2023 NCAA Football Top 25 Rankings
The coaches, media, and now an all-powerful committee of 13 publishes their Top 25 NCAA Football rankings. When you have a field of over 100 Division I-A (FBS) teams and a relatively tiny number of games to judge them by, you will have controversy. Well, I couldn't help myself... so I have applied my rating system to the college football system. This took a little while longer to launch (compared to my NFL ratings) because of the shear number of teams involved. It's not just the 100+ Div I-A teams, but they play the 100+ Div I-AA teams, and they play the vast Div II teams, and they play the vast amount of Div III. Thanks to really fast computations, I have rated over 700 NCAAF teams, most of them I haven't heard of before. You can see the latest rankings by clicking the links above.
Behind the Rankings
The most important thing to understand about my rating algorithm is what it is telling you. My ratings are a measure of what each team has presently accomplished. It is not meant to be a true predictive tool. For example, Team A might have a higher rating than Team B, but that could be due to that fact that Team A had the opportunity to play (and beat) higher quality opponents to date. That does not mean Team A is definitively better than Team B. According to my ratings, I'm stating that Team A has accomplished more thus far than Team B. However, understanding what a team has accomplished can give you insight on which teams are objectively superior to others.
My ratings are an objective measure of which teams have accomplished the most given their results against their opponents. This is very relevant because it is perhaps the first criteria people consider when debating who is the #1 team (or, which teams are the Top Four...), and I will argue, the most important. Sure, you can look at stats, or "eye" tests. But if you are not factoring in the competition in an unbiased method (side note: just saying "SEC is awesome so they have the hardest schedule" is not objective nor scientific), you are missing information to inform your rankings. My ratings do provide a quantitative measure of just that.
My ratings factor in every football game played in Div-IA, Div-IAA, Div-II, and Div-III. This is necessary even if you only care about the Top 25 teams in Div-IA. Why? Well, Top 25 teams play Div-IAA teams (or at least, their opponents do). Div-IAA teams play Div-II teams. Div-II teams play Div-III teams. In order to adjust Team A's rating after a game is played against Team B, I have to know the ratings of Team B. And to calculate the ratings of Team B, I need to know the ratings of all the teams that Team B has played. And to calculate the ratings of all the teams that Team B has played, I need to know the ratings of all of teams that have played the teams that Team B has played. Etc... In summary, a rating system must be comprehensive; otherwise, you will introduce error into the system.
Another aspect of my rating system that makes it unique is that fact that I iterate to converge my ratings. At the beginning of the season, all teams begin with a common rating. However, the disparity of talent in college football requires an iteration process. Applying an iterative scheme to the rating system allows learning of each team later in the season to be applied to early season results. With the sheer number of teams and the vast disparity of talent, I believe this is a necessary step for accurate results. I believe this also set my ratings apart from many other "computer" rankings.
An example will illustrate why this is important. Two teams playing each other very early in the season will be similarly rated. Therefore, the results will be calculated as win/loss of a similarly rated opponent, and the ratings would be adjusted. However, as the season plays out, we might learn that these two teams are any but closely rated. The rating boost that Team A received by beating, what we thought (at the time) was a similarly rated Team B, turned out to be too much. An iterative process uses the learning from later in the season and applies it to the beginning of the season to appropriately reward or penalize teams for every result. (So when Alabama play Wofford early in the season, an iterative scheme learns that Wofford is terrible, and the benefit that Alabama receives for that win is reduced during the iteration process). As you might imagine, each iteration results in a change in a team's rating. So, the process is repeated until the maximum change of any team less than 1% of the previous iteration results.
This can also lead to a team's rating changing during a bye week! Yes, learning from their opponents' results (and their opponents' result, and their opponents' results, etc...) will influence each team's ratings. This effect is also present during weeks in which the team is not on a bye, however, its impacts are a second order effect relative to the rating adjustment calculated from their win/loss/tie and therefore not obvious.
Speaking of opponents and opponent's opponents... there are two metrics that are often discussed when comparing teams' schedules. Strength of Schedule (SoS) is a metric that measures the quality of opponents a team has played. Strength of Record (SoR) is a metric that relates a team's record against its opponents relative to how a typical team (Average Top 25 team for NCAAF, average team for NFL) would perform against that same schedule. You will notice that I post SoS and SoR rankings. It is important to note, however, that SoS and SoR are not inputs in my calculations. SoS and SoR are outputs, meaning that I calculate these value after I've calculated every teams rankings. This is because opponents' strength (and the opponents' opponents, etc...) are intrinsically factored into my rating systems.
In short, my ratings are an objective and quantitative measure of what each team has accomplished. No BS, no bias, no preconceived notions on which teams or conferences are best. Just results and math. Is it a perfect rating system? No. It does not factor in injuries, weather, crowd atmosphere, etc. However, in a sport in which there are over 700 teams and only 12-14 games played, an objective measure of what each team has accomplished (e.g., my ratings) must be primarily considered and factored in to how they have looked doing it (the human subjectivity element) to truly rank teams. As the season matures, you can (and should) use this as a tool along with what you see one the field to formulate your Top 25.
The most important thing to understand about my rating algorithm is what it is telling you. My ratings are a measure of what each team has presently accomplished. It is not meant to be a true predictive tool. For example, Team A might have a higher rating than Team B, but that could be due to that fact that Team A had the opportunity to play (and beat) higher quality opponents to date. That does not mean Team A is definitively better than Team B. According to my ratings, I'm stating that Team A has accomplished more thus far than Team B. However, understanding what a team has accomplished can give you insight on which teams are objectively superior to others.
My ratings are an objective measure of which teams have accomplished the most given their results against their opponents. This is very relevant because it is perhaps the first criteria people consider when debating who is the #1 team (or, which teams are the Top Four...), and I will argue, the most important. Sure, you can look at stats, or "eye" tests. But if you are not factoring in the competition in an unbiased method (side note: just saying "SEC is awesome so they have the hardest schedule" is not objective nor scientific), you are missing information to inform your rankings. My ratings do provide a quantitative measure of just that.
My ratings factor in every football game played in Div-IA, Div-IAA, Div-II, and Div-III. This is necessary even if you only care about the Top 25 teams in Div-IA. Why? Well, Top 25 teams play Div-IAA teams (or at least, their opponents do). Div-IAA teams play Div-II teams. Div-II teams play Div-III teams. In order to adjust Team A's rating after a game is played against Team B, I have to know the ratings of Team B. And to calculate the ratings of Team B, I need to know the ratings of all the teams that Team B has played. And to calculate the ratings of all the teams that Team B has played, I need to know the ratings of all of teams that have played the teams that Team B has played. Etc... In summary, a rating system must be comprehensive; otherwise, you will introduce error into the system.
Another aspect of my rating system that makes it unique is that fact that I iterate to converge my ratings. At the beginning of the season, all teams begin with a common rating. However, the disparity of talent in college football requires an iteration process. Applying an iterative scheme to the rating system allows learning of each team later in the season to be applied to early season results. With the sheer number of teams and the vast disparity of talent, I believe this is a necessary step for accurate results. I believe this also set my ratings apart from many other "computer" rankings.
An example will illustrate why this is important. Two teams playing each other very early in the season will be similarly rated. Therefore, the results will be calculated as win/loss of a similarly rated opponent, and the ratings would be adjusted. However, as the season plays out, we might learn that these two teams are any but closely rated. The rating boost that Team A received by beating, what we thought (at the time) was a similarly rated Team B, turned out to be too much. An iterative process uses the learning from later in the season and applies it to the beginning of the season to appropriately reward or penalize teams for every result. (So when Alabama play Wofford early in the season, an iterative scheme learns that Wofford is terrible, and the benefit that Alabama receives for that win is reduced during the iteration process). As you might imagine, each iteration results in a change in a team's rating. So, the process is repeated until the maximum change of any team less than 1% of the previous iteration results.
This can also lead to a team's rating changing during a bye week! Yes, learning from their opponents' results (and their opponents' result, and their opponents' results, etc...) will influence each team's ratings. This effect is also present during weeks in which the team is not on a bye, however, its impacts are a second order effect relative to the rating adjustment calculated from their win/loss/tie and therefore not obvious.
Speaking of opponents and opponent's opponents... there are two metrics that are often discussed when comparing teams' schedules. Strength of Schedule (SoS) is a metric that measures the quality of opponents a team has played. Strength of Record (SoR) is a metric that relates a team's record against its opponents relative to how a typical team (Average Top 25 team for NCAAF, average team for NFL) would perform against that same schedule. You will notice that I post SoS and SoR rankings. It is important to note, however, that SoS and SoR are not inputs in my calculations. SoS and SoR are outputs, meaning that I calculate these value after I've calculated every teams rankings. This is because opponents' strength (and the opponents' opponents, etc...) are intrinsically factored into my rating systems.
In short, my ratings are an objective and quantitative measure of what each team has accomplished. No BS, no bias, no preconceived notions on which teams or conferences are best. Just results and math. Is it a perfect rating system? No. It does not factor in injuries, weather, crowd atmosphere, etc. However, in a sport in which there are over 700 teams and only 12-14 games played, an objective measure of what each team has accomplished (e.g., my ratings) must be primarily considered and factored in to how they have looked doing it (the human subjectivity element) to truly rank teams. As the season matures, you can (and should) use this as a tool along with what you see one the field to formulate your Top 25.
I'd also be happy to answer questions if you'd rather have someone translate that for you: Post your questions via email, facebook, or comments on this post and I'll get back to you.
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