Ten seeds have been eliminated, only the fifth time in the 32-seed era that the number of first-round upsets has reached double digits. Four of the top ten seeds were among the victims, marking the first time since 1994 that so many top-tenners failed to reach the second round of a Grand Slam.

Things are particularly dramatic in the top half of the draw, where Serena Williams can now reach the final without playing a single top-ten opponent. In a single day of play, my (conservative) forecast of her chances of winning the tournament rose from 42% to 47%, only a small fraction of which owed to her defeat of Vitalia Diatchenko.

However, plenty of obstacles remain. Serena could face Agnieszka Radwanska or Madison Keys in the fourth round, and then Belinda Bencic–the last player to beat her–in the quarters. A possible semifinal opponent is Elina Svitolina, a rising star who took a set from Serena at this year’s Australian Open.

The first-round carnage didn’t include most of the players who have demonstrated they can challenge the top seed. Five of the last six players to beat Serena–Bencic, Petra Kvitova, Simona Halep, Venus Williams, and Garbine Muguruza–are still alive. Only Alize Cornet, the 27th seed who holds an improbable .500 career record against Serena, is out of the picture.

What’s more, early-round bloodbaths haven’t, in the past, cleared the way for favorites. In the 59 majors since 2001, when the number of seeds increased to 32, the number of first-round upsets has had little to do with the likelihood that the top seed goes on to win the tournament.

In 18 of those 59 Slams, four or fewer seeds were upset in the first round. The top seed went on to win five times. In 22 of the 59, five or six seeds were upset in the first round, and the top seed won eight times.

In the remaining 19 Slams, in which seven or more seeds were upset in the first round, the top seed won only five times. Serena has “lost” four of those events, most recently last year’s Wimbledon, when nine seeds fell in their opening matches and Cornet defeated her in the third round.

This is necessarily a small sample, and even setting aside statistical qualms, it doesn’t tell the whole story. While Serena has failed to win four of these carnage-ridden majors, she has won three more of them when she wasn’t the top seed, including the 2012 US Open, when ten seeds lost in the first round and Williams went on to beat Victoria Azarenka in the final.

Taken together, the evidence is decidedly mixed. With the exception of Cornet, the ten defeated seeds aren’t the ones Serena would’ve chosen to remove from her path. While her odds have improved a bit on paper, the path through Keys, Bencic, Svitolina, and Halep or Kvitova in the final is as difficult as any she was likely to face.

]]>Diatchenko wasn’t the only player to exit yesterday without finishing a match. Of the 32 men’s matches, six ended in retirement. On the other hand, none of those were nearly as bad. All six injured men played at least two sets, and five of them won a set.

The prominence of Serena’s first-round match, combined with the sheer number of Monday retirements, is sure to keep pundits busy for a few days proposing rule changes. As we’ll see, however, there’s little evidence of a trend, and no need to change the rules.

**Men’s slam retirements in context**

Before yesterday’s bloodbath, there had been only five first-round retirements in the men’s halves of this year’s Grand Slams. The up-to-date total of 11 retirements is exactly equal to the annual average from 1997-2014 and the same as the number of first-round retirements in 1994.

The number of first-round Slam retirements has trended up slightly over the last 20 years. From 1995 to 2004, an average of ten men bowed out of their first-round matches each year. From 2005 to 2014, the average was 12.2–in large part thanks to the total of 19 first-round retirements last season.

That rise represents an increase in injuries and retirements in general, not a jump in unfit players showing up for Slams. From 1995 to 2004, an average of 8.5 players retired or withdrew from Slam matches *after* the first round, while in the following ten years, that number rose to 10.8.

Retirements at other tour-level events tell the same story. At non-Slams from 1995-2004, the retirement rate was about 1.3%, and in the following ten years, it rose to approximately 1.8%. (There isn’t much of a difference between first-round and later-round retirements at non-Slams.)

Injury rates in general have risen–exactly what we’d expect from a sport that has become increasingly physical. Based on recent results, we shouldn’t be surprised to see more retirements in best-of-five matches, as most of yesterday’s victims would’ve survived to the end of a best-of-three contest.

**Women’s slam retirements**

In most seasons, the rate of first-round retirements in women’s Grand Slam draws is *barely half *of the corresponding rate in other tour events.

In the last ten years, just over 1.2% of Slam entrants have quit their first-round match early. The equivalent rate in later Slam rounds is 1.1%, and the first-round rate at non-Slam tournaments is 2.26%. Diatchenko was the fifth woman to retire in a Slam first round this year, and if one more does so today, the total of six retirements will be exactly in line with the 1.2% average.

One painful anecdote isn’t a trend, and the spotlight of a high-profile match shouldn’t give any more weight to a single data point. Even with the giant checks on offer to first-round losers, players are not showing up unfit to play any more often than they do throughout the rest of the season.

]]>**The Problem**

Quantifying aggression in tennis presents a quandary for the outsider. An aggressive shot and a defensive shot can occur on the same stroke at the same place on the court at the same point in a rally. To know whether one occurred, we need information on court positioning and shot speed, not only of the current shot, but the shots beforehand.

Since this data only exists for a fraction of tennis matches (via Hawkeye) and is not publicly available, using aggressive shots as a metric is untenable for public consumption. In a different era, net points may have been a suitable metric, but almost all current tennis, especially women’s tennis, revolves around baseline play.

Net points also can take on a random quality and may not actually reflect aggression. Elina Svitolina, according to data from the Match Charting Project, had 41 net points in her match against Yulia Putintseva at Roland Garros this year. However, this was not an indicator of Svitolina’s aggressive play so much as Putintseva hitting 51 drop shots in the match.

The Match Charting Project does give some data to help with this problem however. We can use the data to get the length of rallies and whether a player finished the point, i.e. he/she hit a winner or unforced error or their opponent hit a forced error. If we assume an aggressive player would be more likely to finish the point and would be more likely to try to finish the point sooner rather than later in a rally, we can build a metric.

**The Metric**

To calculate aggression using these assumptions, we need to know how often a player finished the point and how many opportunities did they have to finish the point, i.e. the number of times they had the ball in play on their side of the net. To measure the number of times a player finished the point, we add up the points where they hit a winner or unforced error or their opponent hit a forced error. For short, I will refer to these as “Points on Racquet”.

To measure how many opportunities a player had to finish the point, we calculate the number of times the ball was in play on each player’s side of the net. For service points, we add 1 to the length of each rally and divide it by 2, rounding up if the result is not an integer. For return points, we divide each rally by 2, rounding up if the result is not an integer. These adjustments allow us to accurately count how often a player had the ball in play on their side of the net. For brevity, I will call these values “Shot Opportunities”.

If we divide Points on Racquet by Shot Opportunities we will get a value between 0 and 1. If a player has a value of 0, they never finish points when the ball is on their side of the net. If the player has a value of 1, they only hit shots that end the point. As the value increases, a player is considered more aggressive. For short, I will call this measure an “Aggression Score.”

**The Data**

Taking data from the latest upload of the Match Charting Project, I found women’s players with 2000 or more completed points in the database (i.e. all points that were not point penalties or missed points). Eighteen players fitted these criteria. Since the Match Charting Project is, unfortunately, a nonrandom sample of matches, I felt uncomfortable making assessments below a very large number of data points. Using 2000 or more data points, however, an overwhelming amount of data would be required to overcome these assessments, giving some confidence that, while bias exists, we get in the neighborhood of the true aggression values.

**The Results**

Below are the results from the analysis. Tables 1-3 provide the Aggression Scores for each player overall, broken down into serve and return scores and further broken down into first and second serves. They also provide differences between where we would expect the player to be more aggressive (Serve v. Return, First Serve v. Second Serve and Second Serve Return v. First Serve Return).

*Table 1: Aggression Scores*

Name Overall On Serve On Return S-R Spread S Williams 0.281 0.3114 0.2476 0.0638 S Halep 0.1818 0.2058 0.1537 0.0521 M Sharapova 0.2421 0.2471 0.2358 0.0113 C Wozniacki 0.1526 0.1788 0.1185 0.0603 P Kvitova 0.3306 0.347 0.309 0.038 L Safarova 0.2475 0.2694 0.2182 0.0512 A Ivanovic 0.2413 0.247 0.2335 0.0135 Ka Pliskova 0.256 0.2898 0.2095 0.0803 G Muguruza 0.231 0.238 0.2214 0.0166 A Kerber 0.1766 0.2044 0.1433 0.0611 B Bencic 0.1742 0.1784 0.1687 0.0097 A Radwanska 0.1473 0.1688 0.1207 0.0481 S Errani 0.1232 0.1184 0.1297 -0.0113 E Svitolina 0.1654 0.1769 0.1511 0.0258 M Keys 0.3017 0.3284 0.2677 0.0607 V Azarenka 0.1892 0.1988 0.1762 0.0226 V Williams 0.2251 0.247 0.1944 0.0526 E Bouchard 0.2458 0.2695 0.2157 0.0538 WTA Tour 0.209 0.2254 0.1877 0.0377

*Table 2: Serve Aggression Scores*

Name Serve First Serve Second Serve 1-2 Spread S Williams 0.3114 0.3958 0.2048 0.191 S Halep 0.2058 0.2298 0.1587 0.0711 M Sharapova 0.2471 0.2715 0.1989 0.0726 C Wozniacki 0.1788 0.2016 0.121 0.0806 P Kvitova 0.347 0.3924 0.2705 0.1219 L Safarova 0.2694 0.3079 0.1983 0.1096 A Ivanovic 0.247 0.2961 0.1732 0.1229 Ka Pliskova 0.2898 0.3552 0.1985 0.1567 G Muguruza 0.238 0.2906 0.1676 0.123 A Kerber 0.2044 0.2337 0.1384 0.0953 B Bencic 0.1784 0.2118 0.1218 0.09 A Radwanska 0.1688 0.2083 0.0931 0.1152 S Errani 0.1184 0.1254 0.0819 0.0435 E Svitolina 0.1769 0.2196 0.105 0.1146 M Keys 0.3284 0.3958 0.2453 0.1505 V Azarenka 0.1988 0.2257 0.1347 0.091 V Williams 0.247 0.3033 0.1716 0.1317 E Bouchard 0.2695 0.3043 0.2162 0.0881 WTA Tour 0.2254 0.2578 0.1679 0.0899

*Table 3: Return Aggression Scores*

Name Serve 1st Return 2nd Return Spread S Williams 0.2476 0.2108 0.3116 0.1008 S Halep 0.1537 0.1399 0.1778 0.0379 M Sharapova 0.2358 0.2133 0.2774 0.0641 C Wozniacki 0.1185 0.1098 0.132 0.0222 P Kvitova 0.309 0.2676 0.3803 0.1127 L Safarova 0.2182 0.1778 0.2725 0.0947 A Ivanovic 0.2335 0.1952 0.3027 0.1075 Ka Pliskova 0.2095 0.1731 0.2715 0.0984 G Muguruza 0.2214 0.1888 0.2855 0.0967 A Kerber 0.1433 0.1127 0.191 0.0783 B Bencic 0.1687 0.1514 0.197 0.0456 A Radwanska 0.1207 0.1049 0.1464 0.0415 S Errani 0.1297 0.1131 0.1613 0.0482 E Svitolina 0.1511 0.1175 0.1981 0.0806 M Keys 0.2677 0.2322 0.3464 0.1142 V Azarenka 0.1762 0.1499 0.2164 0.0665 V Williams 0.1944 0.1586 0.255 0.0964 E Bouchard 0.2157 0.1757 0.2837 0.108 WTA Tour 0.1877 0.1609 0.2341 0.0732

The first plot shows the relationship between serve and return aggression scores as well as the regression line with a confidence interval (note: since there are only 18 players in the sample, treat this regression line and all of the others in this post with caution).

The second and third plots show the relationships between players’ aggression scores on first serves and their aggression scores on second serves for serve and return points respectively as well as the regression lines with confidence intervals.

The fourth and fifth plots show the relationship between the spread of serve and return aggression scores between first and second serve and the more aggressive point for the player, i.e. first serve for service points and second serve for return points as well as the regression lines with confidence intervals.

We can take away five preliminary observations.

**Sara Errani knows where her money is made.** The WTA is notoriously terrible for providing statistics. However, they do provide leaderboards for particular statistics, including return points and games won. Errani leads the tour in both this year. She also uniquely holds a higher Aggression Score on return points than serve points. From this information, we can hypothesize that Errani may play more aggressive on return points because she has greater confidence she can win those points or because she relies on those points more to win.

**Maria Sharapova is insensitive to context; Elina Svitolina is highly sensitive to context.** She falls outside of the confidence interval in all five plots. More specifically, Sharapova consistently is more aggressive on return points, second serve service points and first serve return points than her scores for service points, first serve service points and second serve return points respectively would predict. She has also lower spreads on serve and return than her more aggressive points would predict.

This result suggests that Sharapova differentiates relatively little in how she approaches points according to whether she is serving or returning or whether it is first serve or second serve. Svitolina exhibits the opposite trend as Sharapova. Considering anecdotal thoughts from watching Sharapova and Svitolina, these results make sense. Sharapova’s serve does not seem to vary between first and second and we see a lot of double faults. Svitolina can vary between aggressive shot-making and big first serves and conservative play. Hot takes are not always wrong.

**Lucie Safarova, meet Eugenie Bouchard;** **Ana Ivanovic, meet Garbine Muguruza. **Looking at the plots, it is interesting to note how Safarova and Bouchard seem to follow each other across the various measures. The same is true for Ivanovic and Muguruza. A potential application of the aggression score is that it can point us to players that are comparable and may have similar results. Players with good results against Safarova and Ivanovic may have good results against Bouchard and Muguruza, two younger players whom they are much less likely to have played.

**Serena Williams and Karolina Pliskova serve like Madison Keys and Petra Kvitova, but they are very different.** Serena, Pliskova, Keys and Kvitova are all players that are known for their serves as their weapons. Serena and Pliskova have the third and fourth highest Aggression Scores respectively. However, they also have wide spreads on serve and return scores and they have much lower second serve service point scores than their first serve scores would predict, whereas Keys is about where the prediction places her and Kvitova is far more aggressive than her first serve points would predict.

While Serena is still a relatively aggressive returner, she rates lower on first serve return aggression than Maria Sharapova. Pliskova falls to the middle of the pack on return aggression. Kvitova and Keys, in contrast, are both very aggressive on return points. My hypothesis for the difference is that while Serena and Pliskova are aggressive players, their scores get inflated by using their first serve as a weapon and they are only somewhat more aggressive than the players that score below them. Kvitova and Keys, on the other had, are exceptionally aggressive players.

**The WTA runs through Victoria Azarenka and Madison Keys.** Oddly, the players who seemed to best capture the relationships between all of the aggression scores and spreads of aggression scores were Victoria Azarenka and Madison Keys. Neither strayed outside of the confidence interval and often ended up on the best-fit line from the regressions. They define average for the WTA top 20.

These thoughts are preliminary and any suggestions on how they could be used or improved would be helpful. I also must beseech you to help with the Match Charting Project to put more players over the 2,000 point mark and get more points for the players on this list to help their Aggression Scores a better part of reality.

]]>Serena Williams is, without question, the best player in women’s tennis right now. She’s held that position off and on for over a decade, and it’s easy to make the case that she’s the best player in WTA history.

The longer one player dominates a sport, the tougher it is to distinguish between her ability level and the competitiveness of the field. Is Serena so successful right now because she is playing better than any woman in tennis history, or because by historical standards, the rest of the pack just isn’t very good?

As we’ll see, the level of play in women’s tennis has remained relatively steady over the last several decades. While there is no top player on tour these days who consistently challenges Serena as Justine Henin or peak Venus did, the overall quality of the pack is not much different than it has been at any point in the last 35 years.

**Quantifying eras**

Every year, a few new players break in, and a few players fade away. If the players who arrive are better than those who leave, the level of competition gets a bit harder for the players who were on tour for both seasons. That basic principle is enough to give us a rough estimate of “era strength.”

With this method, we can compare only adjacent years. But if we know that this year’s field is 1% stronger than last year’s, and last year’s field was 1% stronger than the year before that, we can calculate a comparison between this year’s field and that of two years ago.

Since 1978, the level of play has fluctuated within a range of about 10%. The 50th-best player from a strong year–1995, 1997, and 2006 stand out–would win 7% or 8% more points than the 50th-best player from a weak year, like 1982, 1991, and 2005. That’s not a huge difference. One or two key players retiring, breaking on to the scene, or missing substantial time due to injury can affect the overall level of play by a few percentage points.

The key here is that a dominant season in the mid-1980s isn’t much better or worse than a dominant season now. Perhaps Martina Navratilova faced a stiffer challenge from Chris Evert than Serena does from Maria Sharapova or Simona Halep, but that difference is at least partially balanced by a stronger pack beyond the top few players. Serena probably has to work harder to get through the early rounds of a Grand Slam than Martina did.

**Direct comparisons**

So, Serena’s great, and her greatness isn’t a mirage built on a weak era. Using this approach, how does she compare with the greats of the past?

Given an estimate of each season’s “pack strength,” we can rate every player-season back to 1978. For instance, if we approximate Serena’s points won in 2015 (based on games won and lost), we get a Dominance Ratio (the ratio of return points won to serve points lost) of 2.15. In layman’s terms, that means that she’s beating the 50th-ranked player in the world by a score of 6-1 6-1 or 6-1 6-2. The 2.15 number means she’s winning 115% more return points than that mid-pack opponent. If the pack were particularly strong this season, we’d adjust that number upwards to account for the level of competition.

Repeat the process for every top player, and we find some interesting things.

Serena’s 2.15–the second-best of her career, behind 2.19 in 2012–is extremely good, but only the 21st-ranked season since 1978. By this metric, the best season ever was Steffi Graf‘s 1995 campaign, at 2.42, with Navratilova’s 1986 and Evert’s 1981 close behind at 2.38.

Graf has seven of the top 20 seasons since 1978, Navratilova has four, and Evert has three. Venus’s 2000 ranks sixth, while Henin’s 2007 ranks tenth.

It seems to have become harder to post these extremely high single-season numbers. In the last ten years, only Serena, Henin, Sharapova, Kim Clijsters, and Lindsay Davenport have posted a season above 2.0. Serena has done so four times, making her the only player in that group to accomplish the feat more than once.

**Best ever?**

As we’ve seen in comparing Serena’s best seasons to those of the other greatest players in WTA history, it’s far from clear that Serena is the greatest of all time. Graf and Navratilova set an incredibly high standard, and since the greats all excelled in slightly different ways, against different peer groups, picking a GOAT may always be a matter of personal taste.

Assigning a rating to the current era, however, isn’t something we need to leave up to personal taste. I’m confident in the conclusion that Serena is not simply padding her career totals against a weak era. If anything, her own dominance–during an era when dominating the women’s game seems to be getting harder–is making her peers look weaker than they are.

]]>Karlovic is one of the greatest servers in the game’s history, and he has in fact hit more than 10,000 aces. Ivanisevic was really good at serving, too, and he might even hold the all-time record. But when it comes down to the details in this week’s ATP press releases, all the numbers are wrong.

Last year, Carl Bialik laid out the two main problems with ATP ace records:

- The ATP doesn’t have any stats from before 1991. (Ivanisevic started playing tour-level matches in 1988.)
- ATP totals don’t include aces from Davis Cup matches, even though Davis Cup results are counted toward won-loss records and rankings.

I’ll add one more: There are plenty of other matches since 1991 with no recorded ace counts, too. By my count, we don’t have stats for 14 of Ivanisevic’s post-1991 matches. (They’re not on the official ATP site, anyway.) That doesn’t count Davis Cup, the Olympics (also no stats), and the now-defunct Grand Slam Cup.

If you like tracking records and comparing the best players from different eras, tennis might not be your sport. All of these problems exist for players who retired only recently, and some of the issues persist to the present day. And if you want to compare Federer or Ivanisevic with, say, Boris Becker or–it’s tough to write this without laughing–Pancho Gonzalez, you’re completely out of luck.

We’ll probably never find ace totals from all of the missing matches. But it seems silly to pretend we can identify the true record-holder and celebrate when these “records” are broken when we so obviously cannot.

**Approximate* career* totals***

What we can do is estimate the number of missing aces for each of the top contenders. In Ivanisevic’s case, his 1988-90 seasons, combined with Davis Cup and other gaps in the record, total nearly 200 matches. Even if we can’t pinpoint the exact number of uncounted aces, we can come up with a number that demonstrates just how far ahead of Karlovic he currently stands.

To fill in the gaps, I calculated each player’s rate of aces per game for each surface for every season he played. For 1988-90, I used 1991 rates. (This post at First Ball In, which I discovered after writing mine, suggests that players improve their ace rates the first few seasons of their careers, so we should adjust a bit downward. That may be right. A 5% penalty for Goran’s 1988-90 knocks off about 60 aces from his total below.)

Once we crunch the numbers, we get an estimated 2,368 aces in Ivanisevic’s 195 “missing” matches. That gives him a career total of 12,551–a mark Karlovic couldn’t achieve until the end of 2017, if then.

But wait–Ivo has some missing matches, too! The gaps in his record only amount to 21 matches, mostly Davis Cup. The same approximation method adds 466 aces to his record, meaning he hit that 10,000th ace back in June, in his second-rounder against Alexander Zverev. Even with those nearly 500 “extra” aces, Ivanisevic’s record is almost surely out of reach.

What about Pete Sampras? Officially, Pete is fifth on the all-time list, with 8,858 aces. But like Goran, he played a lot of matches before record-keeping began in 1991. His ace record is missing nearly 200 matches, as well.

In Sampras’s case, we can estimate that he hit 1,815 aces that aren’t reflected in his official total. (In line with the caveat regarding Goran’s total above, we might want to knock that total down by 50 to reflect the possibility that he hit more aces in 1991 than in 1988-90.)

Making similar minor adjustments to the other members of the top five, Federer and Andy Roddick, here’s what the all-time list should look like, at least in general terms:

Player Official Est Missing Est Total Ivanisevic 10183 2368 12551 Sampras 8858 1815 10673 Karlovic 10022 466 10488 Federer 9279 524 9803 Roddick 9074 694 9768

Coincidentally, Karlovic is officially within 200 aces of Ivanisevic’s all-time record, and while he really isn’t anywhere near the record, he *is* that close our estimate of Sampras’s second-place total.

We can be confident that Ivo is a great server. But if we can’t be sure of his own ace total, mostly amassed in the last decade, it seems foolish to pretend that we’ll know when–or even if–he breaks the all-time record.

]]>I can hardly tell you how excited I am about this. When the concept behind the project was first suggested to me in 2012, I hesitated to act, in part because I didn’t think I could convince enough other people of the project’s merits to build a dataset of this size. I’ve been proven hugely wrong. Even at the beginning of 2015, I figured we’d be lucky to hit the four-figure barrier by the end of the calendar year. Instead, we’ve added matches at a faster pace than ever.

Thanks to MCP contributors, the tennis research community now has access to a standardized dataset of 144,000 points and 580,000 shots. Nothing like this has ever existed in a form that is available to anyone who wants to pursue their own research projects.

I want to take this opportunity to thank **all** of the 50+ MCP contributors. Special mention is owed to Lowell, who with 141 matches is our most prolific charter and who is a big reason why the WTA is even more extensively represented in the database than is the ATP. I’d also like to single out Edo, who started contributing less than three months ago and has already added 43 matches to the tally, including many Grand Slam finals.

The first 1,000 is, I hope, just a beginning. Please consider contributing to the project–download the spreadsheet and read more about how it works here.

To keep up with the project, you can always find the full list of charted matches here, or a list organized by player here. I plan to post a bit more about the Match Charting Project next week here at Heavy Topspin, as well.

]]>Nick Kyrgios isn’t quite as tall as Isner or Karlovic, but his numbers are similar. In the last year, he has won 31.7% of return points, third-worst among the top 50, ahead of only those two players. In fact, since 1991, only five players have lasted a full season at tour-level while winning a lower percentage of return points. To make an impact in the upper echelon of the men’s game, the Australian will need to improve his return game in a big way.

To win matches, you need to break serve or win tiebreaks, and most players don’t demonstrate any particular tiebreak skill. That leaves breaks of serve, and to break serve, you need to win return points. Almost all ATP tour regulars win between 29% and 43% of return points, so a single percentage point or two is a meaningful distinction. While Milos Raonic‘s rate of return points won over the last 52 weeks is a Kyrgios-comparable 32.1%, no other top-ten player is below 36%.

If Kyrgios is to crack the top ten without any substantial improvement in his return game, Raonic is the model. Last year, Milos finished the season at #8 in the rankings despite having won only 33.7% of return points. That’s the lowest rate on record for a player with a year-end ranking in the top ten, and only the seventh time since 1991 that a RPW% below 35% earned someone a spot in the top ten.

Even at 33.7%–two percentage points higher than Kyrgios’s current rate–it took a remarkable run of tiebreak success for Raonic to win as many matches as he did. Milos won 75% of tiebreaks last year, a rate that almost no one has ever sustained beyond a single season. In other words, if Raonic is to continue winning matches at the same pace, he’ll probably need to post better return-game results.

To earn a place in the elite of the top five, the return-game threshold is even higher. Only two players–Pete Sampras and Goran Ivanisevic–have finished a season in the top five with a RPW% below 36%, and only two more–Andy Roddick and Stanislas Wawrinka–have done so with a sub-37% RPW%. Roger Federer, the most serve-oriented of the big four, hasn’t posted a RPW% below 38% in fifteen years.

The difference between 32% and 36% is enormous. To use a baseball analogy, a similar gap in batting average would be, roughly, from .240 to .280. The effects are equally meaningful. At 32%, a player is breaking serve roughly once per eight return games–considerably less than once per set. At 36%, he’s breaking serve almost once per five return games. Improve a few more percentage points to 39%, and he’s breaking every fourth game, almost twice as often as Kyrgios is now.

Those break rates are simply a way of quantifying what we already know at a general level: Players with strong return games have the power to decide matches. The more one-dimensional the playing style, the more likely a match is decided by just a few key points. And the smaller that number of points, the more that luck plays a part.

Of course, luck cuts both ways. It’s what makes players like Isner and Kyrgios so dangerous. Someone like Novak Djokovic or Rafael Nadal can usually dictate play, but against an unbreakable opponent, it all comes down to a few points in a couple of tiebreaks. So big servers tend to rocket into the top 30 or 40. A fifty-fifty winning percentage, especially coupled with a big upset and an occasional deep run at a big tournament, is plenty good enough to earn a spot that high in the rankings.

But without at least a mediocre return game, it’s tough for a big server to get beyond that level. Isner has managed it by winning tiebreaks at one of the best rates of all time, and even he has barely dipped his toe in the top ten. Raonic is a substantially better returner than the American, and it remains to be seen whether he can sustain his impressive tiebreak winning percentage and keep a spot among the game’s best.

Fortunately, Kyrgios has plenty of time to improve and break out of the mold of a one-dimensional big server. If he hopes to make a mark beyond the occasional upset and a home at the fringes of the top 20, that’s exactly what he’ll need to do.

]]>The wider the perspective, the more impressive Kei’s deciding-set record. Since last year’s Australian Open, he’s won 27 of 30 matches that went the distance, including a 13-match winning streak from Halle to London. Back in 2011-12, he won 16 deciding sets in a row, including four against top-ten players.

In his career on tour, Nishikori has won 75 deciding-set matches and lost 20, for a winning percentage of 79%. Using any reasonable minimum number of matches, no other player has come close to that mark. You might recognize some of the other names on this list, ranked by record in deciding sets (minimum 80 matches):

Kei Nishikori 78.9% Bjorn Borg 74.7% Novak Djokovic 74.1% Jimmy Connors 69.8% Rafael Nadal 69.5% Andy Murray 69.4% Rod Laver 68.4% John McEnroe 68.1% Pete Sampras 68.0%

Kei’s career accomplishments don’t quite stack up with those of this crowd, but in terms of deciding-set performance, we’re looking at much more than an early-career fluke. While his numbers are a bit padded by matches that shouldn’t have gone the distance (like his early-round hiccups in Memphis this year against Ryan Harrison and Austin Krajicek), he has been almost as good when facing the best players in the game. Against top-ten opponents, he’s 17-6, good for a 74% winning percentage–a mark that would still put him near the top of the list.

Let’s return to Nishikori’s outrageous recent record of 27-3 in his last 30 deciding sets. Sure enough, no one has ever done better. Nine other players have posted an equal mark in a span of 30 deciding-set matches, including Novak Djokovic, Rafael Nadal, Roger Federer, and Nishikori’s coach Michael Chang. Amazingly, Kei himself had already gone 27-3, back in 2011-12.

To break the tie among these accomplishments, we might look at the difficulty of the 30-match span, as measured by deciding sets against top-tenners. When Djokovic went 27-3, between 2011 Dubai and 2012 Canada, he played 15 of those matches against top-ten opponents,winning 14 of them. (Novak is also 27 of his last 30, including 15 of 17 against top-tenners.) When Nadal had his run, between 2008 Dubai and 2009 Paris, he faced 12 top-tenners, beating 10. Kei has faced only six, winning five.

It’s clear that Nishikori’s deciding-set prowess is a skill, not just a statistical fluke built on easy draws and luck. And based on the performance of the other players who have put together equally impressive deciding-set streaks, we can expect Kei to win most of his upcoming three- and five-setters.

Including streaks that overlap, there have been 27 instances in ATP history when a player won 27 of 30 deciding-set matches, excluding Kei’s and Novak’s current spans. In the ten deciding-set matches that followed each of those streaks, in each instance the player won at least five, and the average was just under seven.

Only once in ATP history has a player gone 27-3 in deciding-set matches and followed it up by winning nine of his next ten. If Nishikori is to match or better that mark, at least he’s assembled the right team: The player he’s chasing is Michael Chang.

]]>Updated phenomenal Djokovic stats: Won 47 of 50 w/ 13 bagels, 1.48 DR (ratio return pt % won to serve pt % lost), 21-2 v Top 10 w/ 8 bagels.

— Carl Bialik (@CarlBialik) April 19, 2015

Armed with stats going back 25 years, we can see how Djokovic’s current performance compares with the best in recent ATP history. In some categories, he is indeed atop the list. In others, he’s merely very close to the best ever.

Let’s start with the simple matter of won-loss record. 47 wins in 50 matches is excellent by any standard. Only four players–Roger Federer, Rafael Nadal, Thomas Muster, and Djokovic himself–have done better. Pete Sampras also won 47 of 50 in a stretch in 1993-94.

The category in which Djokovic most clearly stands out is his performance against top-10 opponents. His 21 top-10 wins in a 50-match stretch outpaces the best of Nadal (18, in 2013), Federer (17, in 2006-07), and Andre Agassi (17, in 1994-95). Only 12 different players have won *ten* top-10 matchups in a 50-match stretch, let alone 20. Novak’s 23 top-10 matches is also the highest on record.

Then there are the bagels. In this span, Djokovic has won 13 sets by a 6-0 score. That’s not quite the best: Federer won 14 in his 2006-07 stretch. Sergi Bruguera (1993) and Agassi (1992-93) also show up here, with 13 bagels over the course of 50 matches.

Finally, let’s turn to aggregate statistics. Dominance Ratio (DR) is the ratio of return points won to serve points lost, and serves as a simple yardstick for–you guessed it–dominance. A DR of 1.0 indicates the two players were equal, 1.1 is a narrow win, and anything in the 1.5 range is a comfortable victory.

As Carl noted in that tweet, Djokovic has maintained a DR of nearly 1.5 over his last 50 matches. That’s not the best of all time–in fact, it’s not even Novak’s best. From 2013 Cincinnati to the second round of 2014 Monte Carlo, Djokovic posted a cumulative DR of 1.49, just edging out his current streak.

But neither mark is number one on the list. As with so many other categories, this one belongs to 2006 Federer. From the 2006 Halle final through the end of the 2007 Australian Open, Fed won 49 of 50 matches, 16 of 16 matches against the top 10, served 14 bagels, and posted an overall DR of 1.54. It would take an extremely strong performance from Djokovic over the next few weeks–even by his own standards–to reach those heights.

If you prefer the more traditional metric of total points won, Fed is still your number one, at 56.84% over that 2006-07 span. A different streak of Novak’s–his historic 2011 run–comes in a very, very close second, at 56.77%. Nadal put together a stretch in 2012-13 of 56.6%. The entire top ten is dominated by these three guys; the only other player who has won more than 56% of total points over 50 matches is Guillermo Coria, who did so in 2003.

Comparing Novak’s current streak to the rest of the field merely emphasizes how much distance he has placed between himself and the pack. Federer’s DR over his last 50 matches is a very respectable 1.37, with Nadal not far behind at 1.29. Kei Nishikori and Milos Raonic aren’t far behind in the official rankings, but by this measure they have an immense amount of ground to make up, with cumulative DRs of 1.17 and 1.16, respectively.

For Djokovic right now, a number that starts with 1.1 is a bad day. In his last 50 matches, he has sunk below 1.2 only seven times. Whichever metric you prefer, we’re watching one of the great performances of modern tennis history.

]]>It’s rare that players of Federer’s stature contest such small events, so we don’t expect to see such lopsided head-to-heads very often. In fact, if we limit our view to events where a player faced at least 10 of the other entrants, it is only the 17th time since 1980 that someone has entered an event with a won-loss percentage of 95% or better against the field.

Federer himself represents two of the previous 16 times this has happened. The most notable of them is 2008 Estoril. He had previously faced 14 of the other players in the draw, and had never lost to any of them in 46 meetings. There are only four other instances of players undefeated against a field, all between 1980 and 1984 and in many fewer matches.

The most eye-grabbing of those early-80s accomplishments was Ivan Lendl‘s record entering the 1980 Taipei event. He had faced 15 of the men in the draw, posting a record of 24-0 up to that point. Lendl’s name is the most common on the list, having entered tournaments with a 95% won-loss record against the field on four different occasions, highlighted by a 79-4 mark against the other competitors at Stratton Mountain in 1988.

Federer won the 2008 title in Estoril and Lendl claimed the 1980 trophy in Taipei, but Lendl was ousted in the second round of the 1988 Stratton Mountain event. Federer has also demonstrated that a stratospheric record against the field is no guarantee of success.

After Estoril, Roger’s second-best record entering an event was in Gstaad in 2013. He held a 73-3 record against the field, with each of the three losses coming against different opponents. He lost his opening-round match in straight sets to Daniel Brands. His record against the field of the previous week’s Hamburg event was nearly perfect as well at 137-8, but Federico Delbonis stopped him in the semifinals there.

Rafael Nadal can tell a similar story. His best record against a field was in Santiago two years ago, coming back from injury. He had lost only 1 of 28 career matches against the other players in the draw. That week, Horacio Zeballos doubled Rafa’s loss count.

In fact, of the 16 times that a player went into an event with a 95% or better record against the field, the favorite won only six of them. Expanding the sample to records of 90% or better, the dominant player won 30 of 72 titles. Neither mark is as good as we’d expect if the historically great players continued to win matches at a 95% or 90% clip. In practice, head-to-head records just aren’t as predictive as they seem to be.

As is evident from some of the examples I’ve given, there are mitigating circumstances for many of these losses, and they aren’t entirely random. These days, when a player enters an event that seems below him, there’s a reason for it. Nadal rarely plays 250s; he was doing so to work his way back into match form. Federer rarely seeks out smaller events on clay; he was experimenting with a new racket.

This week, there’s no reason why Fed shouldn’t perform at his usual level–at least his usual level for clay–and win the four matches he needs to claim yet another title. But if he suffers his second loss against the players gathered in Istanbul this week, it won’t be quite as much of a shock as that 59-1 record implies.

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