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# NCAA Football Elo School Ratings

About the NCAA Football Elo School Ratings ▪ Rate Some Matchups ▪ View the Ratings

The Elo rating system is a method for calculating the relative skill levels of players in two-player games. The creator of the system, Arpad Elo, was a professor of physics at Marquette University who wanted an improved chess rating system. Although the system has its roots in chess, today it is used in many other games.

We decided to take Elo's work and apply it to the ranking of college football schools. Our pool consists of all current FBS football schools.

All schools have an initial rating of 1500 points. These ratings are then updated by randomly selecting pairs of schools and having them "play" each other.

We start by computing the win probabilities for each school (let's call them A and B):

```P(A wins) = 1 / (1 + 10^((RB - RA) / 400))
P(B wins) = 1 / (1 + 10^((RA - RB) / 400))

where RA = rating for A
RB = rating for B
```

After the winner has been determined, the ratings of the two schools are adjusted. If A wins the match then the new ratings are:

```RA_new = RA + K * P(B wins)
RB_new = RB - K * P(B wins)
```

The "K" above stands for the "K-factor" and has a value of 24. (The K-factor was later changed to 10 --Ed.)

While if B wins the match then the new ratings are:

```RA_new = RA - K * P(A wins)
RB_new = RB + K * P(A wins)
```

For example, suppose Notre Dame ("ND") has a rating of 2500 and Ohio State ("OS") has a rating of 2450. The win probabilities for each school are:

```P(ND wins) = 1 / (1 + 10^((2450 - 2500) / 400)) = 0.571
P(OS wins) = 1 / (1 + 10^((2500 - 2450) / 400)) = 0.429
```

If ND wins then the new ratings are:

```ND_new = 2500 + 24 * 0.429 = 2510
OS_new = 2450 - 24 * 0.429 = 2440
```

While if OS wins then the new ratings are:

```ND_new = 2500 - 24 * 0.571 = 2486
OS_new = 2450 + 24 * 0.571 = 2464
```

As always, please send us some feedback if you have any comments or questions.