Is this additive + Elo system a better way to rank college football teams?

[SeekerOfTruth007]

I agree that the multiplicative system was giving some dumb results, so I've changed to an additive system. Here's how it would work.

Total Power = Initial Power + Average Opponent's Power. (Max 6.00 points here)

Highest Total Power = Number 1 ranked team. Others are ranked in reverse order, obviously.

Initial Power = Win % + Scoring % + Yardage % (Max 3.00 points here)

Average Opponent's Power = Average Initial Power of all of your opponents. This is iterative with "Initial Power" function above. (Max 3.00 points here)

Thus half your Total Power is from your own performance on the field, and half the Total Power comes from the performance of your opponents on the field.

This I think is better.

Then I would have ChatGPT do the ELO Chess rank (1000 initial ELO points) and average the two ranking systems.

ELO Chess should give a minimum of 25 points for a win against an unranked team, and a max of 100 points for a win if you beat the number 1 ranked team. Likewise you lose a minimum of 25 elo points for a loss and a maximum of 100 points for a loss if a ranked team gets dethroned by an unranked team. There would be bonus points, or penalties, for the following feats on the field.

Shut-out Victory (Opponent scores zero in a game): +10 Elo points

Shut-out Loss: -10 Elo points

Near Shut-out (opponent scores 7 or fewer points): +5 Elo Points.

Near Shut-out loss: -5 Elo points.

Blow-out Victory (Win by 17 or more): +5 Elo points.

Blow-out Loss (Lose by 17 or more): -5 Elo points.

Double-Up (loser scores at least 20, but the winner scores at least double that of the loser): +5 Elo points to the winner and -5 elo to the loser.

Triple-Up (Loser scores at least 17, but the winner scores at least triple that of the loser): +10 Elo points to the winner and -10 Elo to the loser.

Road Win: +5 Elo points.

Home Loss: -5 Elo Points.

It should be possible to generate a VERY reliable top 12 and top 25 teams starting from the top 250 teams with these systems.

[AI Opinion]

Your additive idea is definitely an improvement over a raw multiplicative system 👍

Basing “Initial Power” on win %, scoring %, and yardage % is intuitive, but limiting “Average Opponent Power” to the same 3.00 cap can compress differences between truly elite and just-good schedules. Iterative convergence is fine, but you’d want many passes.

Your Elo extension is workable, but the flat 25–100 band plus many bonuses can overreact to outliers and garbage‑time blowouts. Using expected‑score Elo (margin scaled, diminishing returns) tends to be more stable and predictive 📊

[msc545]

The additive portion is reasonable in principle:

Team performance + strength of schedule
That is much less likely than multiplication to produce bizarre results. But the particular variables still need work.

“Scoring %” and “Yardage %” are not defined. Percent of what? Without exact formulas and adjustments, the system cannot be reproduced.
Raw scoring and yardage are affected by tempo. A fast team gets more possessions and usually more yards than a slow team without necessarily being better.
Yardage can be misleading because of garbage time, field position, turnovers, and teams deliberately running out the clock.
Win percentage is duplicated indirectly: strong teams win more, score more, gain more yards, and inflate their opponents’ strength. The three components are not independent.
“Average opponent power” treats every opponent equally. One game against Georgia and one against a weak FCS team are simply averaged, although the informational value differs considerably.
Using opponents’ Initial Power is not meaningfully iterative. A true iterative strength-of-schedule model would account for opponents’ opponents and repeat the calculation until the ratings stabilize.
Early-season ratings would be extremely unstable because teams have played only a few opponents.
The proposed “Elo” system is the bigger problem. It is not really Elo. Elo calculates an expected probability of victory from the difference between the teams’ ratings and then adjusts both teams according to the difference between the actual and expected outcomes. It does not normally say, “Every win is worth at least 25 points.”

That minimum creates bad incentives and rating inflation. A top team defeating an extremely weak opponent would receive 25 points even though it accomplished almost nothing unexpected. If the loser also loses 25, the system remains zero-sum, but teams that play more games or begin with favorable schedules may still gain distortive advantages.

The proposed bonuses also double-count the same performance:

A 42–0 road victory could receive a shutout bonus, near-shutout bonus, blowout bonus, road bonus, and possibly double-up or triple-up bonuses.
Double-up and triple-up overlap. A 60–20 result satisfies both unless the rules make them mutually exclusive.
A home team losing to a superior opponent is penalized merely for playing at home, even though ordinary Elo can already incorporate home-field advantage into the expected result.
The fixed bonuses have different significance at different rating levels and can overwhelm the actual opponent-based adjustment.
“Ranked” and “unranked” are poor mathematical categories. The difference between No. 25 and No. 26 is essentially arbitrary, yet his rules could treat them quite differently.
Awarding the maximum loss when a ranked team is “dethroned by an unranked team” is backwards unless the size of the upset is calculated from rating difference. Losing to No. 26 is not remotely equivalent to losing to No. 150.
Finally, he cannot simply “average the two ranking systems” unless he specifies what is being averaged. Averaging an Elo rating around 1,000 with a power score ranging from 0 to 6 would make the power score practically irrelevant. Averaging ordinal rankings—say, third in one system and ninth in the other—is possible, but ordinal ranks discard information about how far apart the teams actually are.

A more defensible system would be:

Use a genuine Elo model with home-field advantage and a carefully capped margin-of-victory adjustment.
Use an efficiency rating based on performance per possession, adjusted for opponent strength.
Iterate opponent adjustments until they converge.
Standardize both ratings to the same scale—such as z-scores—before combining them.
Determine the weights by testing several past seasons, not by simply assuming 50/50.
Measure predictive accuracy on games that were not used to tune the model.
So my conclusion would be:

The additive method is a conceptual improvement over the multiplicative method, but the proposed Elo component is not standard Elo, the bonus structure substantially double-counts outcomes, and averaging the systems is undefined. It might produce an interesting ranking, but there is no basis for claiming it would produce a “VERY reliable” Top 12 or Top 25 until it has been precisely specified and validated against historical games.

You improved the framework, but you have not yet constructed a statistically defensible ranking system.

[SeekerOfTruth007]

I think you are somewhat mistaken. "Skill Gaps" should be rewarded in ELO, and the bonus points system ensures that skill gaps are in fact rewarded. I already planned to have "triple up" bonus be mutually exclusive to "double up" so that you cannot get points from both bonuses at the same time. It's not possible to get the "shutout" or "Near-shutout" bonus and the double up and triple up bonus at the same time. They are measuring different on-field performances. Shutout/near-shutout is a defensive performance, while "double up" and "triple up" are measuring sustained offensive performance.

Under the assumption that your rank should carry your "scars", I penalize losing by large margins or being shutout. This may slightly inflate ELO of winning teams and deflate ELO of losing teams, but that's the point. With only a 12 game regular season, I need the wins and losses to matter and I need on-field performances to matter.

the ChatGPT engine asked me to specify these sorts of bonuses and qualifiers for the ELO system, so it has in mind something like what I'm doing.

[SeekerOfTruth007]

I was just going to average the final rank of both systems and go with that, since average some sort of p-test or z-test on a 12 game schedule probably does not have enough data points to be statistically significant. You usually need at least around 100 data points for a real statistical comparison test to work at all, which we obviously don't have a 100 game season in College Football. That might work for Major League Baseball or NBA Basketball though.

[SeekerOfTruth007]

"Scoring Percent" is calculated by taking Team A Score / (Team A Score + Team B Score)

"Yardage Percent" is calculated by taking Team A Yardage / (Team A Yardage + Team B Yardage).

I am not concerned about "Garbage Time," because that is actually baked into team performance and depth too. Second String scoring points or not giving up points is a GOOD thing, because it means your team has DEPTH and is resistant to injury and chance and stuff. In fact, I wanted to give the winning team +5 bonus ELO points if the second string offense scored a touchdown. Again, this measures sustainable performance of a juggernaut team.

[slatyb]

An ELO system requires a lot of results to determine an accurate rating. A ten game season isn't nearly enough.

[SeekerOfTruth007]

I think you're exaggerating. The MMR system on StarCraft 2 is similar to ELO, and it can get you in the correct league with just 5 placement matches among about 100K active players. It takes about 50 games to get you to the exactly correct rank among 100k active players.

I forgot to mention two other bonus scores for my ELO system, starting after all teams have played 6 games:
Defeat an opponent ranked 13 to 25: +5 Elo
Defeat an opponent ranked 1 to 12: +10 Elo

This guarantees the system is rewarding teams who have tough schedules for their victories. This over the long term would discourage teams from joining "weak conferences".

[slatyb]

Basically you are assigning estimated ratings at the start of the season. But why not just use the current ELO formula?

[SeekerOfTruth007]

That's what I was doing, with some slight bonuses for certain on-field "feats" to attempt to measure superb performances: shutouts, doubling or tripling up, etc. I was going to start every team evenly ranked at the beginning of the season at 1000 ELO, and then re-do the calculation every week. This is to remove preseason ranking biases and have everyone ranked only by real on-field performances.

I was then going to average my own ranking system with the elo ranking system for the final rank, but without destroying the data of either initial ranking system either.

I tried ranking last season's games, but ChatGPT now claims it doesn't have enough access to the data to do that. lol. It originally said it did have enough access to data to do that.

[Static_In_The_Attic]

In a way it is a better way to rank college football teams & in a way it isn’t.

[AngryCarl3]

Elo system is generally a good system. At any rate I don't know of a better one.