How a shot gets a value

Data

RallyIQ reads the Match Charting Project, where volunteers record every shot of professional matches by hand: serve direction, stroke, direction, return depth, approaches and how each point ended. This build covers 11,822 matches, 1,877,757 points and 9,467,001 shots, rebuilt 2026-10-04 15:37:42. Matches charted without shot directions are left out of the model.

Positions and choices

A position describes the situation before a shot:

• Serve: first or second, deuce or ad court, tour and surface.
• Return: serve direction, court, first or second serve, and whether the server is rushing the net.
• Rally: phase (serve +1, return +1, rally, long rally), whether the ball arrives on your forehand side, backhand side or the middle, what kind of shot it was, the depth of the return, and who is at the net.

A choice is the stroke plus its direction. Directions are relative to the hitter: crosscourt, down the line, through the middle, or inside-out and inside-in when the forehand is hit from the backhand corner.

Three numbers per shot

For each tour, the model estimates three averages:

• V(position): the chance the hitter wins the point from that position.
• Q(position, stroke): the same chance after choosing a given stroke.
• Q(position, stroke + direction): the same chance after choosing the stroke and its direction.

After a shot, the hitter's chance becomes one minus the opponent's chance from their new position, or 1 or 0 if the point ended. The change splits into three parts:

• Direction choice = Q(stroke + direction) − Q(stroke). The well-identified part: given the stroke, was the direction a good bet?
• Shot selection = Q(stroke) − V(position). This credits approaching, slicing or going for a drop shot, but the chart can't see how good the incoming ball was, so it partly measures the opportunity.
• Execution = what actually happened − Q(stroke + direction). This credits pace, depth, disguise and avoided errors.

The three add up exactly. Across a match, a player's own shots minus the opponent's shots equals their points won above expectation, which is what the match pages break down.

Positions and strokes are also valued separately for each era (to 1999, 2000s, 2010s, 2020s) and surface, pulled toward the all-era value with 30 shots of pseudo-data. A baseline exchange on 1990s grass isn't judged against today's hard courts. Direction differences need the most data, so they stay pooled.

Small samples

Every estimate is pulled toward a broader average in proportion to how little data it has:

• Positions toward their phase average.
• Choices toward their stroke, and strokes toward the position.
• Player numbers toward the tour average: 20 shots of pseudo-data for shot values, 50 for strengths and weaknesses, 30 points for serve and return rates.

Displayed rates carry a 90% interval (± or on hover) from the same sample sizes and pseudo-data. Player ratings use standard errors clustered by match, since shots in one match share an opponent and conditions.

Some charts record an error without its direction. Those shots are spread across directions in proportion to each direction's recorded errors, so a chart that skips error directions doesn't make every direction look safer.

Matchups

Serve plans combine the server's win rate by direction with the returner's rate against that direction, both relative to the tour baseline (log5). Return plans value each return stroke and direction by first or second serve and by the returner's wing: the tour's result with it, the returner's own edge, and what this server concedes when the ball comes back to that side. Rally plans add the hitter's skill with a shot to how much the receiver usually gives up against it; on one surface, each player's record there is pulled toward their all-surface record. Similar players come from a 19-trait tactical fingerprint (serve placement, return depth, forehand share, line changes, slice, drop shots, net play, aggression and errors), standardised within each tour.

Beyond the shot model

• Serve equilibrium. In a mixed-strategy equilibrium every serve direction a player uses wins equally often (Walker and Wooders, 2001). A χ² test of equal win rates by direction, per player and court and compared within the same matches (so a direction used more on grass or against weak returners can't look better for that reason), flags mixes that are off and names the underused direction. Repeating the previous direction costs women about 0.4 points per 100 first serves and costs men nothing.
• Optimal serve mix. Within a match, servers lean on whatever is working, so usage there can't show how returners respond. A server's habitual mix over their previous three charted matches can, because it doesn't feed back from the current match: comparing each server with themselves as their habits drift, a direction used 10 points more often wins 0.19 fewer points per 100 (± 0.13) for women and no measurably fewer points (−0.05 ± 0.15 per 100) for men. The optimal mix maximises points won given that response, within the range servers' habits actually vary, from win rates pulled hard toward the tour's (300 serves of pseudo-data) so noise doesn't read as a gap. Its gain over the current mix is the serve's exploitability. Picked on half of a server's matches and scored on the other half, these mixes win 0.33 (ATP) and 0.42 (WTA) points per 100 first serves. Matchup pages fit the mix against the specific returner.
• Adaptability. For each set from the second on, the change in a player's first-serve direction mix is weighted by how each direction had performed earlier in the same match; adaptation speed does the same every two to three service games. Positive means the mix moved toward what was working. It's a habit, not a gain: a direction's edge in early sets barely predicts later sets. Rally choices showed no consistent habit (a player's odd and even matches don't agree), so they're left out. Whether returners respond when a server leans in can't be separated from noise: the directions servers lean into keep winning slightly more than expected.
• Discovered sequences. Every run of three shots (me, opponent, me) is counted once per point. Lift is measured against the player's own baseline and against the tour on the same sequence, with splits against left-handers.
• Points left on the table. For each shot, the value of the best direction for the same stroke and position (at least 30 tour shots) minus the value of the chosen direction.
• Long-rally execution. A player's execution from the ninth shot of a rally on, minus their own execution on earlier rally shots, in the same matches, so the opponents faced mostly cancel. Each value is pulled toward the tour average in proportion to its match-clustered uncertainty. It needs 2,000 long-rally shots: there, men's odd and even matches agree at 0.54, a real if noisy trait. Too few women reach that many charted long rallies to test it, so it's shown for ATP only. Positions already know the rally is long and what kind of ball arrived; what they can't see is how the rally got there, so a player whose best shots end points early meets tougher long rallies than their position suggests.
• Warm-up. The tour's rally execution by stage of the match (first ten points, rest of the first set, each later set) is on the Evolution page. It answers Tennis Abstract's question of whether groundstrokes break down, holding the difficulty of each position fixed.
• Opponent-adjusted strengths. Every player's serve and return strength is fitted at once over every charted point (a ridge Bradley–Terry model with surface terms), so a record built on weak opponents counts for less. Execution falls by about 2 to 3 points per 100 shots per unit of opponent strength, measured within each player, and player ratings are corrected for the opponents they faced.
• Forecast. The two players' serve and return strengths, on the last three seasons when both were charted enough then and on their careers otherwise. Records against the opponent's lookalikes and in the head-to-head are compared with what each meeting predicted, shrunk with 1,500 points of prior and capped at 3 points. A Markov chain then turns points into games, sets and matches.
• Compatibility. One player's shot mix weighted by their skill with each shot and by the opponent's weakness against it.
• Ecosystem. Points won by each career archetype against the others, by five-year era.

Limits

• Charted matches aren't a random sample. They lean toward finals, stars and the charters' favourite players.
• There is no ball speed, spin or court position, so shot selection and execution partly absorb ball quality.
• Era and surface move the value of positions and strokes, not the differences between directions.
• The returner response behind the optimal serve mix is only measured for modest shifts; a server who went all one way would be read much faster.
• Forecasts use charted matches only. Strengths correct for who a player faced, not for which of their matches got charted, so a player charted mostly in big wins still reads high.
• The match winner is taken from the last charted point, so retirements can show the wrong winner.

License

Source data © The Tennis Abstract Match Charting Project contributors, licensed CC BY-NC-SA 4.0. RallyIQ is non-commercial, and its derived data is shared under the same license.