The Elo formula, step by step
Elo gives every team one number. Before a game the difference between the two numbers, plus a bonus for the home team, sets an expected result between 0 and 1:
After the game the winner takes points from the loser. How many depends on how surprising the result was, how lopsided it was and on the K-factor, which sets the speed of learning:
Here S is 1 for a win, 0 for a loss and 0.5 for a tie, and dw is the winner’s rating edge including home field, with its sign. The second factor in M shrinks the change when a heavy favorite wins big and enlarges it when an underdog wins, which keeps ratings from inflating year over year. The calculator uses the constants from FiveThirtyEight’s published NFL model: K = 20, home field = 65 points.
The same formulas run every week on the NFL power ratings board, and the Elo explainer animates one game from expectation to update. The Elo ratings guide covers the choices behind each constant.
Frequently asked questions
What is the Elo rating formula?
The expected result for team A is 1 / (1 + 10^(−d/400)), where d is A’s rating minus B’s rating plus any home-field bonus. After the game, A gains K × multiplier × (actual − expected) points and B loses the same amount.
What K-factor should football Elo use?
A K of 20 is the value in FiveThirtyEight’s published NFL Elo code and the value this calculator uses. Higher K reacts faster to recent results but also chases noise; with 17 games a season, 20 is a common compromise.
How much is home-field advantage worth in Elo?
FiveThirtyEight used 65 Elo points, about 2.6 points on the scoreboard at 25 Elo points per point. Home teams have won a smaller share of games in recent seasons, so some models now use less.
Why does the margin of victory matter?
A 30-point win says more about the gap between two teams than a 1-point win. The multiplier grows with the log of the margin, shrinks when the favorite wins big and grows when the underdog wins, so strong teams are not rewarded twice for beating weak ones.
How do Elo points convert to a point spread?
Dividing the Elo difference, including home field, by 25 gives an approximate point spread. A 100-point edge is roughly a four-point favorite.