What Are Elo Ratings and How Do They Work?
A deep dive into the mathematics and mechanics of Elo ratings
Elo ratings are a method for calculating the relative skill levels of players or teams in zero-sum competitions—where one side wins and the other loses. While the system was originally designed for chess, it has proven remarkably effective across virtually every competitive sport.
The History of Elo
In the 1960s, Arpad Elo, a physics professor and avid chess player, developed this rating system to create more accurate rankings for chess tournaments. His innovation was recognizing that player skill follows a normal distribution, and that wins and losses should be weighted based on opponent strength.
The World Chess Federation (FIDE) adopted Elo's system in 1970, and it quickly became the gold standard for competitive rankings. Today, the Elo system ranks over 100 million chess players on platforms like Chess.com, and has been adapted for sports including football, basketball, baseball, soccer, and even esports.
How the System Works
1. The Starting Point
Every team begins with a baseline rating. This is typically set at 1500 points for a new or average team. This starting point is arbitrary—what matters is the relative difference between teams.
Example:
New Team A: 1500
New Team B: 1500
2. Calculating Expected Outcome
Before each game, the system calculates the expected result based on the rating difference between the two teams. The formula produces a probability between 0 and 1 (or 0% to 100%).
Example:
Team A: 1650 rating
Team B: 1550 rating
Expected win probability for Team A: ~64%
The larger the rating gap, the higher the win probability for the favored team.
3. Rating Adjustment After the Game
After the game, both teams' ratings are adjusted. The key is that the adjustment depends on how surprising the result was:
- Expected result: Small rating change (the favorite wins)
- Upset victory: Large rating change (the underdog wins)
Example (Team B upsets Team A):
Team A: 1650 → 1622 (-28 points)
Team B: 1550 → 1578 (+28 points)
4. Self-Correcting Over Time
As teams play more games, their ratings become more accurate reflections of their true skill level. A team that consistently wins will rise in the rankings, while a team that loses frequently will fall. The system is self-correcting: if a team is overrated, they'll lose to teams they "should" beat, causing their rating to drop until it stabilizes at their true strength.
The Key Formula Components
While the full mathematics can get complex, the core of Elo comes down to a few key elements:
K-Factor
The maximum number of points that can be gained or lost in a single game. Higher K-factors mean more volatile ratings (bigger swings), while lower K-factors create more stable ratings.
Rating Difference
The gap between two teams' ratings determines the expected outcome. A 100-point difference translates to roughly a 64% win probability for the higher-rated team.
Actual vs. Expected
The difference between the actual result (win = 1, loss = 0) and the expected probability determines how many points change hands. Bigger surprises mean bigger rating adjustments.
Why Elo Works So Well
Simple and Elegant
One formula applies to all teams and all games
Highly Scalable
Works for 10 teams or 10 million teams
Completely Objective
No human bias or subjective opinions
Forward-Looking
Provides win probabilities for future matchups
Elo in the Real World
Beyond chess, Elo ratings are now used across sports and competition worldwide:
- Chess.com ranks over 100 million players using Elo
- FiveThirtyEight uses Elo for NBA, NFL, and MLB predictions
- FIFA used an Elo-based system for their world rankings until 2018
- Esports platforms like League of Legends use Elo-based matchmaking
Learn More
Now that you understand how Elo works, see how we've customized it specifically for high school football.
