{"id":892,"date":"2012-08-30T10:26:38","date_gmt":"2012-08-30T14:26:38","guid":{"rendered":"http:\/\/heavytopspin.com\/?p=892"},"modified":"2012-08-30T10:26:38","modified_gmt":"2012-08-30T14:26:38","slug":"the-five-set-advantage-2","status":"publish","type":"post","link":"https:\/\/www.tennisabstract.com\/blog\/2012\/08\/30\/the-five-set-advantage-2\/","title":{"rendered":"The Five-Set Advantage"},"content":{"rendered":"

Italian translation at settesei.it<\/em><\/a><\/p>\n

Last night, the heavily-favored Janko Tipsarevic<\/a> won his first round match against Guillaume Rufin<\/a> despite dropping the first two sets<\/a>. \u00a0Had Rufin taken the first two sets against Janko in Cincinnati, Monte Carlo, or just about anywhere else on the ATP tour, he would’ve scored his first top-ten scalp.<\/p>\n

Other seeds have similar stories. \u00a0Milos Raonic<\/a>, Marin Cilic<\/a>, Gilles Simon<\/a>, and Alexandr Dolgopolov<\/a> all would be headed home had their matches been judged on the first three sets. \u00a0Only two seeds had the opposite experience: Juan Monaco<\/a> and Tommy Haas<\/a> were each up two sets to love before losing their next three.<\/p>\n

Simply (if tongue-twistingly) put, the five-set format favors favorites.<\/p>\n

In all grand slam first rounds since 1991, seeds have come back from 0-2 or 1-2 down against unseeded players 125 times, while seeds have squandered 2-0 or 2-1 advantages only 71 times. \u00a0Just looking at those 32 matches per slam, that’s almost one upset averted per tournament. \u00a0The US Open draw would look awfully different right now if Tipsarevic, Raonic, Cilic, Simon, and Dolgopolov were among the first-round losers, even if Haas and Monaco replaced them in the second round.<\/p>\n

Set theory<\/strong><\/p>\n

These numbers shouldn’t surprise us, since longer formats should do a better job of revealing the better player. \u00a0There are reasons why the baseball World Series is best-of-7 instead of a single game and the final sets of singles matches aren’t super-tiebreaks<\/a>. \u00a0The difference between best-of-3 and best-of-5 isn’t quite so simple–fitness and mental strength play a part–but from a purely mathematical perspective, there should be fewer upsets in best-of-5s than best-of-3s.<\/p>\n

Take Raonic for example. \u00a0My numbers<\/a> (which don’t differentiate between 3-set and 5-set matches–shame on me) gave him approximately a 70% chance of beating Santiago Giraldo<\/a>. \u00a0If 70% is his probability of winning a three-set match and sets are independent (more on that in a minute), that number implies a 63.7% chance of winning any given set. \u00a0A 63.7% chance of winning a set translates into a 74.4% shot at winning a best-of-five.<\/p>\n

A four- or five-point increase doesn’t radically change the complexion of the tournament, but it does make a different. \u00a0My original numbers suggested that we could expect 20 or 21 first-round upsets. \u00a0If we adjust my odds in the manner I described for Raonic, the likely number of upsets falls to 18.<\/p>\n

The most important implication here is the effect it has on the chances that top players reach the final rounds. \u00a0Earlier this week a commenter took me to task<\/a> for my unintuively low probabilities that Federer and Djokovic would reach the semifinals. \u00a0Obviously, if you give an overwhelming favorite a boost in every round, as the five-set format does, the cumulative effect is substantial. \u00a0For the top seeds, it can halve their probability of losing against a much lower-ranked opponent.<\/p>\n

For Federer, adjusting the odds to reflect the theoretical advantage of the best-of-five format raises his chances of reaching the semis from 52.5%<\/a> to over 65%. \u00a0Djokovic’s numbers are almost identical.<\/p>\n

Dependent outcomes<\/strong><\/p>\n

Everything I’ve said so far seems intuitively sound, with one caveat. \u00a0Earlier I mentioned the assumptions that sets are independent. \u00a0That is, a player has the same chance of winning a particular set no matter what the outcome of the previous sets–there is no “hangover effect” based on what has come before.<\/p>\n

Tennis players, even professionals, aren’t robots, so the assumption probably isn’t completely valid. \u00a0Sometimes frustration with one’s own performance, the environment, or line calls can carry over into the next set and give one’s opponent an advantage. \u00a0Perhaps more importantly, the result of one set sometimes reveal that pre-match expectations were wrong in the first place. \u00a0Had David Nalbandian<\/a> played this week instead of withdrawn, no number of sets would reveal that he was a better player–his health would prevent him from playing at his usual level.<\/p>\n

Another related caveat is that beyond a certain match length, the outcome is no longer dependent on the same skills. \u00a0When Michael Russell<\/a> played Yuichi Sugita<\/a> in the Wimbledon qualifying round, the two men looked equal for four sets. \u00a0In the fifth, Russell’s fitness gave him an advantage that didn’t exist in the first couple of hours. \u00a0In this case, an estimate of Russell’s probability of winning a set against Sugita may be independent of previous outcomes, but it is not the same for every set.<\/p>\n

These allowances aside, there is little doubt that favorites are more likely to win best-of-five matches than best-of-threes. \u00a0Whether you want to watch the entire thing … that’s another story.<\/p>\n","protected":false},"excerpt":{"rendered":"

Italian translation at settesei.it Last night, the heavily-favored Janko Tipsarevic won his first round match against Guillaume Rufin despite dropping the first two sets. \u00a0Had Rufin taken the first two sets against Janko in Cincinnati, Monte Carlo, or just about anywhere else on the ATP tour, he would’ve scored his first top-ten scalp. Other seeds … Continue reading The Five-Set 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":[40,112],"tags":[],"class_list":["post-892","post","type-post","status-publish","format-standard","hentry","category-forecasting","category-the-rules"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/posts\/892","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=892"}],"version-history":[{"count":0,"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/posts\/892\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/media?parent=892"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/categories?post=892"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.tennisabstract.com\/blog\/wp-json\/wp\/v2\/tags?post=892"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}