Tennis Elo Rankings

The ratings themselves come from an Elo model that I built using historical tennis match data going back to the 1980s. It is heavily influenced by Jeff Sackman and the Elo models available on Tennis Abstract, as well as the methodology of FiveThirtyEight who use Elo-based models for a variety of sports.

At its core, Elo ratings work on a simple principle: when two players compete, the ratings update based on the match result compared to expectations. If a higher-rated player wins, their rating increases; if they lose, it decreases. For lower-rated players, wins yield substantial rating gains while losses result in minimal penalties.

The model initializes all players at 1500 Elo points. As players compete, their ratings adjust after each match based on several factors:

Tennis is played on multiple surfaces (hard court, clay, grass), each favoring different playing styles. Our model calculates both an overall Elo rating for each player and surface-specific ratings for hard court, clay, and grass.

When predicting match outcomes, we use a weighted combination (70% overall rating, 30% surface-specific rating) to capture both general skill and surface specialization.

Unlike traditional Elo systems that only consider win/loss outcomes, our model incorporates the decisiveness of victories. This is calculated in two ways:

For matches with complete point-level data:

• - We calculate point differentials between winners and losers
• - Higher point margins yield larger Elo adjustments
• - This data provides the most precise measurement of performance

For matches without point data:

• - We use games won/lost as a proxy for match dominance
• - The logarithm of the games differential (plus a constant) determines the adjustment factor

This approach ensures that dominant victories (like a 6-1, 6-2 win) yield greater rating changes than narrow victories (like a 7-6, 7-5 win).

The model incorporates a dynamic K-factor that decreases as players accumulate match experience. This means newer players' ratings change more dramatically early in their careers, then stabilize as they establish their true skill level.

For Grand Slam and Davis Cup matches played in a best-of-five format, we apply a transformation to predicted win probabilities. This accounts for how the longer format reduces variance and favors the stronger player.

When tested on matches from 1980-2024 (excluding early calibration years), the model correctly predicts approximately 67% of match outcomes on the ATP Tour. This outperforms the naive approach of simply picking the higher-ranked player by about 3 percentage points.

The model also produces well-calibrated probabilities, with a Brier score (a measure of prediction accuracy) that indicates reliable uncertainty estimates. When the model says a player has a 70% chance of winning, they win approximately 70% of the time.