{"id":1872,"date":"2015-10-05T11:57:18","date_gmt":"2015-10-05T11:57:18","guid":{"rendered":"http:\/\/www.tennisabstract.com\/blog\/?p=1872"},"modified":"2015-10-05T11:57:18","modified_gmt":"2015-10-05T11:57:18","slug":"the-slow-but-steady-erosion-of-the-servers-advantage","status":"publish","type":"post","link":"https:\/\/www.tennisabstract.com\/blog\/2015\/10\/05\/the-slow-but-steady-erosion-of-the-servers-advantage\/","title":{"rendered":"The Slow but Steady Erosion of the Server’s Advantage"},"content":{"rendered":"

After a couple of weeks of data-driven<\/a> skepticism<\/a>, I can finally confirm a bit of tennis’s conventional wisdom. Over the course of a typical match, breaks of serve are a little easier to come by.<\/p>\n

This result–based on tens of thousands of matches<\/a> from the last few years–is similar for both men and women. After about twelve games (total, not service games for each player), a hold is roughly 2% less likely than it was in the first few games of the match. By the 25th game, a hold is approximately 5% less likely than at the beginning of the match.<\/p>\n

To control for the vagaries of surface, opponent, and other conditions, I’ve compared each service game to the server’s hold percentage within that match. Only the closest matches are likely to go very long, so it’s important to compare the last games of those matches to games with similarly even opponents.<\/p>\n

It seems that this effect is the result of one or both of two factors: server fatigue (which may have more of an effect on results\u00a0than an equivalent amount of returner fatigue), and the returner’s increasing familiarity with the server. It would be difficult to separate these two–and with this dataset, probably impossible–so for today, let’s stick with the nature of the effect, not its causes.<\/p>\n

The following graph shows the relative probability of a hold of serve based on how much of the match (in games) has been played:<\/p>\n

\"Relative<\/a><\/p>\n

I’ve set the hold probability of the first game at 100%, so all other numbers are relative to that. I’ve excluded tiebreaks from these calculations, though I considered them when counting games–that is, the first game of the second set after a tiebreak is considered the 14th game, not the 13th.<\/p>\n

The results get a lot noisier starting around the\u00a0women’s\u00a025th game and the men’s\u00a035th game, for the simple reason that\u00a0most matches don’t get that far. For example, while\u00a0the WTA calculations are based on 11,000 matches, only one-third reached the 25th game and less than one-tenth made it to the 31st.<\/p>\n

The general downward trend indicates that the fatigue and\/or familiarity effect dwarfs the effect of new balls. I have found that in men’s matches,\u00a0the age of balls has a very small effect on hold percentage, and in women’s matches, it has no effect. In any case, the steady ebb of the server’s advantage is a stronger effect.<\/p>\n

It is likely that some players suffer more from fatigue or familiarity than others. Due to the smaller size of the per-player samples, especially beyond the 20th game or so, I’m reluctant to draw any strong conclusions. Still, there are some intriguing numbers for the players for whom the dataset contains the most matches.<\/p>\n

Here, I’ve calculated the hold percentage for several top players at various stages of the match, relative to their hold percentage in the first ten games. Thus, a number below 100% indicates less frequent holds, while a number above 100% means more frequent holds:<\/p>\n

Player                 Matches  11 to 20  21 to 30  31 to 50  \nTomas Berdych              337     98.5%     98.3%    101.5%  \nDavid Ferrer               330     97.0%     99.4%    102.4%  \nNovak Djokovic             325    100.1%    101.8%    101.7%  \nRoger Federer              325    100.2%     99.6%    100.4%  \nAndy Murray                295     97.7%     98.7%     97.9%  \nRafael Nadal               293     99.2%    100.3%     93.7%  \nJo-Wilfried Tsonga         255    100.4%    100.9%     99.6%  \nPhilipp Kohlschreiber      252    101.4%     97.9%     96.7%  \nJohn Isner                 251    100.4%    100.4%    100.3%  \n                                                              \nPlayer                 Matches  11 to 20  21 to 30  31 to 50  \nKevin Anderson             247    100.0%     98.1%     97.5%  \nRichard Gasquet            246     99.1%     98.4%    105.1%  \nGilles Simon               245    100.1%    103.7%     95.0%  \nMilos Raonic               238     97.1%     96.1%     96.7%  \nMarin Cilic                238     95.4%     97.5%     94.5%  \nFabio Fognini              235    100.4%     99.6%     98.2%  \nKei Nishikori              233    101.8%    104.1%    107.2%  \nGrigor Dimitrov            224    100.9%    100.3%     94.6%  \nAndreas Seppi              221    106.4%    100.4%    103.1%  \nFeliciano Lopez            221     99.2%     99.7%     98.4%  \n                                                              \nTotal                    23326     98.1%     96.1%     95.1%<\/pre>\n
While John Isner<\/a> is steady throughout the stages of the match, other big servers such as Milos Raonic<\/a> and Marin Cilic<\/a> are less dominant as the match progresses. The players whose hold percentage improves through the match–such as Novak Djokovic<\/a> and David Ferrer<\/a>–tend to be those without big serves, so we may be looking at more of an overall fatigue effect in those cases.<\/p>\n
The most extreme number in the table is Rafael Nadal<\/a>‘s relative hold percentage after the 30th game. Perhaps after that much time on court, his opponents finally figure out how to defend against the ad-court slider.<\/p>\n
Here are the same calculations for top WTA players:<\/p>\n
Player                Matches  11 to 15  16 to 20  21 to 40  \nAgnieszka Radwanska       299    101.0%    104.9%     98.0%  \nSara Errani               279     97.7%     91.2%     92.7%  \nCaroline Wozniacki        279    103.1%    102.3%    104.9%  \nSerena Williams           266    102.8%    102.4%    104.9%  \nAngelique Kerber          265    101.9%    103.0%    101.5%  \nSamantha Stosur           253     99.2%    105.0%     97.6%  \nCarla Suarez Navarro      252    102.2%    101.8%     93.7%  \nPetra Kvitova             251     93.9%    100.4%     95.9%  \nRoberta Vinci             250     94.2%     97.9%     95.4%  \nAna Ivanovic              241    100.8%    106.0%     95.2%  \nJelena Jankovic           241    102.2%    108.7%     96.4%  \n                                                             \nPlayer                Matches  11 to 15  16 to 20  21 to 40  \nMaria Sharapova           236    100.1%    105.9%    104.9%  \nVictoria Azarenka         228    100.6%    103.7%     97.8%  \nLucie Safarova            227    102.7%    100.5%     94.4%  \nSimona Halep              224     89.2%     95.3%    101.7%  \nDominika Cibulkova        210     98.7%     89.9%     99.9%  \nAlize Cornet              210     96.2%    102.8%     96.4%  \nAndrea Petkovic           194    101.5%    104.2%    107.5%  \nSloane Stephens           185     97.5%     90.1%     88.7%  \nSabine Lisicki            185     97.4%     97.5%     96.6%  \nEkaterina Makarova        185     96.6%    102.8%     92.8%  \nFlavia Pennetta           180    105.1%     92.9%    103.9%  \n                                                             \nTotal                   22406     98.6%     97.2%     95.0%<\/pre>\n
Here is some confirmation that Serena Williams<\/a>–at least on serve–gets better as the match progresses. Many of the other players with the strongest serve results late in matches are those known for fitness (like Caroline Wozniacki<\/a>) or steeliness (Maria Sharapova<\/a>).<\/p>\n
Whether the root cause is fatigue or familiarity, most players are less effective on serve as the match progresses. With further research, I hope we’ll be able to better understand the cause and determine whether there are advantages to\u00a0serving particularly well at certain stages of the match.<\/p>\n","protected":false},"excerpt":{"rendered":"
After a couple of weeks of data-driven skepticism, I can finally confirm a bit of tennis’s conventional wisdom. Over the course of a typical match, breaks of serve are a little easier to come by. This result–based on tens of thousands of matches from the last few years–is similar for both men and women. After … Continue reading The Slow but Steady Erosion of the Server’s Advantage<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[96,105],"tags":[],"class_list":["post-1872","post","type-post","status-publish","format-standard","hentry","category-research","category-serve-statistics"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/posts\/1872","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/comments?post=1872"}],"version-history":[{"count":0,"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/posts\/1872\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/media?parent=1872"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/categories?post=1872"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/tags?post=1872"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}