Abstract

ATP players like Maxime Cressy and Alexander Zverev have made waves in the past few years, hitting only first serves, including first serves on their second serves. Is it a viable strategy for players? Or is the normal way of play hitting first and second serves still dominant? Using expected mean I can calculate the win probability before a single point for hitting first serves, normal serves, or second serves.

Each serve and each point after hitting the serve in are mutually exclusive events. So on a given point there are 4 mutually exclusive events - hitting the first serve in, winning the point on a first serve in, hitting the second serve in after missing the first serve, and winning the point on a second serve in.

It is also important to note that the probability of 2 mutually exclusive events both occurring (p(A) and p(B)) is equivalent to p(A) x p(B), and the probability of one of 2 mutually exclusive events occurring (p(A) or p(B)) is p(A) + p(B). In this case the events can be split up in 3 ways. winning the point hitting only first serves, winning the point hitting normal serves, and winning the point hitting only second serves.

These 3 events translate to:

The likelihood of winning one point hitting only first serves = p(win the point on the first serve) = (first serve in %) and (first serve win %) OR p(win the point on the second serve) = (first serve out % and first serve in %) and (first serve win %).

Which mathematically translates to:

p(point WP) = p(first serve win) + p(second serve win) = ((first serve in %) x (first serve win %)) + ((1 - first serve in %) x (first serve in %) x (first serve win %))

The likelihood of winning one point hitting normal serves = p(win the point on the first serve) = (first serve in %) and (first serve win %) OR p(win the point on the second serve) = (first serve out % and second serve in %) and (second serve win %)

Which mathematically translates to:

p(point WP) = p(first serve win) + p(second serve win) = ((first serve in %) x (first serve win %)) + ((1 - first serve in %) x (second serve in %) x (second serve win %))

The likelihood of winning one point hitting only second serves = p(win the point on the first serve) = (second serve in %) and (second serve win %) OR p(win the point on the second serve) = (second serve out % and second serve in %) and (second serve win %)

Which mathematically translates to:

p(point WP) = p(first serve win) + p(second serve win) = ((second serve in %) x (second serve win %)) + ((1 - second serve in %) and (second serve in %) x (second serve win %))

Lets say a given player hits their first serve in 60% of the time, wins 90% of first serve points, hits their second serve in 90% of the time, and wins 50% of the points.

first serve in % = 60% = 0.6

first serve win % = 90% = 0.9

second serve in % = 90% = 0.9

second serve win % = 50% = 0.5

What is their point win probability hitting only first serves?

WP = (.6) x (.9) + (1 - .6) x (.6) x (.9) = .54 + .216 = .756,

meaning that over the course of 1000 points, hitting only first serves would win 756 points.

What is their point win probability hitting normal serves?

WP = (.6) x (.9) + (1 - .6) x (.9) x (.5) = .54 + .18 = .720,

meaning that over the course of 1000 points, hitting normal serves would win 720 points.

What is their point win probability hitting second serves?

WP = (.9) x (.5) + (1 - .9) x (.9) x (.5) = .45 + .045 = .495,

meaning that over the course of 1000 points, hitting only second serves would win 495 points.

Mathematically and logically it would make sense for this player to hit only first serves. This is due in part to the fact that they hit their first serve in more often than they win second serve points. They are 1.2 times more likely to hit their first serve in with a 90% win rate than win their second serve point, hitting it in 90% of the time, meaning this player can expect to have won 12 points hitting only first serves, and only 10 points hitting a first and second serve.

For measuring each players serve ability, I will be using expected mean to calculate their point win probability under 3 different circumstances: the likelihood they win a point with the intention of hitting two first serves, the likelihood they win a point with the intention of hitting a first and second serve, and the likelihood they win a point with the intention of hitting two second serves.

Players who should hit only First Serves
Player Point Win Probability Hitting First Serves Point Win Probability Hitting Normal Serves Point Win Probability Hitting Second Serves
Alastair Gray 64.6 % 63.9 % 50.2 %
Alexander Bublik 66 % 65 % 53.3 %
Alexander Zverev 69.2 % 67.5 % 55.6 %
Altug Celikbilek 68.6 % 68.5 % 54 %
Antoine Bellier 69.4 % 66.1 % 51.9 %
Arthur Rinderknech 66.3 % 66 % 51.3 %
Blaise Bicknell 61.2 % 60.4 % 49.1 %
Borna Gojo 67.4 % 65.5 % 54.5 %
Cedrik Marcel Stebe 68.7 % 67.4 % 49.7 %
Christopher Eubanks 68.8 % 67.5 % 54.7 %
Denis Istomin 64.6 % 61.5 % 43 %
Dominic Stricker 67.8 % 67.2 % 52.2 %
Dragos Nicolae Madaras 48 % 47.2 % 36.5 %
Emilio Nava 58.7 % 57.6 % 45.2 %
Feliciano Lopez 56.9 % 56.9 % 44.6 %
Gijs Brouwer 65.7 % 65.1 % 51.4 %
Hugo Grenier 64.9 % 63.6 % 50.3 %
Jiri Vesely 66 % 65.9 % 57.3 %
John Isner 73.2 % 72.4 % 58.2 %
Learner Tien 58.9 % 56.8 % 41.9 %
Lukas Rosol 72.6 % 66.4 % 40.3 %
Marco Trungelliti 65.6 % 63.8 % 47.3 %
Marko Topo 57.5 % 56.9 % 42.2 %
Matheus Pucinelli De Almeida 54.5 % 53.2 % 41.4 %
Max Hans Rehberg 54.8 % 54.5 % 44 %
Max Purcell 58.1 % 57.7 % 43.6 %
Michael Mmoh 61.9 % 60.7 % 51 %
Nicolas Jarry 70 % 69.9 % 54.5 %
Nicolas Kicker 60.3 % 59.3 % 47.7 %
Nicolas Mejia 56.5 % 55.3 % 40.2 %
Philipp Kohlschreiber 62.3 % 61.3 % 48.8 %
Robin Haase 62.7 % 60.5 % 42.7 %
Sam Querrey 65.3 % 64.7 % 51.2 %
Stefan Kozlov 56.3 % 55.8 % 51.8 %
Taro Daniel 61.4 % 61.3 % 47.1 %
Thanasi Kokkinakis 67.4 % 67.4 % 53.5 %
Jarrett Markman | Data: Jeff Sackmann - GitHub

It’s no surprise that someone like Alexander Zverev is on this list, given how much he struggles with his second serve. The reason why many of the players on this list are here is due to the fact that their second serves are very weak. For most these players there is larger than 10% separated between the win probability hitting first serves than the win probability hitting second serves. This can be due to a multitude of factors, such as an extremely low second serve win %, or an extremely low second serve in %, as well as the server possibly having such great first serve numbers. Zverev is a great example of this, because his first serve is great, however, his second serve is extremely inconsistent, often resulting in double faults, or opponents pouncing on the poor serve.

Players who should hit only Second Serves
Player Point Win Probability Hitting Second Serves Point Win Probability Hitting Normal Serves Point Win Probability Hitting First Serves
Christian Harrison 65.5 % 63.6 % 59.2 %
Filip Horansky 68.4 % 63.4 % 58.1 %
Lukas Klein 71.3 % 66.7 % 61.4 %
Nuno Borges 66.4 % 66 % 60.3 %
Sergey Fomin 62.3 % 62.2 % 59.1 %
Timofey Skatov 61.5 % 56.5 % 52.8 %
Jarrett Markman | Data: Jeff Sackmann - GitHub

This is most likely due in part for the opposite reason as only first servers. It’s possible that they have a first serve that struggles to go in, or one that is ineffective, especially in comparison to a second serve that is much more likely to go in. It’s possible that some of these players have very good second serves or very poor first serves, or both.

Players who should hit only Normal Serves
Player Point Win Probability Hitting Normal Serves Point Win Probability Hitting First Serves Point Win Probability Hitting Second Serves
Adrian Mannarino 65.2 % 60.7 % 58.5 %
Albert Ramos 61.2 % 58.3 % 55.4 %
Alejandro Davidovich Fokina 62.2 % 59.4 % 58.5 %
Alejandro Tabilo 60.7 % 59.7 % 51.9 %
Aleksandar Vukic 69.4 % 64.4 % 60.9 %
Aleksandre Metreveli 52.7 % 45.6 % 51.2 %
Alex Bolt 59.6 % 58.7 % 51.4 %
Alex De Minaur 63.1 % 58.2 % 57 %
Alex Molcan 63 % 59.9 % 57.8 %
Alexander Ritschard 60.1 % 57.3 % 50.3 %
Alexei Popyrin 63.1 % 62.3 % 52.7 %
Alexis Galarneau 56.9 % 55.6 % 48.8 %
Aljaz Bedene 60.4 % 57.9 % 50.4 %
Andreas Seppi 59.9 % 57.3 % 49.4 %
Andres Martin 67.6 % 67.1 % 51.2 %
Andrey Rublev 65.8 % 64.6 % 53.9 %
Andy Murray 65 % 62.7 % 54.5 %
Aqeel Khan 66.7 % 63.1 % 59.2 %
Aristotelis Thanos 58 % 56.4 % 51.7 %
Arjun Kadhe 56.5 % 55.6 % 43.3 %
Aslan Karatsev 61.4 % 58.2 % 56 %
Ben Shelton 68.8 % 65.5 % 61.3 %
Benjamin Bonzi 66.5 % 63 % 57.8 %
Benoit Paire 57.4 % 55.6 % 47.6 %
Bernabe Zapata Miralles 55.1 % 52.4 % 50.1 %
Borna Coric 64.7 % 59.7 % 58.1 %
Botic Van De Zandschulp 63.1 % 62 % 55 %
Brandon Holt 62.1 % 58.4 % 54.2 %
Brandon Nakashima 67 % 65 % 56.7 %
Cameron Norrie 64.6 % 62.5 % 55.9 %
Carlos Alcaraz 66.3 % 63.4 % 61.1 %
Carlos Taberner 58.5 % 57.8 % 52.2 %
Casper Ruud 68.1 % 65.8 % 59.2 %
Cem Ilkel 61.4 % 60.2 % 52.5 %
Christopher Oconnell 62.6 % 60.3 % 53.2 %
Chun Hsin Tseng 58.9 % 52.5 % 55.8 %
Corentin Moutet 61.9 % 59 % 56.8 %
Cristian Garin 58.4 % 56.2 % 51.4 %
Damir Dzumhur 57.8 % 54 % 53.3 %
Daniel Altmaier 60.5 % 59.1 % 50.4 %
Daniel Elahi Galan 61.3 % 58.1 % 53.1 %
Daniel Evans 64.2 % 62.4 % 54.4 %
Daniil Medvedev 67.5 % 66.1 % 59.1 %
David Goffin 61.3 % 57.9 % 53.8 %
Denis Kudla 61.5 % 58.7 % 53.7 %
Denis Shapovalov 66.8 % 64.4 % 62.2 %
Dennis Novak 61.8 % 61.6 % 50.4 %
Diego Schwartzman 58.4 % 56.8 % 54.3 %
Dominic Thiem 62.3 % 58.7 % 56.2 %
Dominik Koepfer 59.9 % 56.3 % 59.7 %
Dusan Lajovic 60.8 % 58.6 % 53.8 %
Egor Gerasimov 61.3 % 61.3 % 50.3 %
Elias Ymer 64.4 % 60.6 % 58.6 %
Emil Ruusuvuori 63 % 61.8 % 57.9 %
Emilio Gomez 56.8 % 53.3 % 52 %
Enzo Couacaud 67.5 % 61.1 % 65.2 %
Ernesto Escobedo 59.4 % 57.6 % 55.6 %
Fabio Fognini 59.7 % 55.1 % 57 %
Facundo Bagnis 60.9 % 57.4 % 55 %
Federico Coria 59.7 % 57.4 % 55.1 %
Federico Delbonis 59.4 % 58.1 % 52.8 %
Felix Auger Aliassime 66.5 % 66.1 % 56.1 %
Fernando Verdasco 59.7 % 56.6 % 53.9 %
Filip Krajinovic 62.1 % 59.3 % 54.9 %
Filip Misolic 59.7 % 53.4 % 54.3 %
Frances Tiafoe 64.6 % 60.3 % 55.3 %
Francisco Cerundolo 60.5 % 56.8 % 55.7 %
Franco Agamenone 59.3 % 57 % 54.1 %
Gael Monfils 65.9 % 63.3 % 58.6 %
Gian Marco Moroni 58.2 % 56.4 % 57 %
Gianluca Mager 64.5 % 63.8 % 53 %
Gilles Simon 59.8 % 58.5 % 50.2 %
Giulio Zeppieri 63.9 % 62.4 % 52.9 %
Grigor Dimitrov 66.4 % 64.8 % 57.6 %
Henri Laaksonen 57.6 % 54.3 % 48.8 %
Holger Rune 62.1 % 59.5 % 57.3 %
Hubert Hurkacz 69.4 % 67.4 % 58 %
Hugo Dellien 58.9 % 58 % 53.9 %
Hugo Gaston 58.6 % 53.7 % 51.9 %
Ilya Ivashka 62.8 % 61.4 % 53 %
Ivan Gakhov 63 % 59.4 % 55.4 %
J J Wolf 62 % 61.3 % 50.8 %
Jack Draper 64.4 % 60.2 % 56.9 %
Jack Sock 63.4 % 61.4 % 57 %
James Duckworth 62.7 % 57.5 % 53.8 %
Jan Lennard Struff 64.8 % 60.5 % 58.1 %
Jannik Sinner 65.8 % 61.8 % 57.7 %
Jason Kubler 65.1 % 62.3 % 58.6 %
Jaume Munar 61.1 % 59.2 % 54.8 %
Jay Clarke 58.2 % 51.8 % 55.2 %
Jenson Brooksby 62.2 % 59 % 56.1 %
Jiri Lehecka 62.1 % 59.7 % 55 %
Jo-Wilfried Tsonga 65.5 % 62.8 % 54.5 %
Joao Sousa 62.3 % 58.3 % 54.9 %
Johan Nikles 58.7 % 54.5 % 53.3 %
John Millman 63.1 % 57.1 % 60.6 %
Jordan Thompson 63.3 % 63.1 % 50.3 %
Jozef Kovalik 56.3 % 54.3 % 52.4 %
Juan Alejandro Hernandez Serrano 48.9 % 45.8 % 45.4 %
Juan Ignacio Londero 61.1 % 59.7 % 51.5 %
Juan Manuel Cerundolo 56.7 % 53.9 % 53.2 %
Juan Pablo Ficovich 60 % 59 % 51.5 %
Juan Pablo Varillas 61.6 % 54.6 % 55.8 %
Juncheng Shang 55.8 % 55.4 % 49.7 %
Jurij Rodionov 65.4 % 64.8 % 55.8 %
Kamil Majchrzak 64 % 60.2 % 56.1 %
Karen Khachanov 65.8 % 64.2 % 55.8 %
Kevin Anderson 70.3 % 68.9 % 60.3 %
Kyle Edmund 58 % 57.8 % 44 %
Laslo Djere 64 % 61.6 % 56 %
Leandro Riedi 60.5 % 57.7 % 54.7 %
Liam Broady 60.6 % 58.5 % 53.1 %
Lloyd Harris 64.3 % 63.6 % 50.7 %
Lorenzo Musetti 62.3 % 58.3 % 57.9 %
Lorenzo Sonego 64.2 % 63.5 % 54 %
Luca Nardi 56.7 % 50.2 % 55.8 %
Lucas Catarina 55.6 % 54.7 % 47.9 %
Lucas Pouille 60.2 % 57.3 % 51.6 %
Mackenzie Mcdonald 61.5 % 59.6 % 52.9 %
Malek Jaziri 59.1 % 54.4 % 49.9 %
Manuel Guinard 58.9 % 57 % 54.3 %
Marc Andrea Huesler 67.6 % 63.9 % 59.4 %
Marco Cecchinato 57.6 % 56.7 % 48.4 %
Marcos Giron 63.4 % 59.4 % 55.2 %
Marin Cilic 67.3 % 65.2 % 56.4 %
Marius Copil 56.1 % 55.4 % 45.2 %
Marton Fucsovics 62.7 % 58.9 % 58.1 %
Matteo Berrettini 68.8 % 68.2 % 55.7 %
Maxime Cressy 69 % 66.6 % 68.3 %
Maximilian Marterer 60.8 % 57.6 % 51.3 %
Michail Pervolarakis 58.8 % 55.7 % 49.8 %
Mikael Ymer 59.9 % 57.3 % 55.4 %
Mikhail Kukushkin 59.3 % 53.4 % 58.9 %
Mili Poljicak 52 % 50.2 % 40.5 %
Miomir Kecmanovic 64.5 % 60 % 58.8 %
Mirza Basic 60.3 % 52.7 % 55.2 %
Mitchell Krueger 63.9 % 62.4 % 56.6 %
Mohamed Safwat 68.5 % 64.9 % 60.3 %
Muhammad Shoaib 57.8 % 56.2 % 46.7 %
Nick Kyrgios 71.2 % 70.5 % 63 %
Nicola Kuhn 61.7 % 58.9 % 59.2 %
Nikola Milojevic 59.9 % 56 % 57.4 %
Nikoloz Basilashvili 58.7 % 55.7 % 51.6 %
Norbert Gombos 63.2 % 61.3 % 55.1 %
Novak Djokovic 67.9 % 64.8 % 60.7 %
Oscar Otte 64.7 % 62 % 55.8 %
Otto Virtanen 57.7 % 55 % 47.6 %
Pablo Andujar 57.2 % 55.9 % 53 %
Pablo Carreno Busta 65.8 % 62.8 % 60 %
Pablo Cuevas 63.4 % 61.3 % 56.1 %
Paul Jubb 62.5 % 60.1 % 55.9 %
Pavel Kotov 55.8 % 54.5 % 46.8 %
Pedro Cachin 63.7 % 61.2 % 54.2 %
Pedro Martinez 60.4 % 56.6 % 59.2 %
Peter Gojowczyk 57.5 % 51.5 % 53.7 %
Petros Chrysochos 55.3 % 50.2 % 50.8 %
Petros Tsitsipas 61.4 % 53.6 % 60.4 %
Pierre Hugues Herbert 63 % 61 % 54.2 %
Quentin Halys 66.8 % 65.3 % 54.9 %
Radu Albot 63.3 % 61.7 % 54.7 %
Rafael Nadal 66.6 % 63.8 % 61.9 %
Ramkumar Ramanathan 66.8 % 65.3 % 64.6 %
Reilly Opelka 72.2 % 70 % 62.5 %
Ricardas Berankis 63 % 60.1 % 54.7 %
Richard Gasquet 62.5 % 58.3 % 56 %
Rinky Hijikata 58.8 % 55.3 % 50.6 %
Roberto Bautista Agut 65.9 % 63.6 % 58.3 %
Roberto Carballes Baena 60.6 % 56.2 % 56.9 %
Roman Safiullin 66.6 % 63.7 % 58.2 %
Rowland Phillips 64.6 % 60.2 % 56.4 %
Ryan Peniston 62.3 % 60.8 % 53.8 %
Sanjar Fayziev 59.8 % 54.9 % 51.8 %
Sebastian Baez 61.1 % 59.2 % 58.2 %
Sebastian Korda 61.7 % 59.9 % 53 %
Sebastian Ofner 57.2 % 56 % 43.5 %
Soon Woo Kwon 60.8 % 57.7 % 53.4 %
Stan Wawrinka 63.1 % 58.6 % 52.8 %
Stefano Travaglia 60.8 % 56.1 % 54.8 %
Stefanos Tsitsipas 67.7 % 64.7 % 58.5 %
Steve Johnson 66.5 % 62.8 % 57.8 %
Steven Diez 53.6 % 51.2 % 47.3 %
Tallon Griekspoor 65.1 % 62.7 % 56.9 %
Taylor Fritz 67.5 % 65.2 % 57.2 %
Tennys Sandgren 58.8 % 58.3 % 47.5 %
Thiago Monteiro 66.9 % 64.4 % 58.4 %
Thiago Seyboth Wild 57.8 % 54.5 % 51.9 %
Tim Van Rijthoven 70.8 % 68.4 % 62.5 %
Tomas Machac 61.1 % 56 % 58.1 %
Tomas Martin Etcheverry 58.9 % 58.3 % 52.3 %
Tommy Paul 63.7 % 61.4 % 54.7 %
Ugo Humbert 62.1 % 59.1 % 55.4 %
Vasek Pospisil 67.4 % 67.4 % 53.4 %
Viktor Durasovic 55.5 % 54.9 % 44.1 %
Vit Kopriva 56 % 52.2 % 53 %
Yannick Hanfmann 63.9 % 61.3 % 54.7 %
Yibing Wu 62.8 % 57.5 % 60.9 %
Yoshihito Nishioka 60.6 % 55.9 % 58.1 %
Yosuke Watanuki 62.7 % 58.3 % 53.9 %
Yuki Bhambri 61.6 % 59.6 % 52 %
Zhizhen Zhang 67.5 % 65.3 % 60.1 %
Zizou Bergs 65.4 % 63.1 % 57.6 %
Jarrett Markman | Data: Jeff Sackmann - GitHub

Most players based on last year’s data would appear to find no additional success by changing up their service strategy. This is most likely due in part to having a good/solid first serve, and a good/solid second serve, and not having an outlying statistic causing their percentages to drop - for example a very low first serve in % (ie. 40%) would most likely indicate that they player should not hit many first serves, because they don’t go in often.

Conclusion

For some players, sacrificing the increased likelihood of a double fault is worth it to make up for the low chance of winning a second serve point - whether there is a poor second serve in % or second serve win %. For others, forgoing an inconsistent/ineffective first serve to prevent any double faults and being consistent with each serve is worth it to make up for that inconsistent/ineffective first serve. However, for many players - barring an extremely good or poor first or second serve - it makes the most sense for them to continue to hit normal first and second serves, because it gives them the best chance to win points on a regular basis.