Category: Research

There’s no structural bias toward the player who serves first.  If tennis players were robots, it wouldn’t matter who toed the line before the other.

But the conventional wisdom persists.  Last year, I looked at the first-server advantage in very close matches, and found that depending on the scenario, the player who serves first in the final set may win more than 50% of matches–as high as 55%–but the evidence is cloudy.  And that’s based on serving first at the tail end of the match.  Winning the coin toss doesn’t guarantee you that position for the third or fifth set.

Logically, then, it’s hard to see how serving the first game of the match–and holding that possible slight advantage in the first set–would have much impact on the outcome of the match.  There’s simply too much time, and too many events, between the first game and the pressure-packed crucial moments that decide the match.

Yet, the evidence points to a substantial first-serve advantage.

In ATP main-draw matches this year, the player who served first won 52% of the time.  That edge is confirmed when we adjust for individual players.

39 players tallied at least 10 matches in which they served first and 10 in which they served second.  Of those 39, 21 were more successful when serving first, against 17 who won more often when serving second.  (Marcos Baghdatis didn’t show a preference.)  Weigh their results by their number of matches, and the average tour-level regular was 11% more likely to win when serving first than when serving second.  Converted to the same terms as the general finding, that’s 52.6% of matches in favor of the first server.

That’s not an airtight conclusion, but it is a suggestive one.  One possible problem would arise if lesser players–the guys who play some ATP matches against that top 39, but not enough to show up in the 39 themselves–are more likely to choose returning first.  Then, our top 39 would be winning 52.6% of matches against a lesser pool of opponents.

That doesn’t seem to be the case.  I looked at the next 60 or so players, ranked by how many ATP matches they’ve played this year.  That secondary group served first 51% of the time, indicating that the guys on the fringe of the tour don’t have any kind of consistent tendency when winning the coin toss.

For further confirmation, I ran the same algorithm for ATP Challenger matches this year.  That returned another decent-sized set of players with at least 10 matches serving first and 10 matches serving second–38, in this case.  The end result is almost identical.  The Challenger regulars were 9% more likely to win when serving first, which translates to the first server winning 52.2% of the time.

This is a particularly interesting finding, because in the aggregate, these 38 Challenger regulars prefer to serve second.  Of their 1110 matches so far this year, these guys served first only 503 times–about 45%.  Despite such a strong preference, the match results tell the story.  They are more likely to win when serving first.

When we turn our attention to the WTA tour, the results are so strong as to be head-scratching.  Applying the same test to 2013 WTA matches (though lowering the minimum number of matches to eight each, to ensure a similar number of players), the 35 most active players on the WTA tour are 28% more likely to win when serving first than when serving second.  In other words, when a top player is on the court, the first server wins about 56.3% of the time.  24 of the 35 players in this sample have better winning percentages when serving first than when serving second.

For something that cannot be attributed to a structural bias, a factor that can only be described as mental, I’m reluctant to put too much faith in these WTA results without further research.  However, the simple fact that ATP, Challenger, and WTA results agreed in direction is encouraging.  The first-server advantage may not be overwhelming, but it appears to be real.

Italian translation at settesei.it

This week’s pair of ATP warmups for the Australian Open provide quite the contrast.

In Sydney, only one seeded player (the hardly automatic Andreas Seppi) reached the semifinals, and only one other even made the quarters. Across the ditch in Auckland, three of the final four are among the top four seeds, and the fourth, Gael Monfils, would typically sport a ranking in the same range.

Sydney fits a conventional narrative, while Auckland confounds it. The week before a Grand Slam, many of the top players are out of action, while those who are in action … well, let’s just say warmups don’t always appear to be their top priority.

Winning in 250s

The ATP schedule gives us a convenient natural experiment in order to determine whether slam warmups really are different.

(For convenience, I’m using the term “warmups.” However, we’re only looking at tournaments the week before a slam starts. Sydney is included, but not Brisbane, even though events two weeks before Austrlian and Wimbledon are generally called “warmups.”)

Since 2009, all of the lowest rung of tour-level events have been worth 250 points to the winner. Conveniently, all tourneys the week before slams have fallen into this category.

To see if players seem to treat slam warmups differently from other events, we can simply compare results from warmups to those from other 250s. It isn’t perfect, since a few 250s have draws of more than 32 players and the field quality isn’t identical in all tourneys at this level, but by looking at a few different metrics, we can limit the impact of those quibbles.

Who cares?

Let’s start by simply counting wins and losses of seeded players. In slam warmups from 2009 through 2012, seeds won about 61% of matches against unseeded opponents (224 of 365), while in other 250s, seeds win over 70% of those matches (1499 of 2129). That’s a substantial difference.

To eliminate the quirks of the bigger 250 draw at Queen’s Club, and perhaps toss out some first-round retirements as well, let’s consider the records that seeds have posted in specific rounds.

In the round of 16 at slam warmups, seeds have gone 71-50, for a winning percentage of 58.7%. At other 250s, seeds have won 591 against 223 losses, a percentage of 72.6%.

In the quarterfinals of slam warmups, seeds have beaten unseeded players in 33 of 46 matches–71.7% of encounters. In other 250s, similar matchups have gone to the seeded player 200 of 275 times, or 72.7% of the time.

It seems that many top-ranked players show up at slam warmups with the intent of getting one or two matches under their belt. (Or perhaps fulfilling an obligation to a sponsor.) Those players don’t perform up to their usual standard. But as shown by the comparable records in quarterfinals, those who come to compete play at their usual level.

A few other looks

One issue that seems to have a particular impact in slam warmups is last-minute withdrawals, like that of second-seed Gilles Simon in Sydney this week. Those don’t show up in the won-loss records.

To consider the overall picture, including withdrawals, we can count the number of seeds who reach the semifinals in our different categories of ATP 250s.

In slam warmups, the semifinal fields in the last four years have consisted of 53 seeds and 43 nonseeds–about 55% top-ranked players. In other 250 semifinals, we’ve seen 365 seeds against 191 nonseeds–66% seeds.

Yet another angle is the performance of the top four seeds. In 250s, the 5 through 8 seeds are often barely distinguishable from the rest of the pack. For example, in Sydney this week, those last four seeds are Florian Mayer, Radek Stepanek, Jeremy Chardy, and Marcel Granollers. Not much difference between those guys and unseeded semifinalists Julien Benneteau, Kevin Anderson, and Bernard Tomic.

There’s no clear line between first-rank guys and the rest of the pack, but taking the top half of the seeds seems as good as any other option.

The results are similar to what we saw with the larger pool of seeds. Overall, when a top-four seed played a non-top-four opponent in a slam warmup, he won 65% of matches (129 of 199). In other 250s, he won 74% (978 of 1321).

In the round of 16, top-fours went 51-24 in slam warmups, for a record of 68%, compared to 76% (366-114) in other 250s.

Where the top four seeds differ from other seeds is in the quarterfinal round. In slam warmup QFs, top-fours went 31-20, winning 61% of matches. In other tourneys, they won 71% (261-105). Perhaps the first-round bye in many slam warmups means that top seeds want two warmup matches, but no more.

As mentioned, these experiments give us imprecise results, as they don’t take into account the exact field quality of the various 250s. While they may not be the final word on this question, these numbers do strongly indicate that higher-ranked players don’t view slam warmups as particularly important. Against a similar pool of opponents, they win far more matches in 250s at other times throughout the year.

Perhaps that’s one reason why winning an Aussie Open warmup doesn’t forecast any particular level of success in Melbourne–these are tournaments where some of your most highly-ranked opponents just aren’t trying as hard as usual.

In his remarkable comeback this year, Brian Baker has already recorded two top-20 scalps, along with seven other victories against players in the top 100.   In the same span of six months, he’s also lost to a player barely inside the top 400, and suffered another six defeats against guys outside the top 100.

This is inconsistency of historic magnitude.  The list of players he’s beaten may actually be more impressive than the list of those who have beaten him!  Adding to the confusion, we don’t have any other recent results from him.  We can’t just wave our hands and point to his 2011 performance level as an accurate indicator of his current level.

One measurement of player ability, the ATP ranking system, places him at #78, a number that seems just as ridiculous when he’s beating Philipp Kohlschreiber at a Masters event as when he’s losing to Maxime Authom at a challenger.  But overall, the ATP estimate doesn’t seem too far-fetched.  It’s certainly better than what jrank (my rating system) spits out.  That algorithm doesn’t know what to do with such a limited track record, so it places him far outside the top 100.

We can do better.  As we’ll see, Baker’s results suggest he belongs on the cusp of the top 50.

Uniquely limited results

Imagine a completely unknown player is given a wild card into a major event.  We don’t know where he came from or who he might have beaten in the past.  He’s a completely blank slate.  If we wanted to estimate his ability level, we would have to wait until we got some results.

If that player won an opening-round match against the 17th-best player in the world, our best guess would be that he is better than #17, but we wouldn’t know how much.  If he lost that opening round match, we would assume he is worse than #17.  We might use statistics from that match to estimate how much better or worse than #17.

As our unknown kept playing more matches, we would update our estimate, using additional data as it came in.

(You might protest that in the early going, we should regress our estimate to the mean, since if some random guy came out of nowhere, he probably isn’t one of the 16 best tennis players in the world–there was a reason he was nowhere.  And, in such a real-world scenario, you would be right.  But such a case, what is the mean?  If a baseball player is called up from Triple-A, an intelligent observer, such as a scout or team executive, considers him at least marginally MLB-level, so we would regress our estimate to the level of marginal MLB players.  But if a player receives a wild card into a tennis tournament, what do we know?)

Few tennis players in history have come closer to this unknown than Brian Baker.  Sure, everyone has to start somewhere, but usually “somewhere” is a long string of futures tournaments, followed by an even longer string of challengers.  By the time a player bags his first top-20 scalp, we have lots and lots of data to work with.

When other players were racking up several dozen matches every year, Brian Baker was rehabbing injuries and coaching college tennis.  We can only judge him based on a small number of recent results.  And those results are particularly contradictory.

Working backward

Intuitively, it’s tough to accept that a single player has beaten a bunch of good players and lost to several weaker ones.  No matter how good that guy is, such a set of outcomes is unlikely.

But how unlikely?  That question is the key to estimating Baker’s current level.

Rather than assuming Baker is playing at a certain level (like that of #78) and scratching our heads at his inconsistency, we can work backwards–take his results and determine the likelihood that he is playing at various levels.

For instance, we could assume that Baker is #5 in the world.  If so, some of his results would be very predictable (like the two wins against Blake Strode) and others would be particularly jarring.  We could go further and calculate the probability that the #5 player in the world would amass Baker’s specific match record.  Those odds, of course, are vanishingly small.

If you repeat the process for every possible ranking, you get a probability that #5, or #12, or #77 would win the matches Baker has won and lose the matches he has lost.  One of those probabilities will be higher than the others, and that’s our best guess of how highly we should regard the American.

(If you’re interested in methodology, click “Continue Reading” below.)

Using this method, we discover that Baker has played at the level of someone with about 820 ATP ranking points, putting him around #54, in a tight pack with Grigor Dimitrov, Gilles Muller, Alejandro Falla, and Lukas Lacko.  With every match he plays, we can continue to fine-tune our estimate.

There are many factors we need to ignore to do an analysis like this, largely because of the limited data that led us to the topic in the first place.  Many of Baker’s worst results have come on hard courts; perhaps he will prove over a longer period to be stronger on clay and grass.  If his ability level has changed over the last six months, as seems very likely, this approach fails to take it into consideration.

But because of the unique nature of Baker’s comeback, which makes it difficult to assume anything about his ability level–this approach allows us to a make a reasonably good guess.  And with such a strange mix of great wins and rough losses, a good guess is all we can hope for.

Continue reading How Good is Brian Baker?

For all the talk of 30-somethings at the top of the modern men’s game, tennis players decline quickly.  30 may be the new 20, but 35 is still the same old 35, and 35-year-old tennis players are usually found on the champions tour, the doubles court, or national television.

Yet Tommy Haas, aged 34 years and 5 months, is enjoying a resurgence, having reached three finals in the last two months–on three different surfaces.  He’s one of the hottest players on tour of any age.

34-year-olds don’t do things like that.  In the last ten years, players 34 and older have accounted for fewer than 1% of wins on the ATP tour.  From 2008 to 2011, all 34-year-olds–combined–won a total of 17 tour-level matches.  In the five months since his birthday, Haas has won 22.

To find a point of comparison, we need to go back five years, to the 2007 campaign of Fabrice Santoro, and slightly earlier, to Andre Agassi‘s 2004 season.  Agassi at 34 was better than Haas at 34, winning 37 tour-level matches and reaching two grand slam quarterfinals.  Agassi was the best “old” player since Jimmy Connors and the only man in the discussion since the 1970s.

Yet already, Haas is among the best 34-and-overs in ATP history.  His 22 wins since his 34th birthday are good for 28th on the all-time list, ahead of Fred Stolle and just behind Roy Emerson.  But that understates Haas’s accomplishment.  With the exceptions of Santoro, Agassi, and Connors (whose 178 wins-past-34 are good for 2nd on the all time list, behind Ken Rosewall), everyone on the list retired more than 20 years ago.

Comparisons to Haas’s contemporaries do a better job of illustrating how unusual he is.  The only two older men to have won a match on tour this year are Arnaud Clement and Ruben Ramirez Hidalgo, neither of whom are a factor anywhere but the challenger tour.  The other 34-year-old to win some matches this season is hyper-fit warrior Michael Russell, who took advantage of the weak draws in Atlanta and Los Angeles.

As long as he stays healthy, Haas is far from finished.  According to Jrank, he’s the 11th-best hard court player in the game right now. He may not have another grand slam final ahead of him, as Agassi did at the same age, but he has more wins in his future than most players a decade his junior.

Italian translation at settesei.it

Marathon sets are again the talk of tennis.  We won’t soon forget Roger Federer’s 19-17 third-set win over Juan Martin Del Potro … or Roger’s weak performance in the match that followed.

The unusual Olympic format–best-of-three, no final-set tiebreak–brought several issues to the fore.  Should best of three be enough for slams?  It certainly gave us plenty of dramatics last week.  And is it finally time to end the no-tiebreak madness?  For all of the occasional drama, do we really need to see even more service holds in John Isner matches?

Peter Bodo makes the case for a marathon-free world:

[M]y main reason for embracing the final-set tiebreaker is not the obvious one that would be cited by most time-sensitive television producers. The real problem with deuce sets is that when a match goes as long as Federer v. Delpo or even Jo-Wilfried Tsonga v. Milos Raonic (that one went 25-23, for Tsonga) the reward for the winner’s heroic feat is almost always a quick subsequent loss.

As Bodo goes on to illustrate, this seems anecdotally true.  But who cares about anecdotes?  This is a testable hypothesis.

As we’ll see, there is a noticeable hangover effect when a player has fought through a marathon fifth set.  But the alternative–a fifth-set tiebreak–produces nearly the same hangover.

There have been 146 marathon fifth sets–matches in which the final set reached 6-6–in Grand Slam tennis since the beginning of 2001.  The record of those 146 winners in their next round is dreadful: 43-103, or 29.5%.  It’s even worse than that, actually.  Four times, two marathon men went on to play each other, so four of those wins were inevitable.

However, that isn’t the end of the story.  To prove that fifth-set marathons significantly weaken their winners, we need to establish two things: (1) They had a decent shot at beating their next opponents anyway, and (2) if a fifth-set tiebreak were played, their chances would have been better.

Post-marathon underdogs

The first issue is a bit sneaky.  If a player has to go deep into the fifth set to win in the early rounds, he’s hardly a dominating presence in the draw.  Consider the extreme case of Yen Hsun Lu, who in 2010, beat Andy Roddick in a 9-7 fifth set, advancing to play Novak Djokovic in the Wimbledon quarters.  Sure, Lu was tired, but what were the odds of an upset even if Roddick lost in three?  Top players rarely need five hours to push through an early-round opponent.

To quantify this, we can turn to jrank-driven predictions.  Using these measures of each player’s ability level at the time of the match, we can estimate the actual chances of our 146 marathon men.

The marathon men would have been underdogs in their next match no matter what.  On average, each one had a 43.4% chance of winning, meaning that of the 146 matches, they should have won 63 of them.  Even adjusting for their underdog status, they seem to have suffered from their marathons–they won 43 of those matches, barely two-third the number that they “should” have won.

Almost-but-not-quite marathons

We’ve established that once a player enters the uncharted territory beyond 6-6, his chances of winning the next match are substantially weakened.  But surely the fatigue didn’t set in right at the moment the chair umpire called “6-6.”  Even if the fifth set is a bagel, simply playing five sets of professional-level tennis is exhausting, and might impact one’s performance a day or two later.

The most relevant set of matches for comparison are US Open five-setters that went to a final-set tiebreak.  Since 2001, we have 40 of those.  In their next matches, the winners of the almost-marathons went a dismal 11-29 (27.5%)–worse than the marathon men!

Compared to their expectations, though, they did a bit better.  Those forty men, on average, had a 38% chance of winning their next matches, meaning we would expect them to win about 15 of the 40.  Relative to the predictions we would have made at the time, this small sample of fifth-set-tiebreak winners outperformed the marathon men, but just barely.

For a bigger sample, we can turn to the slightly shorter–but still epic–matches that end 7-5 in the fifth.  Of the 95 such matches since 2001, the 7-5 winners went on win 49, or 51.5% of their next matches!  This despite the fact they were collective underdogs, expected to win only 48%, or 46 of those matches.

What now?

Since the 7-5 group performed so differently in their next matches, it’s tempting to speculate why they did so.  My best guess: If a player manages a break before the set goes 6-6, he’s relatively fresh, physically and mentally.  The sort of player who can break at 5-5 or 6-5 is one who can come back a day or two later and plow through another three or four hard-fought sets.

By contrast, matches that get to 6-6–whether they end in a tiebreak or not–are usually battles of attrition.  Think Isner-Mahut: The longer it lasted, the less likely either player could challenge the other’s serve.  That brand of tennis had set in before 6-6 in the fifth: If one of the players pulled out a 7-4 tiebreak, it wouldn’t say much about his fitness or mental stamina, simply that someone is bound to get lucky for a point or two.

Based on the limited data we have, there just isn’t much difference between the after-effects of fifth-set marathons and fifth-set tiebreaks.  In both cases, the marathon men weren’t going to be favored anyway, and their fatigue hurts them even more.  Changing format to fifth-set tiebreaks would have little effect on future outcomes–it would just make those matches a bit more dependent on a lucky bounce.