Ashleigh Barty’s Fully Baked Double Bagel

Not every double bagel is created equal. Today in Melbourne, Ashleigh Barty beat Danka Kovinic without losing a game, dropping only ten points. By contrast, a memorable Stuttgart first-rounder from 2015 saw Sabine Lisicki lose 6-0 6-0 to Zarina Diyas, requiring 88 points and well over an hour to play. Lisicki won 37.5% of total points played that day, while Kovinic snuck off with just 16.7%.

Barty’s performance was among the most dominant in recent WTA history. I have mostly complete match stats for the women’s tour going back to about 2010, and in that time frame, only two main draw double bagels have finished in fewer than 60 points:

Points  Year  Event       Round  Winner     Loser          
57      2017  Hua Hin     R32    Golubic    Wisitwarapron  
59      2019  New Haven   R32    Cepelova   Small          
60      2021  Aus Open    R128   Barty      Kovinic        
60      2019  Madrid      R16    Halep      Kuzmova        
61      2010  Estoril     R32    Garrigues  De Lattre      
62      2017  Bol         R32    Mrdeza     Thombare       
63      2013  Aus Open    R64    Sharapova  Doi            
63      2015  Bastad      R16    Barthel    Zanevska       
64      2015  Toronto     R64    Vinci      Knapp          
64      2017  Tokyo       R32    Krunic     Date           
64      2011  Luxembourg  R32    Garrigues  Kremer         
64      2012  Copenhagen  R32    Cornet     Ejdesgaard     
65      2010  Moscow      R16    Kirilenko  Bondarenko

Today’s drubbing is even a bit more impressive than it looks on that list. Barty lost only 10 points–among the matches listed above, that’s equal to Jana Cepelova, two more than Viktorija Golubic, and fewer than everyone else. Not all 60-pointers are identical: Because Kovinic forced one deuce game today, Barty had to win 50 points instead of the minimum 48. Simona Halep only needed 48 in her 2019 Madrid double bagel, meaning that she lost 12 of the 60 points played that day.

Double bagel probability

There’s a bit of luck involved in winning twelve games in a row, even for a player at the top of her game. Kovinic won 10 points today, so even if she did exactly the same thing in her next match, one can imagine her “bunching” her points differently and putting a game or two on the board. Unlikely, but possible.

For any match, we can take the winner’s rate of service points won and return points won, and then generate the probability that she wins twelve games in a row. I did this exact exercise last January during the ATP Cup when Roberto Bautista Agut handed a 6-0 6-0 loss to Aleksandre Metreveli. Metreveli lasted 97 points, or 61% longer than Kovinic. If Metreveli had continued to play at that level, his chances of losing twelve games in a row would have been a mere 14.8%.

Barty won 88.9% of her service points and 78.8% of her return points against Kovinic today. If she continued at those rates, assuming no unusual streakiness or significantly better or worse performance at certain point scores, she would hold serve 99.8% of the time and break in 97.2% of return games. (By contrast, Bautista Agut’s probabilities were “only” 98.9% and 73.6%.)

The likelihood of a 6-0 6-0 bagel is simply that of six holds and six breaks. For Barty: (99.8% ^ 6) * (97.2% ^ 6), or 83.6%. In other words, the way she was playing today, Ash would score the double bagel five out of six times.

This probability is the number that really tells you how dominant a player was, even if it’s a few levels more complex than counting points and points lost. And by this measure, only Golubic’s great day holds a place on the list ahead of Barty’s. The p(DB) column shows the probability of a double bagel.

p(DB)  Year  Event       Round  Winner          Loser           
88.7%  2017  Hua Hin     R32    Golubic         Wisitwarapron   
83.6%  2021  Aus Open    R128   Barty           Kovinic         
80.0%  2019  New Haven   R32    Cepelova        Small           
76.8%  2019  Madrid      R16    Halep           Kuzmova         
75.4%  2017  Tokyo       R32    Krunic          Date            
68.8%  2011  Luxembourg  R32    Garrigues       Kremer          
66.9%  2010  Estoril     R32    Garrigues       De Lattre       
64.9%  2017  Bastad      R32    Krejcikova      Beck            
64.1%  2017  Bol         R32    Mrdeza          Thombare        
62.0%  2010  Moscow      R16    Kirilenko       Bondarenko      
60.7%  2016  US Open     R128   Suarez Navarro  Pereira         
59.2%  2013  Aus Open    R64    Sharapova       Doi             
59.2%  2018  US Open     R128   Gavrilova       Sorribes Tormo

Gotta love the coincidence here. 13th on this list is a 2018 US Open first-rounder between Daria Gavrilova and Sara Sorribes Tormo. Both players are still going strong (except when Sorribes Tormo was up 6-0 4-0 on Aryna Sabalenka in Ostrava last October), both are in Melbourne, and they drew each other again this week. Gavrilova won again, though not quite as easily. Her reward? A second-round match on Thursday with Ashleigh Barty.

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