First Serve Percentage and Points Won Calculator
First Serve Percentage and Points Won Calculator
First-serve percentage is not first-serve points won, and a player can lead on one and trail on the other. All four published service rates from one set of counts, each with its denominator printed.
The four service rates from four counts
First serves in ÷ service points175 service points, 112 first serves in, 74 points won on first serve, 30 on second
Four rates, three denominators
First-serve points won = (points won on first serve ÷ first serves in) × 100
Second-serve points won = (points won on second serve ÷ (service points played − first serves in)) × 100
Service points won = ((points won on first serve + points won on second serve) ÷ service points played) × 100
- whose definitions these are
- the ATP publishes THREE of these four by name on its own stats leaderboard — % 1st Serve, % 1st Serve Points Won and % 2nd Serve Points Won — and publishes no definition of any of them: the page carries no tooltip and about 5,000 characters of mostly JavaScript template. The fourth, service points won, it does not publish at all. The LTA, the ITF’s national association for Great Britain, defines three of them in words but states no denominator. The only source read that states every denominator is Rod Cross’s Grand Slam Statistics primer of June 2009, and the arithmetic here follows it
- why second-serve points won looks bad
- its denominator includes the double faults. A double fault is a second-serve point that was lost, so it sits in the denominator and not the numerator, and a player who double-faults ten times in a match carries ten guaranteed losses in that one rate and in no other. Second-serve points won in the fifties is good; first-serve points won in the fifties is not
- the identity that ties them together
- Cross’s decomposition “p = fw + (1 – f) s”, with “f = N1/(N1 + N2), w = W1/N1 and s = W2/N2” — an identity rather than a model, and the same number as “p(A) = (W1 + W2)/(N1 + N2)”. The Service points won row above is that figure, and it is what the game and set win probability calculator wants. A player who takes pace off the first serve raises f and lowers w, and the two can cancel here entirely: that trade is the tactical content of serving and no single rate above can see it
Worked example
175 service points, 112 first serves in, 74 points won on first serve, 30 on second
112 ÷ 175 = 0.6400, so the first-serve percentage is 64.0%
74 ÷ 112 = 0.6607, so first-serve points won is 66.1%
175 − 112 = 63 second serves played, and 30 ÷ 63 = 0.4762, so second-serve points won is 47.6%
74 + 30 = 104 service points won, and 104 ÷ 175 = 0.5943, so service points won is 59.4%
These are Rod Cross's published figures for Nadal in the 2009 Australian Open men's final, where he gives 64%, 66% and 48% — reproduced to the figures he prints
Check the identity: 0.6400 × 0.6607 + 0.3600 × 0.4762 = 0.5943, the same as 104 ÷ 175
Double all four counts — 350, 224, 148, 60 — and every percentage is unchanged, which is the check that these really are rates
Enter 120 first serves in from 175 service points with 130 points won on first serve and the panel refuses: you cannot win more points on first serve than you landed first serves
The four rates, and the four things they divide by
| Rate | Numerator | Denominator | Where the definition was read |
|---|---|---|---|
| First-serve percentage | First serves in | Service points played — every point starts with a first serve | Cross, Grand Slam Statistics, June 2009; named % 1st Serve by the ATP |
| First-serve points won | Points won on first serve | First serves in — not the service points played | Cross: “fraction of good first serves won by the server”; named % 1st Serve Points Won by the ATP; LTA in words |
| Second-serve points won | Points won on second serve | Second serves played — service points minus first serves in, double faults included | Cross: “fraction of second serves won by the server”; named % 2nd Serve Points Won by the ATP |
| Service points won | Points won on first and second serve together | Service points played again | Cross: “p(A) = (W1 + W2)/(N1 + N2)” |
One player leads on first-serve percentage by twenty points and wins fewer service points
| Player X | Player Y | Who leads | |
|---|---|---|---|
| Service points played | 100 | 100 | Level |
| First serves in | 70 | 50 | X |
| Points won on first serve | 42 | 38 | X |
| Points won on second serve | 12 | 20 | Y |
| First-serve percentage | 70.0% | 50.0% | X, by twenty points |
| First-serve points won | 60.0% | 76.0% | Y, by sixteen |
| Second-serve points won | 40.0% | 40.0% | Level |
| Service points won | 54.0% | 58.0% | Y |
Two numbers that look like the same number
A stats sheet prints first-serve percentage next to first-serve points won and they are not the same kind of figure. The first asks how often the first serve landed in; the second asks how often the player then won the point. A player who lands 70 first serves in 100 points and wins 42 of them has a first-serve percentage of 70.0 and a first-serve win rate of 60.0, and the two describe different things about the same hundred points.
The four figures divide by three different things, and that is the whole reason they are confused. First-serve percentage divides by every service point played, because every service point starts with a first serve. First-serve points won divides by the first serves that landed in. Second-serve points won divides by the second serves played, which is every service point where the first serve missed — double faults included, which is why the figure looks low. And service points won divides by every service point played again: those two are the only pair on the page that share a denominator. A double fault is a second-serve point lost, so it sits in that third denominator and in no numerator anywhere. Second-serve points won in the low fifties is a good day’s work; first-serve points won in the low fifties is a bad one, and reading the two on one scale is how a reader concludes that a professional cannot hit a second serve.
Where these definitions come from is not where you would expect, and the page says so rather than dressing it up. The ATP publishes three of the four by name on its own stats leaderboard and publishes no definition of any of them: the page read carried no tooltip, no glossary and about 5,000 characters of navigation and unfilled template placeholders, with the figures themselves rendered by JavaScript. The LTA, the ITF’s national association for Great Britain, defines three of them in words — first-serve points won is the “Number of points won after a player lands a first serve” — and states no denominator for any. Two fetches of the 2026 WTA Official Rulebook never reached its glossary. The only source read that states every denominator is Rod Cross’s Grand Slam Statistics primer of June 2009, a physicist’s teaching page rather than a governing body’s document.
Cross’s numbers are the worked example above, from the 2009 Australian Open men’s final: 175 first serves, “112 of those or 64% were good”, “66% of his good 1st serves, or 74 out of 112”, and “48% or 30 of his 63 2nd serves”. The 175 is corroborated by a second, independent record of the same match. He also gives the identity that ties the four rates together, “p = fw + (1 – f) s”: put those figures in and it returns 0.5943, which is 104 divided by 175 — and that is the input the game and set win probability calculator asks for. Only his service-point figures are used here, because those are the ones a second source corroborates; his game-level counts for the same match do not reconcile with each other and are handled on the page that needs them. For the games these points add up to see the dominance and service hold calculator, and for the points that decide a service game, the break point conversion and save calculator.
Frequently asked questions
What is a good first serve percentage in tennis?
No governing body or tour publishes a threshold, so this page prints no bands and claims no target. What can be said is the trade: raising the percentage usually means taking pace off the serve, which lowers first-serve points won, and the two can cancel entirely in the service-points-won figure. The percentage alone is the least informative of the four rates here.
Is first serve percentage the same as first serve points won?
No, and they have different denominators. The percentage is first serves in over service points played; points won is points won on first serve over the first serves that went IN. A player can lead one and trail the other by a wide margin — the table above constructs a case with a twenty-point gap one way and sixteen the other.
Why is second serve points won so much lower?
Because its denominator contains every double fault: the second serves played are the points where the first serve missed, and a double fault is one of them, lost. A second serve is also slower and safer, hit under the threat of losing the point outright, so the opponent attacks it. Both effects push the same way.
Where do aces and double faults fit in these four rates?
An ace is a point won, almost always on a first serve, so it sits inside points won on first serve and nowhere else. A double fault is a second-serve point lost, so it sits in the second-serve denominator and in no numerator. Neither has a rate of its own here: the ATP publishes both as averages per match, and a per-match average is not a rate of the kind this page computes.
Can these figures be compared between two sources?
Only with care. The counts are objective, but whether a let, a stoppage or a retired match is included is the compiler’s convention, and no tour publishes its convention anywhere read here. Take all four counts from one sheet and one period.
Related calculators
References
- Cross R. “Grand Slam Statistics”, June 2009, physics.usyd.edu.au/~cross/StatisticsPrimer.htm. A physicist’s teaching page, and the only source read that states every DENOMINATOR: first serve % is the “fraction of first serves that went in”, winning % on 1st serve the “fraction of good first serves won by the server”, winning % on 2nd serve the “fraction of second serves won by the server”, and break point conversion the “fraction or percentage of break point opportunities won (converted) by the receiver”. It gives the decomposition “p = fw + (1 – f) s” with “f = N1/(N1 + N2), w = W1/N1 and s = W2/N2”, equal to “p(A) = (W1 + W2)/(N1 + N2)”. Its worked figures are the 2009 Australian Open men’s final: 175 first serves, 112 in (64%), 74 of 112 won (66%), 30 of 63 second serves won (48%), and “16 opportunities to break Federer’s serve” with “7 occasions” successful. Its game-level figures — “they each stepped up to serve 25 times”, 18/25 and 19/25, and Federer breaking “6 times” at a stated 32% — do not reconcile with each other or with the published 51-game score, and the batch says so on the pages that use it.
- ATP Tour. “Stats Leaderboard”, atptour.com/en/stats/leaderboard. Read for the statistic NAMES the tour publishes: % 1st Serve, % 1st Serve Points Won, % 2nd Serve Points Won, % Service Games Won, Avg. Aces/Match and Avg. Double Faults/Match; and on the return side % 1st Serve Return Points Won, % 2nd Serve Return Points Won, % Return Games Won and % Break Points Converted. The page carries NO definitions and no tooltips: about 5,000 characters came back, mostly navigation and unfilled template placeholders such as {{playerData.PlayerFirstName}}, so the figures themselves are rendered by JavaScript and were not in the fetch. Cited as evidence of what the tour publishes and what it does not.
- Lawn Tennis Association. “Tennis stats explained”, lta.org.uk/fan-zone/tennis-stats-explained/. The ITF’s national association for Great Britain. First serve points won is the “Number of points won after a player lands a first serve” and second serve points won the same “after a player lands a second serve”; serve percentage is “How often a player lands their serve in”; a break point is where “the returner can win the game (AKA break serve) if they win the next point”, converted “as a returner – resulting in a break of serve” and saved “as the server – preventing their opponent from breaking their serve”. It states no denominator for any of them and does not define service games won or return games won at all.
- voodemar.com, “AO09 Nadal–Federer” match page. Read as a second, independent source for the service-point totals in that final: “19 % Nadal – 34 of 175” and “23 % Federer – 40 of 172”, so 175 and 172 service points, the two totals Cross also uses. Its points-by-set line, “42-36, 27-36, 52-50, 25-36, 27-16”, sums to 173 and 174. It credits no source, so it is used only to corroborate figures another source already states.
- WTA. 2026 Official Rulebook, “Copyright 2026 WTA Tour, Inc.”, fetched from photoresources.wtatennis.com. Section I.C: “The ITF Rules of Tennis shall apply to all WTA Tournaments except as amended by the Rules.” RECORDED AS A NON-CLAIM: the document runs past 560 pages and neither of two fetches reached its scoring provisions, its Glossary (Appendix M) or its ITF Rules excerpt (Appendix N). No WTA scoring rule and no WTA statistical definition is asserted anywhere in this batch, because none was read.