Tennis Dominance and Service Hold Calculator
Tennis Dominance and Service Hold Calculator
Service games won, return games won, and the ratio between breaking and being broken. The two rates are published by the ATP as names; the ratio is an analytics convention with no governing body behind it, and this page says which is which.
Hold, break and the ratio between them
Service games won ÷ played22 of 26 service games won, and 6 of 25 return games won
Two rates, one ratio, and who publishes what
Return games won = (return games won ÷ return games played) × 100
All games won = ((service games won + return games won) ÷ all games played) × 100
Games dominance ratio = return-game win rate ÷ service-game loss rate
- holding and breaking
- the same arithmetic from the two ends of the court: holding is winning a game you served, breaking is winning a game your opponent served. The ATP publishes % Service Games Won and % Return Games Won on its own leaderboards and defines neither, and the LTA’s glossary defines neither either — which is as close to an official source as this batch could find. Service alternates every game, so the two players’ counts differ by at most one, and a source that gives both players 25 service games in a 51-game match has an error in it
- the dominance ratio, and whose it is not
- nobody’s, officially. The only published arithmetic read for one is Ultimate Tennis Statistics’ glossary, published by Strange Forest Software: “Points Dominance Ratio: % of return points won divided by % of service points lost”. That glossary also lists a Games Dominance Ratio without printing its arithmetic, and cites no source for either. Tennis Abstract’s glossary names DR and declines to define it, saying only that “DR is similar to total points won, as a good first-order proxy of how well a player performed”. The row on this page applies the published POINTS definition to GAMES, which is this site’s own choice and not a standard
- how to read the ratio
- the break rate divided by the rate at which this player’s own serve was broken, so above one is a player winning the exchange of breaks. It has no upper bound and it is undefined — shown as no row at all — for a player never broken. The points version of the published definition needs return points won and service points won instead, which are on the first serve percentage and points won calculator
Worked example
22 of 26 service games won, and 6 of 25 return games won
22 ÷ 26 = 0.8462, so service games won — the hold rate — is 84.6%
6 ÷ 25 = 0.2400, so return games won — the break rate — is 24.0%
(22 + 6) ÷ (26 + 25) = 28 ÷ 51 = 0.5490, so all games won is 54.9%
26 − 22 = 4 times broken, against 6 breaks, so net breaks is +2
The ratio is 0.2400 ÷ (1 − 0.8462) = 0.2400 ÷ 0.1538 = 1.56: this player broke about one and a half times as readily as they were broken
Double all four counts — 44 of 52 and 12 of 50 — and both percentages and the ratio are unchanged
Halve the service games played to 13 with 22 won and the panel refuses, so for a rate check use a valid pair: 11 of 13 is 84.6% as well, the same rate from half the games
Set the service games won equal to the service games played — 26 of 26 — and the ratio row vanishes rather than printing a huge number: a player who was never broken has no ratio
These counts are CONSTRUCTED, not observed: the one published set of game-level figures this batch found does not reconcile with itself
Who publishes what, on this page’s four figures
| Figure | Published by a governing body or tour? | What this page does |
|---|---|---|
| Service games won (hold %) | The ATP publishes the rate by name — % Service Games Won — on its own stats leaderboard, with no definition anywhere read | Computes it and names the publisher of the name |
| Return games won (break %) | The ATP publishes % Return Games Won the same way, again with no definition | Computes it and names the publisher of the name |
| All games won | No. It is the sum of the two numerators over the sum of the two denominators | Computes it as plain arithmetic and claims no publisher |
| Dominance ratio | No. The only published arithmetic read is Ultimate Tennis Statistics’ “% of return points won divided by % of service points lost”, over points and not games; Tennis Abstract names DR and does not define it | Computes the games analogue and says on the page that it is this site’s choice, not a standard |
| Pressure indices and tracking-data metrics | No, and each vendor fits its own | Not offered. No single formula to implement |
Hold and break across a range, with both refusals and the undefined ratio
| Service games | Hold % | Return games | Break % | All games % | Ratio | Net breaks |
|---|---|---|---|---|---|---|
| 26 of 26 | 100.0% | 6 of 25 | 24.0% | 62.7% | No row — never broken | +6 |
| 22 of 26 | 84.6% | 6 of 25 | 24.0% | 54.9% | 1.56 | +2 |
| 22 of 26 | 84.6% | 4 of 25 | 16.0% | 51.0% | 1.04 | 0 |
| 22 of 26 | 84.6% | 2 of 25 | 8.0% | 47.1% | 0.52 | −2 |
| 11 of 13 | 84.6% | 3 of 12 | 25.0% | 56.0% | 1.63 | +1 |
| 44 of 52 | 84.6% | 12 of 50 | 24.0% | 54.9% | 1.56 | +4 |
| 13 of 26 | 50.0% | 13 of 25 | 52.0% | 51.0% | 1.04 | 0 |
| 0 of 26 | 0.0% | 6 of 25 | 24.0% | 11.8% | 0.24 | −20 |
| 30 of 26 | Refused | 6 of 25 | Refused | Refused | Refused | Refused |
Holding, breaking, and one figure with no publisher
A tennis match is won in games, and a game is either one you served or one your opponent served. Winning the first is holding; winning the second is breaking. The two rates are the cleanest summary of a tennis match there is, because unlike a points figure they are already in the currency the scoreboard uses. The ATP publishes both on its own stats leaderboard, as % Service Games Won and % Return Games Won, and publishes no definition of either: the page read carried the names, no tooltips and about 5,000 characters of mostly JavaScript template. The LTA’s glossary, which does define several serving statistics in words, does not mention service games won at all.
The counts are tied together more tightly than they look. Service alternates game by game, so the two players’ service-game totals differ by at most one, and one player’s return games played is exactly the other’s service games played. That is a useful arithmetic check on any statistics sheet, and it caught a problem in the one published set of game-level figures this batch found. One caution about the source of those numbers. Cross’s primer says of that final that “they each stepped up to serve 25 times”, and the published score — 7–5, 3–6, 7–6(7–3), 3–6, 6–2 — is 51 games once the tie-break is counted as the one game it is, so one player served 26 and the other 25 and the two cannot both be 25. Its own break counts disagree with its game counts by one in the same direction. The service-point figures are internally consistent and are corroborated by a second source, so those are the ones used here; the game-level figures are not. So the worked example above is constructed, and labelled as constructed, rather than quoting figures that cannot all be right.
The third figure needs a different kind of honesty, because a “dominance ratio” is widely used and published by nobody official. Ultimate Tennis Statistics, published by Strange Forest Software, prints arithmetic — “Points Dominance Ratio: % of return points won divided by % of service points lost”, over points and not games — and separately lists a Games Dominance Ratio without printing its arithmetic or citing a source for either. Tennis Abstract’s glossary names DR and declines to define it, offering only that “DR is similar to total points won, as a good first-order proxy of how well a player performed”. Neither is a governing body or a tour. So the ratio here is the published points definition applied to games, stated as this site’s choice rather than as the standard, and it reads simply: above one, you broke more readily than you were broken.
One behaviour of it is worth naming, because it is why the row sometimes disappears. Its denominator is the rate at which this player’s own serve was broken, and a player who held every service game has a denominator of nought. That is not an infinite ratio, it is no ratio: the quantity does not exist, so the row is suppressed rather than filled with a very large number. For the points inside these games see the break point conversion and save calculator and the first serve percentage and points won calculator, and for what a hold rate implies about a set and a match, the game and set win probability calculator takes a game-win probability and works the set out in closed form.
Frequently asked questions
What is a hold percentage in tennis?
Service games won divided by service games played. The ATP publishes the rate by name as % Service Games Won; no governing body or tour publishes a definition or a threshold for it anywhere read here, so this page prints no bands and claims no target. At professional level it is much higher than the break rate, because the server wins most points.
What is the dominance ratio in tennis?
It is a figure from the analytics community rather than from a governing body. The only published arithmetic found is Ultimate Tennis Statistics’, which defines a Points Dominance Ratio as the percentage of return points won divided by the percentage of service points lost. This page computes the games analogue — break rate divided by the rate at which the player’s own serve was broken — and says that the choice is this site’s rather than a standard.
Why does the ratio row sometimes disappear?
Because its denominator is the rate at which this player was broken, and a player who held every service game was broken at a rate of nought. A ratio with a zero denominator has no value rather than an infinite one, so the row is suppressed. Every other figure on the page still computes.
Is all games won the same as total points won?
No, and the two can disagree about who played better. In the 2009 Australian Open men’s final the winner took 173 points of 347 and the loser 174, on two sources’ agreeing figures, so the player who won more points lost the match. A points-based summary and a games-based one are different statistics and neither is wrong.
How does a hold percentage relate to a set win probability?
Through a per-game probability, but not directly. A hold rate describes only the games this player served, and a set contains both kinds. The set calculation on the probability page takes one per-game probability and says plainly that treating every game alike is an approximation.
Related calculators
References
- 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.
- Ultimate Tennis Statistics, glossary at ultimatetennisstatistics.com/glossary, © 2015-2026 Strange Forest Software. The only PUBLISHED arithmetic found for a dominance measure: “Points Dominance Ratio: % of return points won divided by % of service points lost”. The same glossary lists a Games Dominance Ratio without printing its arithmetic, and cites no source for either. Not a governing body and not a tour.
- Tennis Abstract (Heavy Topspin). “Point-by-Point Stats: Glossary”, tennisabstract.com/blog/?p=3727. “BP Conv: Break points converted (as returner), as a percentage of break point opportunities” and “BP Saved: Break points saved (as server), as a percentage of break points faced”. The same page names DR without defining it, saying only that “DR is similar to total points won, as a good first-order proxy of how well a player performed”. The post carries no byline; the site’s analytics are credited to Jeff Sackmann.
- 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.
- 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.
- Wikipedia. “2009 Australian Open – Men’s singles”. Read for one fact: the final’s score, “7–5, 3–6, 7–6(7–3), 3–6, 6–2”. Used because the games in it — 12 + 9 + 13 + 9 + 8 = 51, a tie-break counting as one game — are what shows that a secondary source’s “they each stepped up to serve 25 times” cannot be right. Nothing else is taken from it.
- 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.