Category: Double faults

The best players are able to work around their weaknesses. Coco Gauff is so solid that she has overcome two: an unreliable forehand and a second serve that hands too many points to her opponents. On Wednesday in Wuhan, Gauff coughed up 5 double faults out of 19 second serves. Despite surrendering more than 10% of her serve points for the fifth consecutive match, she eased past Viktoriya Tomova. The Bulgarian managed just three games.

The forehand is a subject for another day. Lately, the serve has been a bigger concern, the one blot on an eight-match win streak (and counting) in China.

Start with season totals. Through last week’s Beijing final, Gauff has missed more than one in five of her second serves. The result: She has double-faulted 8.9% of her 2024 service points. No other woman in the WTA top 60 has double faulted so often.

The typical tour regular loses barely half so many points this way. Tour average is 5.1%. Fellow elites Iga Swiatek, Jessica Pegula, and Jasmine Paolini come in at 3% or lower; Emma Navarro just misses that mark at 3.1%. Even Aryna Sabalenka, with her recurring bouts of service shakiness and occasional risk-taking on the second serve, gives away only 4.5% of points.

Still, Coco rates as the fourth-best player in the world. She’ll be back to #3 on Monday, and she has a good chance of ending the season there. The rest of her game is so sturdy that she has piled up nearly 50 wins on the season despite committing 274 more double faults than Swiatek has.

This is uncharted territory. In the last 15 years–the extent of my serve stats for women’s tennis–only two players have hit double faults so often and still managed to finish in the top five. No one has cracked the top three:

DF Rate  Player             Year  Rank  
  10.4%  Aryna Sabalenka    2022     5  
   9.6%  Maria Sharapova    2011     4  
   8.9%  Coco Gauff         2024     ?  
   8.7%  Elena Dementieva   2009     5  
   8.4%  Maria Sharapova    2015     4  
   8.1%  Dinara Safina      2008     3  
   7.9%  Dinara Safina      2009     2  
   7.9%  Maria Sharapova    2014     2  
   7.9%  Karolina Pliskova  2021     4  
   7.6%  Victoria Azarenka  2013     2  
   7.6%  Aryna Sabalenka    2021     2  
   7.5%  Maria Sharapova    2013     4  
   7.3%  Maria Sharapova    2012     2  
   7.0%  Venus Williams     2010     5

The typical year-end number one double faults only 4.1% of the time. Victoria Azarenka’s 2012 season, at 6.8%, was the only such occasion over 6%. This isn’t exactly a law of physics, but if Gauff is to dislodge the two women atop her in the ranking table, she’ll probably need to make a substantial move in that direction.

What-ifs

It’s no easy task to fix a leaky serve. The good news for Coco is that it may be all she needs to do.

Back to the season totals. Gauff is basically tied with Swiatek as the best returner in the game. The American has won 48.4% of her return points this year, compared to Iga’s 48.5%. Gauff has played slightly weaker opposition, but in any case, it’s a minor gap. Both women stand well above the pack; no one else tops 47.5%. With no double faults working against her, Coco’s return game is worthy of a world number one.

By service points won–where the double faults come into play–Gauff ranks a more pedestrian 12th. That’s entirely because of the deliveries that miss. She wins more first-serve points than anyone except for Qinwen Zheng and Elena Rybakina. In an era without megastars, the combination of 1st or 2nd on return and 12th on serve might be good enough to lead the field, but with an all-rounder like Swiatek and a dominant slugger like Sabalenka to contend with, it doesn’t do the job.

Here, then, is the what-if. Wave a magic wand and proclaim that all of Gauff’s second serves find the box. The 9% of her service points that end in double faults turn into second serves in play: points that she wins at a 56% clip.

Do that, and her rate of serve points won–currently at 60.2%, good for 12th place–becomes 65.3%, better than anybody. A double-fault-free Coco Gauff would rack up more serve points than anyone on tour, while still winning almost as many return points as Iga does. A handful of key points might swing the year-end number one in either direction, but statistically, the American would be the best player in the world.

You might argue that even in the rosiest real-life scenario, Coco isn’t going to eliminate double faults entirely. Fair enough. Reduce her double fault rate to tour average, and she wins 62.5% of service points. Not as good as Swiatek, Sabalenka, or Rybakina (or, technically, Lulu Sun in her limited tour-level action), but ahead of everybody else.

Combine serve and return into total points won (TPW%), and we see how these wishful adjustments move Gauff clear of the field–or, at least, everyone except for Iga:

TPW%   Player                      
56.9%  Coco Gauff (no dfs)  
56.5%  Iga Swiatek                 
55.4%  Coco Gauff (avg dfs)  
54.3%  Coco Gauff (actual)  
54.3%  Aryna Sabalenka             
53.7%  Elena Rybakina              
53.1%  Karolina Muchova            
52.9%  Qinwen Zheng                
52.8%  Danielle Collins            
52.7%  Mirra Andreeva              
52.6%  Jessica Pegula              
52.3%  Victoria Azarenka           
52.3%  Maria Sakkari               
52.3%  Paula Badosa                
52.1%  Madison Keys                
52.0%  Jasmine Paolini

Actual-Coco is already near the top of the list. Take away all or half of her double faults, and at the very least she looks stronger than Sabalenka and Rybakina.

The specifics

This may seem a bit too abstract, especially since the total-points-won list has so many differences from the official ranking table. Greatness is not measured by points, but by titles, and some trophies count much more than others.

Remember that these points we’re changing took place in real–often close–matches. Reversing just a few of the double faults would have tipped the scales in Gauff’s direction. In the counterfactual, she probably didn’t lose 15 matches this year. She likely picked up more than two titles.

Take the most painful loss of the season: Coco’s fourth round defeat at the US Open. Against Emma Navarro, she committed a gut-wrenching 19 double faults. Despite that, she won 46.8% of total points. All else equal, had she landed those 19 second serves, Gauff would have almost exactly flipped the tally, winning 53.0% of points. Even with a tour-average double fault rate, she would have won 51.0% of points and–barring bad luck or a ill-timed choke–earned a victory.

Run the same exercise for the American’s other defeats this year, and we see just how strong her season could have been. If we reduce her double faults to a tour-average 5.1%, 4 of her 15 losses probably would have gone her way. Two more matches would have ended within a point of 50/50, safely in the range where a clutch (or lucky) break point or two can reverse the result.

Cut out double faults entirely, and Gauff wins at least 50.8% of points in six of the losses. She would have cleared 48% in four more, putting those in the range where luck could hand her the victory.

Even in the more conservative scenario, Gauff’s campaign looks quite different. Instead of losing to Anna Kalinskaya in the Dubai quarters, she would have faced off with Iga in the semi-finals. She wouldn’t have lost to Marta Kostyuk in Stuttgart: She’d have played Marketa Vondrousova for a place in the final. In Madrid, she would have handily beaten Madison Keys, earning a quarter-final date with Ons Jabeur. Flip the Navarro result in New York, and Coco could well have defended her US Open title.

Today’s action in Wuhan offered a glimpse of a sturdier future. Gauff cast aside Kostyuk with nary a double fault, advancing to the quarters in just 61 minutes. It was her quickest match since April–against an opponent who has bedeviled her in the past–and her first double-fault-free outing in 14 months.

The American has somehow established herself as a top-five player and grand slam champion despite handing her opponents more free points than any of her peers. A stingier Coco Gauff could soon be the best player in the world.

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We all know that double faults aren’t good, but it’s less clear just how bad they are. Over the course of an entire match, a single point here or there doesn’t seem to matter too much, especially when a double fault creeps in at a harmless moment, like 40-love. Yet many missed second serves are far more costly. Let’s try to quantify the impact of tennis’s most enervating outcome.

To do this, we need to think in terms of win probability. In each match, a player wins a certain percentage of service points and a certain percentage of return points. If those rates are sufficiently dominating–say, Mihaela Buzarnescu’s 65% of service points won and 59% of return points won in last week’s San Jose final–the player’s chance of winning the match is 100%. No matter how unlucky or unclutch she was, those percentages result in a win. But in a close contest, in which both players win about 50% of points (often referred to as “lottery matches”), the result is heavily influenced by clutch play and luck. In Buzarnescu’s tour de force, flipping the result of a single point would be meaningless. But in a tight match, like the Wimbledon semifinal between John Isner and Kevin Anderson, a single point could mean the difference between a spot in the championship match and an early flight home.

My aim, then, is to measure the average win probability impact of a double fault. To take another example, consider last week’s Washington quarter-final between Andrea Petkovic and Belinda Bencic. Bencic won nearly 51% of total points–59% of her service points and 42% on return–but lost in a third-set tiebreak. Those serve and return components were enough to give her a 56.3% chance of winning the match: claiming more than half of total points usually results in victory, but so close to 50%, there’s plenty of room for things to go the other way.

I refer to this match because double faults played a huge role. Bencic tallied 12 double faults in 105 service points, a rate of 11.4%, more than double the WTA tour average of 5.1%. Had she avoided those 12 double faults and won those points at the same rate as her other 93 service points, she would have ended up with a much more impressive service-points-won rate of 67%. Combined with her 42% rate of return points won, that implies an 87% chance of winning the match–more than 30 percentage points higher than her actual figure! Roughly speaking, each of her 12 double faults cost her a 2.5% chance (30% divided by 12) of winning the match.

A double fault rate above 10% is unusual, but a cost of 2.5% per offense is not. When we run this algorithm across the breadth of the ATP and WTA tours, we find that the cost of double faults adds up fast.

Tour averages

Using the method I’ve described above–replacing double faults with average non-double-fault service points–and taking the average of all tour-level matches in 2017 and 2018 through last week’s tournaments, we find that the average WTA double fault costs a player 1.83% of a win. Put another way, every 55 additional double faults subtracts one match from the win column and adds one to the loss column.

In the men’s game, the equivalent number is 1.99% of a win. The slightly bigger figure is due to the fact that men, on average, win more service points, so the difference between a double fault and a successful service offering is greater.

There is, however, an alternative way we could approach this. By comparing double faults to all other service points, we’re trading a lot of the double faults for first serve outcomes. We might be more interested in knowing how a player would fare if his or her second serve were bulletproof–still eliminating double faults, but replacing them specifically with second serves instead of a generic mix of service points.

In that case, the algorithm remains very similar. Instead of replacing double faults with non-double-fault serve points, we replace them with non-double-fault second serve points. Then the cost of a double fault is a little bit less, because second serve points result in fewer points won than service points overall. The second-serve numbers are 1.61% per double fault in the women’s game and 1.70% per double fault in the men’s game. For the remainder of this post, I’ll stick with the generic service points, but one approach is not necessarily better than the other; they simply measure different things.

Building a player-specific stat

Odious as double faults are, they are not completely avoidable. Very few players are able to sustain a double fault rate below 2%, and tour averages are around twice that. Since the beginning of 2017, the ATP average has been about 3.9%, and the WTA average roughly 5.1%, as we saw above.

We can measure players by considering their match-by-match double fault rates compared to tour average. In Bencic’s unfortunate case, her 12 double faults were 6.7 more than a typical player would’ve committed in the same number of service points. In contrast, in the same match, Petkovic recorded only 3 double faults in 102 service points, 2.2 double faults fewer than an average player would have.

We know that each WTA double fault affects a player’s chances of winning the match by 1.83%, so compared to an average service performance, Bencic’s excessive service errors cost her about a 17% chance of winning (6.7 times 1.83%), while Petkovic’s stinginess increased her own odds by about 6.6% (2.2 times 1.83%).

Repeat the process for every one of a player’s matches, and you can assemble a longer-term statistic. Let’s start with the WTA players who, since the start of last season, have cost themselves the most matches (“DF Cost”–negative numbers are bad), along with those who have most improved their lot by avoiding double faults:

Player                   DF%  DF Cost  
Kristina Mladenovic     7.7%    -3.84  
Daria Gavrilova         7.9%    -3.77  
Jelena Ostapenko        7.7%    -3.58  
Petra Kvitova           8.1%    -3.01  
Camila Giorgi           8.3%    -2.63  
Oceane Dodin           10.2%    -2.51  
Donna Vekic             7.0%    -1.91  
Venus Williams          6.7%    -1.71  
Coco Vandeweghe         6.4%    -1.60  
Aliaksandra Sasnovich   6.7%    -1.55  
…                                      
Agnieszka Radwanska     2.3%     1.27  
Sloane Stephens         2.1%     1.43  
Caroline Wozniacki      3.2%     1.43  
Barbora Strycova        3.5%     1.47  
Elina Svitolina         3.9%     1.48  
Simona Halep            3.5%     1.53  
Qiang Wang              2.6%     1.54  
Anastasija Sevastova    3.1%     1.57  
Carla Suarez Navarro    2.1%     1.67  
Caroline Garcia         3.6%     1.82

And the same for the men:

Player                  DF%  DF Cost  
Benoit Paire           6.2%    -4.51  
Ivo Karlovic           5.8%    -3.63  
Fabio Fognini          5.0%    -2.38  
Denis Shapovalov       6.3%    -2.26  
Grigor Dimitrov        5.1%    -2.25  
Gael Monfils           5.0%    -2.22  
David Ferrer           5.2%    -2.06  
Jeremy Chardy          5.3%    -2.00  
Fernando Verdasco      4.8%    -1.94  
Jack Sock              4.8%    -1.73  
…                                     
Roger Federer          2.1%     0.88  
Tomas Berdych          2.9%     0.89  
Juan Martin del Potro  2.8%     0.93  
Albert Ramos           3.1%     0.97  
Pablo Carreno Busta    2.2%     1.07  
Richard Gasquet        2.6%     1.12  
John Isner             2.6%     1.23  
Dusan Lajovic          1.9%     1.23  
Denis Istomin          1.9%     1.23  
Philipp Kohlschreiber  2.5%     1.24

Situational double faults

These aggregate numbers have the potential to hide a lot of information. They consider only two things about each match: how many double faults a player committed, and how close the match was. This statistic would treat Bencic the same whether she hit nine of her double faults at 40-love, or nine of her double faults in the third-set tiebreak. Yet the latter would have a colossally greater impact.

While this is an important limitation to keep in mind, it appears that double faults are distributed relatively randomly. That is, most players do not hit a majority of their double faults in particularly high- or low-leverage situations. The player lists displayed above show both the most basic stat–double fault percentage–along with my more complex approach. For players with at least 20 matches since the beginning of last season, double fault rate is very highly correlated with the match-denominated cost of double faults. (For men, r^2 = 0.752, and for women, r^2 = 0.789.) In other words, most of the variance in double fault cost can be explained by the number of double faults, leaving little room for other factors, such as the importance of the situation when double faults are committed.

That said, there’s plenty of room for additional analysis into those specific sitations. Instead of taking a match-level look at win probability, as I have here, one could identify the point score of every single one of a player’s double faults, and see how each event affected the win probability of that match. I suspect that, for most players, that would amount to a whole lot of extra complexity for not a lot of added insight, but perhaps there are some players who are uniquely able to land their second serve when it matters most, or particularly prone to double faults at key moments. This match-level look has made it clear how costly double faults can be, and it’s possible that for some players, missed serves are even more damaging than that.