conferences most seasons. Yes, I'm aware the ACC did very well with Miami in the final last year, but that seems to be an anomaly.

The system could be improved by actually scheduling non-conference games in a manner which allowed a "truth table" of teams to be constructed to better rank the best individual team and the best conference.

In the past, I did this by "re-ranking" the Top 10 teams based on their body of work. If I was a bit better at computer programming, I could re-rank the top 250 teams in all divisions combined, and have a more accurate and precise truth table developed.

I invented this system a long time ago, the year a two-loss LSU team won the national title with Matt Flynn as the QB, I predicted they were in fact the best team based on body of work and based on the fact they were the only team which had no losses in regulation even though they lost 2 overtime games. They went on to win the National Title. I've used it with less perfect success in some other years too.

[msc545]

No. It is objective in the limited sense that it applies the same arithmetic to every team, but that does not make it statistically sound.

The formula

Power=(Win %)(Scoring %)(Yardage %)(Opponents’ Win %)\text{Power}= (\text{Win \%}) (\text{Scoring \%}) (\text{Yardage \%}) (\text{Opponents’ Win \%}) has several problems:

The terms are arbitrarily selected and implicitly given equal importance. Multiplication does not establish that each variable predicts team strength equally well.
“Scoring percent” and “yardage percent” are undefined. Percent of what—points attempted, total points in the game, national maximum, or points relative to opponents?
Scoring, yardage, and winning are strongly related, so the formula may count the same underlying performance several times.
Multiplication creates extreme and unjustified interactions. A low value in any one category can crush the entire rating, while a zero makes everything else irrelevant.
Opponents’ win percentage is a crude strength-of-schedule measure. It ignores whom those opponents played and can be distorted by games against the team being rated.
Raw scoring and yardage depend on pace, possessions, garbage time, weather, conference style, and home-field advantage.
It does not distinguish a 1-point win from a 40-point win unless “scoring percent” somehow captures margin.
There is no statistical validation showing that the formula predicts future games better than simpler alternatives.
A statistically defensible system would define every variable precisely, adjust performance per possession and for opponent quality, estimate the weights from historical data, and test predictions on games that were not used to construct the model. Systems such as Elo ratings, opponent-adjusted efficiency models, or properly validated regression models would be much more defensible.

The shortest answer is: It is a numerical formula, but not yet a statistical model. Calling it “objective” does not demonstrate that it measures team strength accurately.

[SeekerOfTruth007]

Okay, you need to realize Scoring Percent is a more sound way of comparing victories to one another than is "scoring margin".

If LSU beats Auburn by the score of 30-0, then that is 100% scoring percent, but a 30 scoring margin.

If Oklahoma beats Oklahoma State by the score of 60 to 30, that's also a 30 scoring margin, but only 66 scoring percent. So LSU's performance was likely better, because they shut out their opponent while in this example "Oklahoma" gave up 30 points. If I just used "Scoring Margin" in a calculation, that would NOT correctly convey the value of a SHUTOUT, while Scoring Percent = 100% is a shutout DOES convey the power of a Shutout correctly.

Getting a "Zero" in any category means your team SUCKED, so yes, their score would have to be a Zero. I'm sure no team in history ended a season with "zero yards gained and zero points scored" so that's a non-issue anyway, although some teams have ended with zero wins, so if you score zero wins, you're obviously the worst or tied for worst team in the Division.

I don't see a problem here.

[abc3643]

Do some hypothesis testing on last season's data and you can answer your own question.

In other words, take last season's data and rank the teams and see if your metrics at least echo which teams made the playoffs. If they are poor at predicting that, then your metric is worthless.

[SeekerOfTruth007]

The same exact teams would NOT make the playoff in some cases. Notre Dame would have made the playoff, and 3-loss Alabama would NOT have made the playoff with this ranking system. That's the point. Polls are biased toward traditional powerhouses. An actual numerical ranking system is not biased.

[abc3643]

Regardless of polls, the top teams face each other in a genuine playoff system. That helps eradicate the biases.

This shit is all born out of the disaster of 1994 in which both Penn State and Nebraska were both undefeated. (So, obviously, they never played each other.) Nebraska won the polls though and so was declared national champion. The fact that the two teams did not play each other for a genuine championship became a big issue. It took a long time before we finally got a real playoff system.

[AviatorTom]

Strength of schedule is determined by the win % of each of the teams they played multiplied by each team's strength of schedule. The calculation has to be made iteratively.

[SeekerOfTruth007]

That's correct, and it gets too complicated to do by hand. I want to program a computer to do it using seasonal data, but I'm not sure how to legally get that much data on every game and load it into a computer. At least, I'd need to contact NCAA and ask them for the data after every game, because manually loading all D1 teams into a computer every week would also be unacceptable. It simply takes too much time and work to do it manually.

[Iron_Man]

So far No. The university of Miami hurricane should be ranked a lot higher. People are talking about them winning the national championship this year. They play Notre Dame at Notre Dame that will be a big game

[MrChinaski]

I dunno. But it's a testable hypothesis. Get the data, do the analysis.