Research – Page 8 – Heavy Topspin

Serving First in Marathon Sets

Last night, when Jo Wilfried Tsonga finally defeated Milos Raonic, it was on a match-ending break of serve. Conventional wisdom suggests that’s often how it goes. Whoever serves first in a long set seems to have the advantage. There’s less pressure to hold serve at 7-7 (or 47-47) than there is at 7-8.

Tsonga won his contest with a match-ending break point; Isner finished off his 70-68 set on Mahut’s serve; and when Federer and Roddick went to 14-14 in the 2009 Wimbledon final, Roger held for 15-14 before breaking the American. Is it a trend?

As it turns out, those three high-profile matches have misled us. Based on the limited data available, the first server in fifth-set epics has little or no advantage.

(Third-set epics are so rare that we might as well ignore them–the Olympics is the only tournament where men play best-of-three with no tiebreak in the final set.)

We don’t know who served first for every marathon fifth set in tennis history, but we can figure it out for some. The ATP has limited stats for most matches back to 1991, and those stats include numbers of service games. When the number of service games is equal for both players, we’re stuck at square one. When one player has more than the other, that guy must have served the first game of the match–and the last. Since marathon sets must contain an even number of games, we know who served first in the final set.

The result is a pool of 138 matches in which the fifth set ended at 8-6 or higher and we know who served first. Of those, the guy who served first–at 0-0, 1-1, 6-6, and so on–won the match 67 times (48.6%). It’s a coin toss.

If we take pressure out of the equation, this makes perfect sense. If two guys have gotten to 6-6 in the fifth set, they’re playing as equally as two tennis players can play. It’s only when we consider the stress of serving to stay in the match that we start to suspect that one player–but not the other–won’t be able to hold up his end.

For a bigger dataset, we can look to similar situations. Consider 5-setters that end 7-5 in the fifth. Those don’t have the cachet of matches that go farther, but they are quite epic in their own right. We know who served first in 86 such matches, and of those, the man who served first won only 38 (44.2%). It’s not exactly proof that the first server has a disadvantage, but it does cast more doubt on the conventional wisdom.

If want more than 200 or so matches, we need to weaken our definition of “epic.” Tiebreaks aren’t relevant here, since we’re looking for instances where one player was broken under pressure. But we can use best-of-three contests that ended 7-5.

With so many more best-of-three matches on the schedule, our dataset is now much bigger. We know who served first for 753 tour-level matches that ended 7-5 in the third. Of these, the player who served first went 412-341, winning nearly 55% of matches.

If you want evidence that the conventional wisdom is correct, there you go. If a match reaches 5-5 in the deciding set and ends with a break, there is, altogether, a 53% chance that the first server wins.

But with our more limited data, it’s impossible to draw the same conclusion about five-setters once they head into the barely-charted territory beyond 6-6.

Who Benefits From Byes?

Italian translation at settesei.it

Roughly two-thirds of ATP tour-level tournaments have byes in the draw. 31 events–including the two this week, in Kitzbuhel and Los Angeles–have 28-man fields, with first-round byes for the top four seeds.

The obvious beneficiaries are the top four seeds. They get free passes into the second round, eliminating the chance they’ll be handed a first-round exit. It’s also a guarantee of greater prize money and more ranking points. First-round byes are such a feature of the ATP tour, at least in part, because they help smaller tournaments convince big-name players to sign up.

Of course, you can’t simply hand an advantage to the top four seeds without affecting others. In this most common format, a 28-man field with eight seeds and four byes, there are three important groups: The top four seeds, the bottom four seeds, and the rest of the field.

The top four seeds: The main effect of byes on the top four seeds is that, as noted, they don’t have play first-round matches. The extent of that effect depends on how much of a threat the first-rounder would’ve been.

To quantify these effects, I ran simulations for the 2012 Estoril tournament. First, I simulated the draw as the tournament was played, with 28 players and top seeds of Juan Martin Del Potro, Richard Gasquet, Stanislas Wawrinka, and Albert Ramos. Second, I added the next four players on the alternate list to the draw in place of the byes. To eliminate any bias stemming from the specific arrangement of the draw, I re-generated the brackets for each simulation.

In the 32-man field, Delpo won his first round match about 90% of the time, Gasquet and Wawrinka about 80%, and Ramos just under 60%. Accordingly, Delpo didn’t benefit too much from the bye, but Ramos gained enormously.

However, when measured by expected ranking points, none of these four men gained as much as skipping the first round would suggest. For instance, if Delpo would win only 90% of his first-round matches, removing that impediment would be expected to raise his other outcomes by (1/0.9 – 1), or 11%. In fact, in the 28-man simulation, he gained only 9.5% over his 32-man expectation.

The slight difference is due to the other top seeds. If Delpo is more likely to reach, say, the semifinals, then the same effect applies to Gasquet and Wawrinka, the two men who would be most likely to knock him out of the draw. So while the bye itself increases Delpo’s expected ranking points by 11%, the increased probability of facing the other top seeds reduces it a bit.

Still, the net effect on the top four seeds is overwhelmingly positive. For Gasquet and Wawrinka, the bye itself increases their expectations by 27% each, for a net effect of 24%, while for Ramos, the bye is a 74% increase, resulting in a net effect of 70%.

The next four seeds: The men seeded five through eight are the losers. They must play a first-round match–which, in the Estoril example, they each have about a 60% chance of winning–but they are more likely to face one of the top four seeds later on.

The average effect of adding byes to the draw is a 5% decrease in expected ranking points for these lower four seeds. They aren’t guaranteed to reach the quarterfinal, but in the 28-man version, if they do reach the quarters, they are at least 10% more likely to face a higher-ranked opponent.

The rest of the pack: Nearly everyone else benefits. The effect of byes touches unseeded players in two ways, which work in opposite directions. First, and most significantly, no one has to play a top-four seed in the first round. In Estoril, the toughest first round opponent was 5th-seed Denis Istomin, not exactly a fearsome name in the locker room. Because of the byes, nearly every player has a 40% chance of reaching the second round.

The countervailing force is a minor one–not enough to neutralize the advantage of missing top seeds in the first round. When the field shrinks from 32 to 28, the average opponent is a bit better. If four additional players were added to the Estoril field, they wouldn’t be automatically placed in the positions of the byes. They would be randomly placed in the draw like everyone else. Having those four lower-ranked players would give some players even easier first-round matches.

But on balance, for unseeded players, the goal is simply to win a match or two. The best way to increase their chances of doing so is to keep the best players out of their path for as long as possible. Byes take care of that. The net benefit to unseeded players is an addition of 1% to 3% of their expected ranking points. Generally speaking, the worse the player, the bigger the benefit.

The one exception to this rule is if an unseeded player is actually better than some of the seeds. According to jrank, Igor Andreev was a better player than 8th-seed Flavio Cipolla going into Estoril. Thus, the logic that applies to the bottom seeds applies to him. He was likely to advance to the quarterfinals, so the effect of the byes was mainly to give him a tougher quarterfinal opponent. In each tournament, this might affect one or two players–in Estoril, Andreev was the only one.

One more consideration: As we’ve seen, 23 of the 28 players benefited from the byes. And the five players who were negatively affected didn’t lose too much. How is that possible?

There’s one more group we haven’t talked about: The four players who aren’t included in a 32-man draw. They don’t have much of a chance of reaching the final rounds, but they wouldn’t be much worse than the rest of the unseeded pack.

One of the players I used for this example, Igor Sijsling, just missed the cut, but in a 32-man draw, he would have been expected to take home 23 ranking points and about $9,000. By adding four byes, the tournament is essentially taking what it would have given to Sijsling and three other players and divvying it up among the remaining 28. The pie is the same size, but fewer players can claim a slice.

In the end, those four “missing” players are the only real losers, and they always have the option to head to a challenger for the chance of picking just as many points, even if they probably don’t come with as many dollars.

The winners, beyond the top seeds and the tournament organizers, are ultimately the fans. When top players have more reason to play small tournaments, we get to watch more high-profile matchups, and ATP 250s look a bit less like Kitzbuhel and a bit more like Doha.

The Historically Weak Fields in Kitzbuhel and Los Angeles

With the Olympics starting in just a few days, it’s no surprise that this week’s two ATP 250 events barely qualify as sideshows. No man inside the top 20 is participating in either one, and journeymen such as Bjorn Phau and Blaz Kavcic are seeded.

In fact, Kitzbuhel and Los Angeles sport two of the weakest fields in recent history, handing out some of the cheapest ranking points ever offered by tour-level events.

To the naked eye, it’s plenty clear that these tournaments don’t measure up to the standard of, say, Halle or Doha. But attaching numbers to those claims is more difficult. You could compare average or median ranking, the cut, the ranking of the lowest seed, or even the ranking of the top seed. However, none of these provide the whole picture.

To quantify field strength using just a number or two, in a way that allows us to compare 28-man 250s to 48, 56, or 64-player 500s, to 128-player slams, let’s turn to a method suggested by Carl Bialik. We’re most concerned with how difficult these tournaments are to win. So, since some player ranked roughly #10 in the world is in the field at almost every event, let’s compare the probability that the #10-ranked player would take the title.

At most grand slam and masters-level tournaments, the #10 player in the world has a 1-3% chance of winning. It’s awfully unlikely, though definitely nonzero. At a lower-level tournament like Atlanta last-week, the #10 player–in this case, John Isner–was the most likely winner, though he had some high-quality competition from Mardy Fish, Kei Nishikori, and eventual winner Andy Roddick. In more extreme cases, like this week’s Los Angeles event, no one inside the top 40 is participating. So if #10 entered, he would be the overwhelming favorite.

The field in Kitzbuhel this week is so weak that, had a hypothetical #10 player entered, he would have a 45% chance of winning the title. That’s the highest we’ve seen on the ATP tour in at least the last four years. The LA draw is stronger in this regard. Thanks in part to the currently underrated Sam Querrey, the hypothetical #10 would have a mere 31% chance of winning. As we’ll see in a moment, though, that doesn’t tell the whole story.

10 events have had sufficiently weak draws to give the #10-ranked player a 30% or better chance of winning, but Kitzbuhel is the worst of all. Los Angeles, while relatively stronger, is the weakest hard court event. In the last year, there have been 42 events flying the ATP 250 banner. By this metric, the average 250 draw would give the #10 player a 23.6% of winning. By comparison, the #10 player has, on average, a 10.4% chance of winning an ATP 500 event. (Hamburg last week was an aberration, clocking in at 22%, higher than half of the 250s.)

Much like next week’s 500-level event in Washington, LA’s Farmers Classic is a direct casualty of the Olympics. As part of the US Open Series, it typically attracts quite a few top hard-courters. Last year’s field included both Fish and Juan Martin Del Potro, and the #10 player would have a had mere 16% chance of winning, on par with the relatively strong 250 fields in Buenos Aires and ‘s-Hertogenbosch.

A slightly different metric exposes the true dearth of quality players in Los Angeles this week. In addition to calculating the probability that the #10 player would win, we can check the probability that the #50 player would win an event. For a draw of any quality, that number is close to zero. For these weaker 250 fields, the additional perspective gives us more nuance. If an event is packed with guys ranked around #100, as LA is, it is easy pickings for someone like Benoit Paire or Xavier Malisse. If there are plenty of top-70 or top-80 players, the #50 entrant will have a much tougher time.

Measured by the probability of the #50 player winning an event, Los Angeles has the weakest field of any tournament back to 2009. The hypothetical #50 would have an 11.7% chance of winning, better than the chances for the #10 player in Doha, Halle, or Queen’s Club! It’s also the only time I found that #50 would have been better than a 10% chance. Unsurprisingly, Kitzbuhel checks in near the top, in third place, with a 6.9% chance of the #50 player winning.

To some extent, the Olympics are to blame. But more generally, it is a reminder than all ranking points aren’t created equal. It’s another flaw in the ranking system: Simply because the ATP awards the same 250 to a wide range of events does not mean that they are equally challenging.

Put another way, the massive gaps between 250s (and, to a lesser extent, 500s) are an opportunity for enterprising players. While some players were resting last week, Juan Monaco picked up the cheapest 500 points on offer all year to jump into the top ten. In Washington, another cheap 500 will go to a player who probably would’ve lost in the first two rounds at the Olympics. There may be more to tennis than ranking points, but there’s certainly more to ranking points than meets the eye.

Below, find more on the rather complicated methodology of this study, along with a table comparing all tournaments of the last 52 weeks.

Continue reading The Historically Weak Fields in Kitzbuhel and Los Angeles

The Aging Wimbledon Men’s Draw

Italian translation at settesei.it

Men’s tennis is getting older, and the drift toward middle age is evident at Wimbledon this week.

Of the 128 men in the main draw, 34 are at least 30 years old, while only two are in their teens. This is just the latest step in a trend that has been evident for at least a decade.

The 34 30-somethings are not just a modern-day record–the number blows recent years out of the water. Last year’s main draw had 24 30-somethings, and that was the highest such total since 1979. Teenagers have been on the wane for years–there have only been two in the main draw in each of the last four years, but as recently as 2001, there were eight. In several years in the late 80s and early 90s, there were more teenagers than 30-year-olds.

Whatever the explanation for this–and there are many possible ones–it’s clear that something is going on. It takes longer than it ever has for a young rising star to establish himself on tour, and top players are able to stay healthy and competitive for as long as ever before.

After the jump, find a table with more detailed results.

Continue reading The Aging Wimbledon Men’s Draw

The Luck of the (2012 French Open) Draw

Without a single player setting foot on a match court, many players have already seen their chances of winning the French Open change quite a bit.

A Grand Slam draw can give, and it can take away. Novak Djokovic is set to player Roger Federer in the semifinals (again), while Rafael Nadal won’t have to play either until the final. Potito Starace will have to beat Novak Djokovic in order to reach the second round, while many of his unseeded fellow players have only to defeat a qualifier. Life isn’t fair.

At every stage of the draw, there are winners and losers. As I did last year, we can quantify the impact of the draw by comparing each player’s probability of reaching each round before and after the draw was set. For instance, before the draw was set, Starace had a 66% chance of facing another unseeded player and a decent chance of reaching the second or third round. Now that the draw was set, he might as well book his flight home.

To measure the impact, I used expected prize money, which wraps up in one number the probability that a player reaches each round. For instance, Roger Federer was expected to win 329,000 euros before the draw was set; even with the unfortunate semifinal pairing, he’s still on track for roughly 329,000 euros. Nadal saw a 3% improvement in expected prize money, largely because Fed and Djok are elsewhere, while Djokovic’s number stayed the same. Yes, Fed in the semis is a rough draw, but Novak gets the benefit of a relatively easy path to the semis, with men like Jurgen Melzer and Fernando Verdasco standing in his way.

The Winners

Of the seeded players, the biggest winner of the draw was John Isner. (This is a case where life might be fair–this is the guy who drew Nadal in last year’s first round.) Isner’s expected prize money increased from 71,400 to 92,200, nearly a 30% jump. Until he faces David Ferrer in the round of 16, there’s little standing in his way–and even Ferrer pales in comparison to some of the other top eight players who Isner could have drawn.

The other big winner is Richard Gasquet, whose expected prize money increased from 102,600 to 125,700. While he is seeded outside of the top 16, his probable third-round opponent is the #16 seed Alexander Dolgopolov. Numerically, anyway, you can’t get any luckier than that.

Taking into account the entire draw, no one got luckier than Alex Bogomolov Jr, whose expected takings rose from 26,600 to 36,000. Bogie isn’t expected to get far, but he’ll face Arnaud Clement, then probably Radek Stepanek and Feliciano Lopez. As Starace can tell you, it could be much worse.

The Losers

It’s a bad year for Italians at the French. Among the top four worst draws–all players who lost about one-quarter of their expected prize money this morning–not only Starace but also Simone Bolelli are included. After all, Bolelli drew Nadal!

The toughest luck among seeds fell to Viktor Troicki (loser of 26% of his expected prize money) and Gilles Simon (loser of 18%). Both players are in Djokovic’s quarter, putting an effective end to any title hopes they may have … if they even make it that far. Troicki drew one of the toughest clay-courters from the unseeded pool, Thomaz Bellucci, and if he gets to the second round, would play Adrian Mannarino or Fabio Fognini. After that? Jo-Wilfried Tsonga.

In actuality, Simon might have the toughest road. His possible second-rounder is Brian Baker, the man who has taken Nice by storm. My rankings don’t give Baker much credit yet–after all, he only has a recent few pro matches under his belt under Nice goes on the books–so it’s likely that he is more dangerous than my numbers give him credit for. Simon’s already unfortunate French Open draw is worse than it looks.

The Unaceables

Last night, Florian Mayer solved the John Isner serve, breaking the American three times en route to a straight-set victory. Mayer is known as a tricky opponent, but not as a particularly good returner. He had never played Isner before, though he beat Ivo Karlovic in Miami last year.

One element of his success is that he got his racquet on the Isner serve. Over the last 52 weeks, Isner has amassed a 17.1% ace rate, meaning that about one in six of his serves are untouchable. Last night, he barely managed 10%, as Mayer allowed him only six aces.

We might wonder: Is this is a skill of Mayer’s that we’ve failed to notice before? At first glance, it doesn’t appear to be. While Mayer often holds his opponents to low ace numbers, he’s had some horrible performances in that department, allowing Feliciano Lopez a 20.4% ace rate in Shanghai last year, Thomaz Bellucci 15.5% in Madrid on clay, and while playing injured, he ignominiously allowed Ivo Karlovic a 50% ace rate at last year’s Cincinnati Masters.

We can answer this question not just for Mayer, but for every regular on the ATP tour. While some servers hit far more aces than others, ace rate is influenced by both the server and the returner. Mayer himself is a good example. In the last 52 weeks, he’s had eight matches in which at least one in ten serves went for an ace. But in five other matches, he didn’t hit a single one! Some of the variation is due to good and bad serving performances, but a substantial part can be explained by the man on the other side of the net.

As it turns out, last night was an aberration for the German. Mayer is below-average at ace prevention, allowing 8% more aces than an average player, ranking 80th among the 139 active players whose results I analyzed.

I looked at every 2011 and 2012 match, using only those matches in which both players racked up 10 matches in the last fifteen months. After calculating each player’s ace rate, I generated an “expected” number of aces for each returner. Simply tallying how many aces a player allowed isn’t good enough–this way, we adjust for the quality of the server.

Mayer, for instance, played 70 matches in that span against opponents who also played at least 10 matches. (I excluded guys who played fewer than 10 because their ace rate in such a small number of matches may say more about their opponents than themselves.) In his 4812 return points, he allowed 345 aces. But based on the serving abilities of his opponents, he should have allowed only 321. Those numbers will look a little better after last night, but not enough to move him up very much in the rankings.

By contrast, the best returners get their racquets on just about everything. Atop the list is Gael Monfils, who allows barely half the aces that we would expect him to. The top eight returners all reduce expected ace rates by at least a third.

In the table below, I’ve shown these stats for the ten players who appear to be the best at avoiding aces, along with 20 other players of interest.

Player                 Rank  Matches  vAce%  expAce%    Diff  
Gael Monfils              1       62   3.5%     6.8%    -48%  
Benoit Paire              2       23   3.8%     6.3%    -40%  
Andy Murray               3       81   4.4%     7.3%    -39%  
Stanislas Wawrinka        4       61   4.2%     7.0%    -39%  
Cedrik Marcel Stebe       5       12   3.2%     5.2%    -38%  
Viktor Troicki            6       70   4.3%     7.0%    -38%  
Gilles Simon              7       77   4.7%     7.3%    -36%  
David Ferrer              8       90   5.1%     7.8%    -35%  
Carlos Berlocq            9       53   4.7%     7.0%    -32%  
Mardy Fish               10       71   5.7%     8.3%    -31%  

Jo Wilfried Tsonga       14       89   5.7%     7.9%    -28%  
Roger Federer            20       92   6.0%     7.9%    -24%  
Novak Djokovic           22       89   6.4%     8.4%    -24%  
Kei Nishikori            32       63   5.8%     7.0%    -17%  
Rafael Nadal             34       91   7.4%     8.8%    -16%  
Nikolay Davydenko        38       60   5.8%     6.7%    -14%  
Sam Querrey              39       35   6.7%     7.8%    -14%  
Milos Raonic             40       60   6.7%     7.6%    -12%  
Kevin Anderson           53       74   7.5%     8.0%     -6%  
John Isner               59       68   7.6%     7.8%     -2%  

Radek Stepanek           73       62   8.6%     8.0%      6%  
Lukasz Kubot             74       44   8.5%     8.0%      7%  
Ivo Karlovic             78       45   7.9%     7.3%      7%  
Juan Martin Del Potro    81       84   8.8%     8.1%      9%  
Tomas Berdych            91       87   8.5%     7.6%     12%  
David Nalbandian        102       43   9.4%     7.9%     20%  
Arnaud Clement          120       17   9.3%     7.2%     29%  
Andy Roddick            130       55  11.8%     8.3%     42%  
Bernard Tomic           135       38  12.8%     8.5%     50%  
Olivier Rochus          139       36  14.7%     7.2%    103%

Before we go anointing Monfils and Benoit Paire the greatest returners in the game, it’s important to remember the serious limitations of the ace stat. Much more important is getting the return in play. But except for Grand Slam matches, we don’t have those numbers. In the meantime, we can use ace rate and return points won as proxies for return skills.

Who Can Stop John Isner?

Last week, John Isner beat world number one Novak Djokovic. Earlier this year, the victim was Roger Federer. At least year’s French Open, Rafael Nadal had to go to five sets to eliminate the big man. Between Isner’s massive serve and the general improvement in his game, it seems that he can beat anybody.

To beat big John, you need either a strong return game or solid tiebreaker skills. Ideally, you’d have both. (The only alternatives are to catch him on an off-day or to play him on a slow clay court.) Let’s take a look at how opponents have fared against the Isner serve over the course of his career.

One surprising indicator of return prowess is ace-rate-against. We tend to think of ace rate as a function only of the server’s ability, perhaps coupled with surface speed. But returner’s have plenty to say about it, too. Simply looking at Isner’s 17 tour-level matches this year, we see a remarkable range of ace rates, from 36.6% of points against Gilles Muller in Memphis down to 5.6% against Federer in Indian Wells. Surface plays a role, as do a variety of other factors (maybe Isner was tired after beating Djokovic in the semifinal last week), but some players are considerably better than others at getting the ball back in play.

A thorough look at that phenomenon is a subject for another day. There’s plenty to do simply comparing performances against Isner. As I’ve noted before, a big serve doesn’t necessarily make a player more unpredictable, though of course such a weapon might make him a better player.

63 players have faced Isner at least twice in tour-level events. Of those, the most effective has been Lleyton Hewitt, holding Isner’s ace rate under 10% and winning almost half of Isner’s serve points. However, the most recent of those two matches was almost two years ago. Still, it’s not surprising to see a world-class counterpuncher atop this list–Hewitt limits aces and service holds against just about everybody.

We find more of the same near the top of the list, with Juan Ignacio Chela, Gilles Simon, and Nikolay Davydenko all in the top 10, ranked by the rate of return points won. Height might also help in handling the physics-defying bounces of the Isner serve: both Tomas Berdych and Juan Martin Del Potro are among the top 15, though some other tall guys (Kevin Anderson and Ivo Karlovic are shown below) have generally weak return games, so the argument doesn’t seem to apply to them.

The unexpected contrast on this list is to find Nadal several spots below Djokovic, Federer, and Andy Murray. Nadal allows about the same ace rate as Djokovic and Murray, but he doesn’t perform as well on the balls he gets back in play. One popular theory is that because of his height, Isner is able to neutralize some of Rafa’s spin. Regardless of the reason why, it’s even more unexpected to see Rafa so far down the list, since two of the three Nadal-Isner matches have taken place on clay.

Here are some of the raw results for players who have faced Isner two or more times. I’ve shown the 20 opponents who have won the most return points, along with ten other notable players, whose ranks (out of 63) are shown in parenthesis.

Opponent                 SvPts  Matches   Ace%  SvPtsWon  
Lleyton Hewitt             124        2   8.9%     53.2%  
Tomas Berdych              300        3  11.7%     57.7%  
Thiemo De Bakker*          165        2   9.1%     60.0%  
Mikhail Youzhny            258        2  16.3%     61.6%  
Juan Ignacio Chela         269        3   6.7%     62.1%  
Novak Djokovic             191        2  14.1%     62.3%  
Andy Murray                224        2  13.8%     62.5%  
Roger Federer              243        3  11.5%     63.0%  
Gilles Simon               244        2  15.2%     63.9%  
Nikolay Davydenko          248        3  18.5%     64.1%  

David Ferrer               326        4  14.7%     64.4%  
Viktor Troicki             234        3   9.0%     64.5%  
Juan Martin Del Potro      201        3  16.4%     64.7%  
Robin Haase                233        2  15.0%     64.8%  
Rafael Nadal               336        3  13.7%     64.9%  
Richard Gasquet            221        2  19.0%     65.2%  
Marat Safin                115        2  13.9%     65.2%  
Mardy Fish                 424        4  13.4%     65.6%  
David Nalbandian           259        2  19.7%     65.6%  
Feliciano Lopez            207        2  19.3%     66.2%  

(22) Jurgen Melzer         177        2  16.4%     66.7%  
(25) Fernando Gonzalez     185        2  16.8%     68.6%  
(27) Gael Monfils          651        6  15.4%     69.1%  
(29) Andy Roddick          466        5  20.0%     69.5%  
(32) Jo Wilfried Tsonga    227        2  13.2%     70.5%  
(40) Kevin Anderson        443        6  16.9%     71.6%  
(41) Ivo Karlovic          289        3  15.9%     71.6%  
(46) Lukasz Kubot          167        2  21.0%     73.1%  
(57) Alex Bogomolov Jr     221        3  23.1%     77.4%  
(63) Andrey Golubev        127        2   9.4%     84.3%

(De Bakker gets an asterisk because one of his two matches immediately followed Isner-Mahut, and John was playing injured.)

An interesting avenue for further research is whether return quality against Isner differs much from return quality against players in general. Sure, Isner wins more points on serve and hits more aces, but looking at the list above, it doesn’t seem to differ much from a ranking of the game’s best returners. For all of his uniqueness, he’s simply one very big server in a game full of big servers. As he goes deeper in more tournaments, perhaps we’ll gain a better grasp of what players need to do to stop him.

Top Four Domination

Every time the big four fills up all four spots in the semifinals, we hear the same trivia–how rarely the top four seeds all reach the semifinals; how often this particular group of four has done it, and so on. There’s no doubt that the current big four has dominated men’s tennis in a way that has rarely been seen before.

Words like “domination” aren’t very easy to quantify, which is why commentators fall back on those few bits of trivia. We can take a closer look to determine whether the current big four stands out as much as we think it does.

Won-loss record

Last year, the big four played 251 tour-level matches (not counting Davis Cup) against everybody else. They won 228 of them, for a winning percentage of 90.8%. My database goes back to 1991, and there hasn’t been a year in that time frame where the top four players did any better.

(For today’s purposes, each year’s top four are defined as the four men at the top of the year-end rankings. All numbers exclude Davis Cup and go back to 1991.)

In fact, four of the five best W-L records have come since 2004. 2008 and 2009, when the current top four was already reigning, are ranked 3rd and 4th. (The second best season for the top four, by this measure, was 2005, when Andy Roddick and Lleyton Hewitt complemented Roger Federer and Rafael Nadal.)

Slam performance

What really matters are the majors, right? Last year, the big four played 82 matches against everybody else at the slams, and won 80 of them, for a jaw-dropping 97.6% winning percentage. You might guess that it, as well, is the best in the last 20 years.

In fact, the second and third best top-four slam performances came in 2007 and 2008–each one including Federer, Nadal, and Novak Djokovic. (In 2007, Nikolay Davydenko was the year-end number four.) Both of those years, the top four lost only four grand slam matches to others.

Masters performance

The majors give us a small (though important) sample; the masters series offers more tournaments with similar high-quality fields. Largely due to Andy Murray‘s dreadful March, this is where the 2011 foursome falters a bit. Their record against everybody else of 90-13 is “only” third-best of the last twenty years.

But wait–the top masters series record was in 2009, of course with the same top four. And the second-best masters series record was in 2005, when Federer and Nadal ruled the world.

Beating the rest of the top 10

It’s no shock when the top four cruise through the early rounds of tournaments. What makes the current top four special is the way they regularly shut everyone else out of the last rounds, defeating excellent players such as Jo-Wilfried Tsonga, Tomas Berdych, and Juan Martin Del Potro.

Last year, the top four went 34-12 (73.9%) against the rest of the year-end top 10. That’s fourth-best of the last twenty years. The standout season, once again, was 2005, when Federer, Nadal, Roddick, and Hewitt went 30-4 (!) against the next six guys in the rankings. In both 2004 and 2006, the top four won exactly three-quarters of their matches against five through ten, just beating out last year’s top four.

To put these numbers in perspective, it is by no means a foregone conclusion that the top four beat up on the next six. In 1991, the top four of Edberg, Courier, Becker, and Stich actually posted a losing record against guys ranked five through ten. In both 1996 and 2000, the record was an even .500.

The bigger picture

Of course, there’s more to domination than performance in a single year. Much of the current big four’s reputation stems from their longevity atop the rankings, and looking at single years ignores that.

But as we’ve seen, there’s no need to look at more than one season. The big four was, in 2011, one of the most dominating quartets of the last 20 years by several measures, and according to two such measures, they were the most successful top four in recent memory.

Why? (In brief)

Here are three theories that might explain why the big four has so distanced itself from the pack:

These four guys are historically good.
The rest of the field these days is not that good. Or, at least, they are overawed by the big four.
Court speeds have become more uniform, meaning that top players win all year round, instead of a few specialists racking up big points for only a couple months.

The first two are possible. Certainly, Federer and Nadal are historically good, and Djokovic’s 2011 season was astounding. I doubt the rest of the pack is to blame–they seem plenty good to me, even if few of them are that good very much of the time.

I’m tempted by the third theory. As recently as 2003, there was almost always one clay-court specialist in the year-end top four–Juan Carlos Ferrero, Gustavo Kuerten, Sergei Bruguera. At the same time, guys like Pete Sampras, Pat Rafter, and Goran Ivanisevic rarely made a dent on clay.

Thus, no matter how many slams Sampras won, or how many clay titles Kuerten took, the top four just weren’t dominant year round. The idea that the same four players would reach the quarters, or even semis of every slam was borderline ridiculous. Now, it’s almost expected.

Of course, we can argue about the causes of this as well. Are the top four successful on all surfaces because the surfaces are more uniform? Because they are historically good? Because the game (or its equipment) has changed in such a way to make surface differences less meaningful? That’s a subject for another day.

The Non-Threatening Dr. Ivo

The perception in tennis is that some players are always dark horses, guys who on any given day might play well above their ranking. Often, these players have “top ten talent” coupled with mental lapses–think Gael Monfils, Marcos Baghdatis, Thomaz Bellucci, Philipp Kohlschreiber. Their rankings sag because of brainless losses (Monfils to Lukasz Kubot at Wimbledon, Baghdatis to somebody every third week), but they occasionally flash their brilliance with a surprising result.

Put it together, and you have a dark horse. There’s a special sort of dark horse upon whom everyone seems to agree: the freakishly tall ace machine. Rob Koenig sounds sensible tweeting about Roger Federer‘s third round match against Ivo Karlovic: “Karlovic v Fed?? Even though Fed has a good record against him, he’s not a guy you wanna see on your side of the draw.” That’s the official line before just about every match Ivo or John Isner plays. The unstoppable serves make them capable of anything.

Or do they? A barrage of bombs starting almost ten feet in the air and bouncing over your head doesn’t sound like a fun day on the court, but does it translate into more losses for top players?

The short answer is no. If anything, Karlovic has shown himself far less likely than the average player to perform above or below his ranking. Last August, I created a metric called ‘Upset Score’ designed to measure how often a player wins against a superior opponent or loses to an inferior one. (Player ability is measured by my ranking system, which predicts match outcomes better than ATP rankings and considers surface.) The metric counts extreme upsets more heavily, so Ivo beating David Ferrer is scored as much more meaningful than defeating, say, Stanislas Wawrinka. Of the 87 players who had 40 or more ATP-level matches in the 20-month span I analyzed, Karlovic had the tenth lowest Upset Score.

This flies directly in the face of conventional wisdom. Looking at the current rankings, we find Ivo just below the likes of Santiago Giraldo and Olivier Rochus–neither one of whom would be viewed as a “tricky” third round opponent. Yet both have Upset Scores in the top half of active players. While there’s no doubt Karlovic was once a very dangerous opponent (as his peak ranking of 14 suggests), he has only one top ten scalp in his last twelve tries, dating back to 2009 Wimbledon. We have to go back to the first half of 2007 to find a stretch in which he was a consistent threat to top players.

Isner isn’t as predictable, but delivers fewer upsets than 60% of the guys on tour. Same story as with Ivo: more often than not, he wins and loses according to past performance. Big John has won two of his last fourteen matches against the top ten, and one of those was an ‘upset’ of Nikolay Davydenko, who by this metric is the least predictable man on the tour.

Massive servers may make for more interesting matches–against any opponent, it’s safe to say that Isner and Karlovic are more likely to deliver a tiebreak or four. But if you’re a top player deciding who you’d like to see coming up in your bracket, you probably don’t care whether you win 6-1 or 7-6(8). Whatever the score, Karlovic is best seen as a steady player on the fringes of the top 50, not some loose cannon who will knock out a top seed one day and lose to a qualifier the next.

Graduating From Challengers

The best players don’t take long before they show you how good they are. Tennis fans are rightfully excited about guys like Bernard Tomic and Milos Raonic, youngsters who have already established themselves at ATP level–if they are this good at 18, or 21, imagine how good they will be.

I’m always looking for ways to quantify that promise. In the past, I’ve focused on the rankings, noticing that nearly everyone who reached #1 had broken into the top 100 before their 19th birthday. Another angle is to see how long a player lasts at the challenger level.

The best players seem to skip the challenger level altogether. It’s a bit like baseball players and Triple-A: some prospects are ready for the big time, so they never play in the highest level of the minor leagues. Roger Federer only played eight events in his challenger career, Nadal played 12, and Djokovic played 11–out of which he won three titles. Andy Roddick also won three challenger titles in only six events at that level.

A player can only move so quickly if they gain entry to tour-level events and they take advantage of the opportunities. Roddick won 20 matches as a wild card in 2001. Djokovic reached the third round of both Wimbledon and the U.S. Open on his first try. A few accomplishments like that, plus the points from a couple of challenger titles, and you’re ranked in the top 100, good enough to earn direct entry into most ATP events. That’s essentially what happened to Milos Raonic after he reached the fourth round in Melbourne last year.

This suggests a new type of filter to separate the prospects from the wannabes. If someone takes two years to consistently go deep at challenger events and fails to make an impact at the ATP level, they probably aren’t headed for the top 10. But if someone gets into the top 50 or 60 with only a couple dozen challengers in their past, they just might be something special.

I investigated the challenger careers of everyone currently in the ATP top 100. Eight of the ten guys who played the fewest challengers are (in order): Roddick, Federer, Juan Carlos Ferrero, Djokovic, Nadal, Gael Monfils, Andy Murray, and Juan Monaco.

The other two? Milos Raonic and Bernard Tomic, who played 16 and 18 challengers, respectively. Other prospects in the same range are Kei Nishikori (22), Cedrik-Marcel Stebe (25), and Ryan Harrison (28). While Stebe and Harrison may play a few more, they still haven’t reached the totals of Jo-Wilfried Tsonga (29), Richard Gasquet (32), or David Ferrer (34). Nikolay Davydenko spent even longer (41 events) on the challenger tour before beginning his ascent to world #3.

More than half of the top 100 played at least 50 challengers, and that’s generally the half you don’t want to be in. The most promising career trajectory for challenger vets is that of Janko Tipsarevic, who played 89 challengers (winning 10) before putting it all behind him. Most of the men near him on the list (Tobias Kamke, 88; Andreas Beck, 90; Dudi Sela, 90) can only dream of doing so well.

With a few exceptions like Tipsarevic (and Monaco, who largely skipped the challenger tour but hasn’t become a consistent threat on tour), this is a filter with some potential. It overlaps quite a bit with age–if you see a 20-year-old in the top 100, he probably hasn’t played nearly as many challengers as a 27-year-old who finally broke in. Where “number of challengers” might trump age is when comparing players who–for reasons that may not be purely attributable to talent–started playing professionally at much different times. John Isner, for example, has only played 20 challengers, but didn’t break into the top 100 until he was nearly 23. His advanced age would have told us he had little potential while hiding the fact he spent years playing college tennis. The length of his challenger tour career indicates that once he went pro, it wasn’t long before he was ready to play with the big boys.

Whichever metric (age or challenger experience) you prefer, it’s tough to get excited about someone like Alex Bogomolov Jr., who was 28 when he first cracked the top 100, after a career including 151 challengers. Among the current top 100, only Michael Russell and Ricardo Mello have played more. Another man with little promise is (I’m sad to say) Flavio Cipolla, 28 years old and #75 in the world. The Italian has played 136 challengers and won only 51% of his matches in those events.

Another lesson from these numbers is that you can watch a whole lot of challenger-level matches without seeing any real prospects. (That isn’t to say that Kenny de Schepper versus Michael Yani isn’t entertaining. It is.) If future top-tenners play only a handful of challenger events, your average player in a challenger is a guy whose best hope is a peek into the top 50. Or–if you’re lucky–Janko Tipsarevic.