Surface & Form Indices: How We Rate Tennis Players

Why one ranking is not enough

Tennis is played on three surfaces, hard, clay and grass, and many players are much better on one than on the others. The ATP ranking adds everything together, so it cannot tell you that a player ranked 20th overall may be top 5 on clay and outside the top 50 on grass.

Rankings are also slow. They cover a whole year, so a top 10 player in a bad run and a lower-ranked player winning match after match look the same as they did a month ago. We use two measures to fix both problems: a rating per surface and a form index.

Surface ratings

Every player has three separate Elo ratings, one per surface. A rating changes only after a match on its own surface, so winning at Roland Garros moves a player's clay rating and leaves the grass rating alone. Ratings are seeded every January from ATP ranking points, so each season starts from the current pecking order.

After each match the winner takes points from the loser. How many depends on how surprising the result was and on a K-factor, which sets the size of the step. Ours starts at 32 and grows with the stakes:

• Tournament weight: Grand Slam 2.5, Masters 1000 1.8, ATP 500 1.2, ATP 250 1.0
• Round weight: final 1.5, semifinal 1.3, quarterfinal 1.2, round of 16 1.1, earlier rounds 1.0
• Rating gap: when the two players are more than 400 points apart, the step grows by up to 2x, and by a further 1.5x if the lower-rated player wins

A Grand Slam final multiplies the step by 3.75 (2.5 × 1.5), a Masters 1000 semifinal by 2.34 (1.8 × 1.3), an ATP 250 first round by 1. The final K always stays between 16 and 128, so no single match can swing a rating too far.

The form index: results against expectations

The form index does not simply count wins. It asks how much better or worse a player did than their surface rating predicted.

Points per match

Before each match, the surface ratings give both players a win probability. The difference between the result (1 for a win, 0 for a loss) and that probability is the surplus. A win is worth 0.5 plus the surplus, a loss −0.5 plus the surplus:

• Upset win (25% chance, won): 0.5 + 0.75 = 1.25
• Routine win (95% chance, won): 0.5 + 0.05 = 0.55
• Expected loss (25% chance, lost): −0.5 − 0.25 = −0.75
• Shock loss (95% chance, lost): −0.5 − 0.95 = −1.45

Match importance uses the same tournament and round weights as the surface ratings, so a semifinal upset at a Masters 1000 counts 2.34 times an early win at an ATP 250. A favourite who keeps winning collects steady, modest credit, while a lower-ranked player stringing upsets together rises fast. On the power rankings page, players outside the Elo top 30 whose form is climbing are tagged Rising.

The last 15 matches, newest first

The index adds up a player's last 15 matches, each weighted 0.85 times the one after it. The most recent match carries about 13% of the total, the fifth about 7% and the fifteenth about 1.5%. One bad loss does not wipe out weeks of good results.

Few matches, smaller score

A player with fewer than 5 matches in the window has the score scaled by n/5. One upset is not enough to top the form table.

Time off fades form

Form fades quickly when a player is not competing:

After a week without a match about 70% of the score is left, after two weeks 50%, after three weeks 35%, after a month 22% and after two months 5%. A player coming back from a long break, injury or otherwise, starts almost from zero and has to rebuild form with results.

How the indices feed the predictions

Surface ratings and the form index are inputs to our neural network models, next to overall Elo, Glicko-2 ratings and past meetings between the two players, overall and on each surface. The models learn how much each input matters. This is how a clay specialist in good form can come out close to, or ahead of, a higher-ranked player whose clay rating is weak.

Note: both indices update after every match, and neither decides a prediction on its own.

In short

Rankings ignore surface and react slowly. Surface ratings keep hard, clay and grass apart, and the form index compares each player's last 15 results with what was expected, fading fast when a player stops competing. Together with the overall Elo ratings and Glicko-2, they give the models a fuller picture of each player. All current ratings are on the power rankings page.