The Odds of Successfully Serving Out the Set

Serving for the set is hard … or so they say. Like other familiar tennis conceits, this one is ripe for confirmation bias. Every time we see a player struggle to serve out a set, we’re tempted to comment on the particular challenge he faces. If he doesn’t struggle, we ignore it or, even worse, remark on how he achieved such an unusual feat.

My findings–based on point-by-point data from tens of thousands of matches from the last few seasons–follow a familiar refrain: If there’s an effect, it’s very minor. For many players, and for some substantial subsets of matches, breaks of serve appear to be less likely at these purportedly high-pressure service games of 5-4, 5-3 and the like.

In ATP tour-level matches, holds are almost exactly as common when serving for the set as at other stages of the match. For each match in the dataset, I found each player’s hold percentage for the match. If serving for the set were more difficult than serving in other situations, we would find that those “average” hold percentages would be higher than players’ success rates when serving for the set.

That isn’t the case. Considering over 20,000 “serving-for-the-set” games, players held serve only 0.7% less often than expected–a difference that shows up only once every 143 attempts. The result is the same when we limit the sample to “close” situations, where the server has a one-break advantage.

Only a few players have demonstrated any notable success or lack thereof. Andy Murray holds about 6% more often when serving for the set than his average rate, making him one of only four players (in my pool of 99 players with 1,000 or more service games) to outperform his own average by more than 5%.

On the WTA tour, serving for the set appears to be a bit more difficult. On average, players successfully serve out a set 3.4% less often than their average success rate, a difference that would show up about once every 30 attempts. Seven of the 85 players with 1,000 service games in the dataset were at least 10% less successful in serving-for-the-set situations than their own standard.

Maria Sharapova stands out at the other end of the spectrum, holding serve 3% more often than her average when serving for the set, and 7% more frequently than average when serving for the set with a single-break advantage. She’s one of 30 players for whom I was able to analyze at least 100 single-break opportunities, and the only one of them to exceed expectations by more than 5%.

Given the size of the sample–nearly 20,000 serving-for-the-set attempts, with almost 12,000 of them single-break opportunities–it seems likely that this is a real effect, however small. Strangely, though, the overall finding is different at the lower levels of the women’s game.

For women’s ITF main draw matches, I was able to look at another 30,000 serving-for-the-set attempts, and in these, players were 2.4% more successful than their own average in the match. In close sets, where the server held a one-break edge, the server’s advantage was even greater: 3.5% better than in other games.

If anything, I would have expected players at lower levels to exhibit greater effects in line with the conventional wisdom. If it’s difficult to serve in high-pressure situations, it would make sense if lower-ranked players (who, presumably, have less experience with and/or are less adept in these situations) were not as effective. Yet the opposite appears to be true.

Lower-level averages from the men’s tour don’t shed much light, either. In main draw matches at Challengers, players hold 1.4% less often when serving for the set, and 1.8% less often with a single-break advantage. In futures main draws, they are exactly as successful when serving for the set as they are the rest of the time, regardless of their lead. In all of the samples, there are only a handful of players whose record is 10% better or worse when serving for the set, and a small percentage who over- or underperform by even 5%.

The more specific situations I analyze, the more the evidence piles up that games and points are, for the most part, independent–that is, players are roughly as effective at one score as they are at any other, and it doesn’t matter a great deal what sequence of points or games got them there. There are still plenty of situations that haven’t yet been analyzed, but if the ones that we talk about the most don’t exhibit the strong effects that we think they do, that casts quite a bit of doubt on the likelihood that we’ll find notable effects elsewhere.

If there is any truth to claims like those about the difficulty of serving for the set, perhaps it is the case that the pressure affects both players equally. After all, if a server needs to hold at 5-4, it is equally important for the returner to seize the final break opportunity. Maybe the level of both players drops, something we might be able to determine by analyzing how these points are played.

For now, though, we can conclude that players–regardless of gender or level–serve out the set about as often as they successfully hold at 1-2, or 3-3, or any other particular score.

The Pervasive Role of Luck in Tennis

No matter what the scale, from a single point to a season-long ranking–even to a career–luck plays a huge role in tennis. Sometimes good luck and bad luck cancel each other out, as is the case when two players benefit from net cord winners in the same match. But sometimes luck spawns more of the same, giving fortunate players opportunities that, in turn, make them more fortunate still.

Usually, we refer to luck only in passing, as one possible explanation for an isolated phenomenon. It’s important that we examine them in conjunction with each other to get a better sense of just how much of a factor luck can be.

Single points

Usually, we’re comfortable saying that the results of individual points are based on skill. Occasionally, though, something happens to give the point to an undeserving player. The most obvious examples are points heavily influenced by a net cord or a bad bounce off an uneven surface, but there are others.

Officiating gets in the way, too. A bad call that the chair umpire doesn’t overturn can hand a point to the wrong player. Even if the chair umpire (or Hawkeye) does overrule a bad call, it can result in the point being replayed–even if one player was completely in control of the point.

We can go a bit further into the territory of “lucky shots,” including successful mishits, or even highlight-reel tweeners that a player could never replicate. While the line between truly lucky shots and successful low-percentage shots is an ambiguous one, we should remember that in the most extreme cases, skill isn’t the only thing determining the outcome of the point.

Lucky matches

More than 5% of matches on the ATP tour this year have been won by a player who failed to win more than half of points played. Another 25% were won by a player who failed to win more than 53% of points–a range that doesn’t guarantee victory.

Depending on what you think about clutch and momentum in tennis, you might not view some–or even any–of those outcomes as lucky. If a player converts all five of his break point opportunities and wins a match despite only winning 49% of total points, perhaps he deserved it more. The same goes for strong performance in a tiebreaks, another cluster of high-leverage points that can swing a match away from the player who won more points.

But when the margins are so small that executing at just one or two key moments can flip the result–especially when we know that points are themselves influenced by luck–we have to view at least some of these tight matches as having lucky outcomes. We don’t have to decide which is which, we simply need to acknowledge that some matches aren’t won by the better player, even if we use the very loose definition of “better player that day.”

Longer-term luck

Perhaps the most obvious manifestation of luck in tennis is in the draw each week. An unseeded player might start his tournament with an unwinnable match against a top seed or with a cakewalk against a low-ranked wild card. Even seeded players can be affected by fortune, depending on which unseeded players they draw, along with which fellow seeds they will face at which points in the match.

Another form of long-term luck–which is itself affected by draw luck–is what we might call “clustering.” A player who goes 20-20 on a season by winning all of his first-round matches and losing all of his second-round matches will not fare nearly as well in terms of rankings or prize money as someone who goes 20-20 by winning only 10 first-round matches, but reaching the third round every time he does.

Again, this may not be entirely luck–this sort of player would quickly be labeled “streaky,” but combined with draw luck, he might simply be facing players he can beat in clusters, instead of getting easy first-rounders and difficult second-rounders.

The Matthew effect

All of these forms of tennis-playing fortune are in some way related. The sociologist Robert Merton coined the term “Matthew effect“–alternatively known as the principle of cumulative advantage–to refer to situations where one entity with a very small advantage will, by the very nature of a system, end up with a much larger advantage.

The Matthew effect applies to a wide range of phenomena, and I think it’s instructive here. Consider the case of two players separated by only a few points in the rankings–a margin that could have come about by pure luck: for instance, when one player won a match by walkover. One of these players gets the 32nd seed at the Australian Open and the other is unseeded.

These two players–who are virtually indistinguishable, remember–face very different challenges. One is guaranteed two matches against unseeded opponents, while the other will almost definitely face a seed before the third round, perhaps even a high seed in the first. The unseeded player might get lucky, either in his draw or in his matches, cancelling out the effect of the seeding, but it’s more likely that the seeded player will walk away from the tournament with more points, solidifying the higher ranking–that he didn’t earn in the first place.

Making and breaking careers

The Matthew effect can have an impact on an even broader scale. Today’s tennis pros have been training and competing from a young age, and most of them have gotten quite a bit of help along the way, whether it’s the right coach, support from a national federation, or well-timed wild cards.

It’s tough to quantify things like the effect of a good or bad coach at age 15, but wild cards are a more easily understood example of the phenomenon. The unlucky unseeded player I discussed above at least got to enter the tournament. But when a Grand Slam-hosting federation decides which promising prospect gets a wild card, it’s all or nothing: One player gets a huge opportunity (cash and ranking points, even if they lose in the first round!) while the other one gets nothing.

This, in a nutshell, is why people like me spend so much time on our hobby horses ranting about wild cards. It isn’t the single tournament entry that’s the problem, it’s the cascading opportunities it can generate. Sure, sometimes it turns into nothing–Ryan Harrison’s career is starting to look that way–but even in those cases, we never hear about the players who didn’t get the wild cards, the ones who never had the chance to gain from the cumulative advantage of a small leg up.

Why all this luck matters

If you’re an avid tennis fan, most of this isn’t news to you. Sure, players face good and bad breaks, they get good and bad draws, and they’ve faced uneven challenges along the way.

By discussing all of these types of fortune in one place, I hope to emphasize just how much luck plays a part in our estimate of each player at any given time. It’s no accident that mid-range players bounce around the rankings so much. Some of them are truly streaky, and injuries play a part, but much of the variance can be explained by these varying forms of luck. The #30 player in the rankings is probably better than the #50 player, but it’s no guarantee. It doesn’t take much misfortune–especially when bad luck starts to breed more opportunities for bad luck–to tumble down the list.

Even if many of the forms of luck I’ve discussed are truly skill-based and, say, break point conversions are a matter of someone playing better that day, the evidence generally shows that major rises and falls in things like tiebreak winning percentage and break point conversion rates are temporary–they don’t persist from year to year. That may not be properly classed as luck, but if we’re projecting the rankings a year from now, it might as well be.

While match results, tournament outcomes, and the weekly rankings are written in stone, the way that players get there is not nearly so clear. We’d do well to accept that uncertainty.

How Important is the Seventh Game of the Set?

Few nuggets of tennis’s conventional wisdom are more standard than the notion that the seventh game of each set is particularly crucial. While it’s often difficult to pin down such a well-worn conceit, it seems to combine two separate beliefs:

  1. If a set has reached 3-3, the pressure is starting to mount, and the server is less likely to hold serve.
  2. The seventh game is somehow more important than its immediate effect on the score, perhaps because the winner gains momentum by taking such a pivotal game.

Let’s test both.

Holding at 3-3

Drawing on my database of over 11,000 ATP tour-level matches from the last few years, I found 11,421 sets that reached three-all. For each, I calculated the theoretical likelihood that the server would hold (based on his rate of service points won throughout the match) and his percentage of service games won in the match. If the conventional wisdom is true, the percentage of games won by the server at 3-3 should be noticeably lower.

It isn’t. Using the theoretical model, these servers should have held 80.5% of the time. Based on their success holding serve throughout these matches, they should have held 80.2% of the time. At three-all, they held serve 79.5% of the time. That’s lower, but not enough lower that a human would ever notice. The difference between 80.2% and 79.5% is roughly one extra break at 3-3 per Grand Slam. Not Grand Slam match–an entire tournament.

None of that 0.7% discrepancy can be explained by the effect of old balls [1]. Because new balls are introduced after the first seven games of each match, the server at three-all in the first set is always using old balls, which should, according to another bit of conventional wisdom, work against him. However, the difference between actual holds and predicted holds at 3-3 is slightly greater after the first set: 78.9% instead of the predicted 79.8%. Still, this difference is not enough to merit the weight we give to the seventh game.

The simple part of our work is done: Servers hold at three-all almost as often as they do at any other stage of a match.

Momentum from the seventh game

At 3-3, a set is close, and every game matters. This is especially true in men’s tennis, where breaks are hard to come by. Against many players, getting broken so late in the set is almost the same as losing the set.

However, the focus on the seventh game is a bit odd. It’s important, but not as important as serving at 3-4, or 4-4, or 4-5, or … you get the idea. The closer a game to the end of the set, the more important it is–theoretically, anyway. If 3-3 is really worth the hoopla, it must grant the winner some additional momentum.

To measure the effect of the seventh game, I took another look at that pool of 11,000-plus sets that reached three-all. For each set, I calculated the two probabilities–based on each player’s service points won throughout the match–that the server would win the set:

  1. the 3-3 server’s chance of winning the set before the 3-3 game
  2. his chance of winning the set after winning or losing the 3-3 game

In this sample of matches, the average server at three-all had a 48.1% chance of winning the set before the seventh game. The servers went on to win 49.4% of the sets [2].

In over 9,000 of our 3-3 sets, the server held at 3-3. These players had, on average, a 51.3% chance of winning the set before serving at 3-3, which rose to an average of a 57.3% chance after holding. In fact, they won the set 58.6% of the time.

In the other 2,300 of our sets, the server failed to hold. Before serving at three-all, these players had a 35.9% chance of winning the set, which fell to 12.6% after losing serve. These players went on to win the set 13.7% of the time. In all of these cases, the model slightly underestimates the likelihood that the server at 3-3 goes on to win the set.

There’s no evidence here for momentum. Players who hold serve at three-all are slightly more likely to win the set than the model predicts, but the difference is no greater than that between the model and reality before the 3-3 game. In any event, the difference is small, affecting barely one set in one hundred.

When a server is broken at three-all, the evidence directly contradicts the momentum hypothesis. Yes, the server is much less likely to win the set–but that’s because he just got broken! The same would be true if we studied servers at 3-4, 4-4, 4-5, or 5-5. Once we factor in the mathematical implications of getting broken in the seventh game, servers are slightly more likely to win the set than the model suggests. Certainly the break does not swing any momentum in the direction of the successful returner.

There you have it. Players hold serve about as often as usual at three-all (whether they’re serving with new balls or not), and winning or losing the seventh game doesn’t have any discernible momentum effect on the rest of the set [3]. Be sure to tell your friendly neighborhood tennis pundits.

Continue reading How Important is the Seventh Game of the Set?

The Match Charting Project: Quick Start Guide

You’ve heard about the Match Charting Project, you’ve seen the amazingly detailed stats it generates, and you’ve decided it’s time to contribute. Here’s the simplest way to get started.

1. Choose a match. Check the list of charted matches (by date, or by player) and the Google doc of matches in progress. Once you’ve decided to chart a match, feel free to add yourself (along with the match) to the Google doc so that no one else will work on the same one.

Try to choose a relatively short match, and unless you really like Rafa, I’d suggest you avoid lefties for your first couple of attempts. It makes things a lot easier.

You can find full matches in many ways. There are plenty (though few very recent ones) on YouTube, many more on Asian video sites such as Soku, Daum, and Mgoon, and lots more if you have access to something like ESPN 3, TennisTV, or Tennis Channel Plus. There are also hundreds of archived ATP Challenger matches.

TennisTV and TC Plus are great because their players have buttons to skip forward or backward 10 seconds. Another alternative is to download videos to your local machine and then use a media player like SMPlayer or VLC, which allow you to move forward and backward through the match with quick keyboard shortcuts. Of course, DVRs work great for this, too.

2. Download the Match Charting Project spreadsheet and read through the “Instructions” tab. Charting a match involves a lot of details, but try not to get too bogged down. The most important things for beginners are:

  • serve direction (4 = wide, 5 = body, 6 = down the t)
  • the most common shot codes (f = forehand, b = backhand, s = backhand slice, r = forehand slice)
  • codes to indicate how the point ended (@ = unforced error, # = forced error, and * = winner)
  • codes to indicate the type of error (n = net, w = wide, d = deep, x = wide and deep).

The instructions cover several optional parts of the charting process, like shot direction and return depth. Including those makes things a lot more difficult, so for your first match, ignore them!

3. Start climbing the learning curve. I won’t deny it: It can be a bit frustrating to get started. The codes are a lot to remember, but trust me, it gets easier, especially if you stick to the basics. Many points look something like this:

4ffbbf*

That means: serve out wide, forehand return, forehand, backhand, backhand, forehand winner. That’s all!

It gets more complex when players approach the net or use less common tactics like dropshots. For your first match or two, you’ll probably consult the instructions frequently. Here’s another sample point:

6svlon@

Translated: Serve down the t (6), slice return (s), forehand volley (v), lob (l), overhead/smash (o) into the net (n) for an unforced error (@).

4. Be patient! After a few dozen points, you’ll start to get the hang of it. There will be plenty of rewinding, re-watching, and checking the instructions, but it will get considerably faster.

That’s it!

Once you’ve finished charting every point of the match, send me the spreadsheet and I’ll add it to the database.

After a match or two…

Of course, more data is more valuable, so once you’ve gotten the hang of the basics, it’s time to track more details of the match. But again–don’t rush into this! Adding these additional levels of complexity before you’re comfortable with the above will be very frustrating.

5. Shot direction. For every shot after the serve, use the number 1, 2, or 3 to indicate direction. 1 = to a right-hander’s forehand (or a lefty’s backhand), 2 = down the middle, or 3 = to a right-hander’s backhand. For example:

5f2f3b3b1w#

Translated: Serve to the body (5), forehand return down the middle (f2), forehand to (a righty’s) backhand side (f3), backhand crosscourt (b3), backhand down the line (b1) that missed wide (w) for a forced error (#).

When you’re comfortable with that:

6. Return depth. For service returns only, use an additional numeral for depth. 9 = very deep (the backmost quarter of the court), 8 = moderately deep (the next quarter, still behind the service line), and 7 = shallow (in the service boxes). For instance:

6s17f1*

Meaning: Serve down the T (6), shallow slice return to (a righty’s) forehand side (s17), cross-court forehand winner (f1*).

Again, I have to ask you be patient with return depth: It’s the hardest step to add. In a very short period of time, you need to note the serve direction, return shot type, return direction, and return depth. It takes a bit of practice, but I’m convinced that recording return depth is worth it.

Finally, when you’re comfortable with all that, there’s one more thing to add:

7. Court position. A few symbols are used to record where players were when they hit certain shots. Most of the time they aren’t needed — a volley is almost always hit at net, while a backhand is almost always hit from the baseline. Use these codes for exceptions only:

  • The plus sign (+) is used for approach shots, including serves when a player serve-and-volleys.
  • The dash (-) indicates that a shot is hit at the net. Again, you don’t need to use it for “obvious” net shots like volleys, half-volleys, and smashes. It’s also unnecessary for the shot after a dropshot.
  • The (=) indicates that the shot was hit at the baseline. This is the least common, and usually is used for smashes hit from the baseline.

A couple more examples:

4+s28v1f-3*

Translated: Server came in behind a serve out wide (4+), moderately deep slice return down the middle (s28), volley to (a righty’s) forehand side (v1), forehand winner hit from near the net (f-3*).

One more, which is just about as messy as it gets:

5r37b+3m2l1o=1r#

Meaning: Body serve (5), shallow forehand slice/chip return to (a righty’s) backhand side (r37), backhand crosscourt approach shot (b+3), backhand lob down the middle (m2), forehand lob to (a righty’s) forehand side (l1), crosscourt overhead/smash from the baseline (o=1), forehand slice/chip forced error (r#).

Happy charting! If you have any questions, please email me.

 

Should Andy Murray Skip the Tour Finals to Prepare for Davis Cup?

After advancing to the Davis Cup final, Andy Murray floated the idea that he might skip the World Tour Finals to prepare. The Belgian hosts are likely to choose clay for November’s Davis Cup tie (in part to make Murray less comfortable), and if Murray reached the final round in London the week before, he would have only four days off to recover and adjust to the different surface.

A lot of factors will go into Murray’s ultimate decision: how much importance he gives each event, how much he thinks fatigue will affect him, and how likely it is that the ATP would sanction him for skipping a required event. For today, I’ll have to ignore all of those and focus on the one most amenable to analysis: The effect of switching surfaces right before a Davis Cup tie.

Shifting from one surface to another immediately before Davis Cup is common. From 2009 to the present, there have been just over 2,000 World Group, Group 1, and Group 2 Davis Cup singles rubbers, and almost 450 of those involved at least one player who had played the previous week [1] on a different surface. It’s very rare that both players switched surfaces, so we have a sample of 432 matches in which one player changed surfaces from the previous week, and the other player either played or (presumably) prepared on the same surface.

At the simplest level of analysis, the switchers have been surprisingly effective. In those 432 matches between switchers and non-switchers, the switchers won 275, or 63.6% of the time. When we narrow the sample to the 130 times the switcher reached at least the round of 16 the week before Davis Cup (and, thus, had even less time to adjust), the results are surprisingly similar: 82 wins, or 63.1% in favor of the switchers.

Of course, there are all sorts of biases that could be working in favor of the switchers. The better the player, the less likely he can change his schedule to better prepare for Davis Cup, leaving him stuck on the “wrong” surface the week before a tie. And the better the player, the more likely he was a switcher in the smaller sample, one of those who reached the round of 16 the week before.

To evaluate the effect of switching, then, we must proceed with more subtlety. If switchers are more likely to be the favorites, we need to consider each player’s skill level and estimate how often switchers should have won. To do that, we can use JRank, my player rating system with surface-specific estimates for each competitor.

Immediately, we lose about 15% of our sample due to matches involving at least one player who didn’t have a rating at the time [2]. These are almost all Group 2 matches, so its doubtful that we lose very much. In the slightly smaller pool of 361 matches, the switcher won 62.0%, and when the switcher reached the round of 16 the previous week, he won 60.0%.

JRank confirms that the sample is strongly biased toward switchers. The player changing surfaces was favored in 69.8% of these contests. To take an extreme example, Murray went from hard courts at the 2013 US Open to clay courts in the World Group playoff against Croatia. Against Borna Coric, who hadn’t played the week before, Murray was a 99.1% favorite, and of course he won the match.

Once we calculate the probability that the switcher won each of the 361 matches, it turns out that the switchers “should have” won 227, or 62.8% of the time. That’s almost indistinguishable from the historical record, when the switchers won 224 matches. In the smaller sample of 120 matches when the switcher reached the round of 16 the previous week, switchers “should have” won 72 matches. As it happened, they won exactly 72.

In other words, it doesn’t appear to be a disadvantage to play Davis Cup matches on an unfamiliar surface. JRank-based predictions are primarily based on “regular” matches, so if switchers are performing at the level that JRank forecasts for them, they’re playing as well as they would at, say, the third round of a Slam, when the surface is familiar.

This isn’t a clear answer to Murray’s dilemma, of course. If he plays, say, Roger Federer and Novak Djokovic in back-to-back three-setters on Saturday and Sunday, then travels to a different venue, handles tons of press, and practices with a different set of coaches and fellow players before a big match the following Friday, he faces more of a challenge than your typical surface-switcher in our dataset.

However, there’s little evidence that surface-switching alone is a good reason to skip the Tour Finals. If history is any guide, Murray will play very well on the Belgian clay–just as well as he would at the same venue in the middle of the clay season.

Continue reading Should Andy Murray Skip the Tour Finals to Prepare for Davis Cup?

Unlikely Davis Cup Finalists and an Early Forecast for Ghent

Among nations that have reached Davis Cup finals, neither Great Britain or Belgium quite fits the mold.

The fortunes of the UK team depend almost entirely on Andy Murray. If you have to choose one player, you couldn’t do much better, but it’s hardly a strategy with lots of room for error. While the Belgian team is a bit more balanced, it doesn’t boast the sort of superstar singles player that most successful nations can send into battle.

Thanks to injury and apathy, the Brits and the Belgians haven’t defeated the level of competition usually required of Davis Cup finalists. Belgium hasn’t had to face any singles player better than Leonardo Mayer, and the only top-ten singles player to show up against Britain was Gilles Simon.

Measured by season-best singles rankings, these are two of the weakest Davis Cup finalists in the modern era [1]. The last time a finalist didn’t have two top-50 singles players was 1987, when the Indian team snuck past the Australians in the semifinals, only to be trounced by a powerhouse Swedish side in the final. This year, neither side has two top-50 players [2].

It’s even worse for the Belgians: David Goffin, their best singles player, has never topped 14th in the rankings. Only three times since 2000 has a nation reached the final without a top-ten player, and to find a side that won the Davis Cup without a top-tenner, we must go back to 1996, when the French team, headed by Arnaud Boetsch and Cedric Pioline, claimed the Cup.

Even when a nation reaches the final without a top-ten singles player, they typically have another singles player in the same range. Yet Belgium’s Steve Darcis has only now crept back into the top 60.

Despite a widespread belief that you can throw logic out the window in the riot that is Davis Cup, the better players still tend to win. Here are Elo-rating-based predictions for the four probable rubbers on clay:

  • Murray d. Darcis (94.3%)
  • Goffin d. GBR-2 (90.1%)
  • Murray d. Goffin (86.7%)
  • Darcis d. GBR-2 (78.1%)

Predicting the outcome of any doubles matches–let alone best-of-five-setters with players yet to be determined, probably including one very good but low-ranked player in Andy Murray–is beyond me. But based on the Murray brothers’ performance against Australia and the Belgians’ lack of a true doubles specialist, the edge has to go to Britain–let’s say 65%.

If we accept these individual probabilities, Great Britain has a 65.2% chance of winning the Davis Cup. That doesn’t take into account home court advantage, which will probably be a factor and favor the Belgians [3].

It’s a huge opportunity for the Brits, but it’s still quite a chance for Belgium, which hasn’t been this close to the Davis Cup for a century.  After all, the Cup is inscribed with country names, not judgments about that nation’s easy path to the final.

Continue reading Unlikely Davis Cup Finalists and an Early Forecast for Ghent

The Case for Novak Djokovic … and Roger Federer … and Rafael Nadal

By winning the US Open last weekend and increasing his career total to ten Grand Slams, Novak Djokovic has pushed himself even further into conversations about the greatest of all time. At the very least, his 2015 season is shaping up to be one of the best in tennis history.

A recent FiveThirtyEight article introduced Elo ratings into the debate, showing that Djokovic’s career peak–achieved earlier this year at the French Open–is the highest of anyone’s, just above 2007 Roger Federer and 1980 Bjorn Borg. In implementing my own Elo ratings, I’ve discovered just how close those peaks are.

Here are my results for the top 15 peaks of all time [1]:

Player                 Year   Elo  
Novak Djokovic         2015  2525  
Roger Federer          2007  2524  
Bjorn Borg             1980  2519  
John McEnroe           1985  2496  
Rafael Nadal           2013  2489  
Ivan Lendl             1986  2458  
Andy Murray            2009  2388  
Jimmy Connors          1979  2384  
Boris Becker           1990  2383  
Pete Sampras           1994  2376  
Andre Agassi           1995  2355  
Mats Wilander          1984  2355  
Juan Martin del Potro  2009  2352  
Stefan Edberg          1988  2346  
Guillermo Vilas        1978  2325

A one-point gap is effectively nothing: It means that peak Djokovic would have a 50.1% chance of beating peak Federer. The 35-point gap separating Novak from peak Rafael Nadal is considerably more meaningful, implying that the better player has a 55% chance of winning.

Surface-specific Elo

If we limit our scope to hard-court matches, Djokovic is still a very strong contender, but Fed’s 2007 peak is clearly the best of all time:

Player          Year  Hard Ct Elo  
Roger Federer   2007         2453  
Novak Djokovic  2014         2418  
Ivan Lendl      1989         2370  
Pete Sampras    1997         2356  
Rafael Nadal    2014         2342  
John McEnroe    1986         2332  
Andy Murray     2009         2330  
Andre Agassi    1995         2326  
Stefan Edberg   1987         2285  
Lleyton Hewitt  2002         2262

Ivan Lendl and Pete Sampras make much better showings on this list than on the overall ranking. Still, they are far behind Fed and Novak–the roughly 100-point difference between peak Fed and peak Pete is equivalent to a 64% probability that the higher-rated player would win.

On clay, I’ll give you three guesses who tops the list–and your first two guesses don’t count. It isn’t even close:

Player           Year  Clay Ct Elo  
Rafael Nadal     2009         2550  
Bjorn Borg       1982         2475  
Novak Djokovic   2015         2421  
Ivan Lendl       1988         2408  
Mats Wilander    1984         2386  
Roger Federer    2009         2343  
Jose Luis Clerc  1981         2318  
Guillermo Vilas  1982         2316  
Thomas Muster    1996         2313  
Jimmy Connors    1980         2307

Borg was great, but Nadal is in another league entirely. Though Djokovic has pushed Nadal out of many greatest-of-all-time debates–at least for the time being–there’s little doubt that Rafa is the greatest clay court player of all time, and likely the most dominant player in tennis history on any single surface.

Djokovic is well back of both Nadal and Borg, but in his favor, he’s the only player ranked in the top three for both major surfaces.

The survivor

As the second graph in the 538 article shows, Federer stands out as the greatest player of all time at his age. Most players have retired long before their 34th birthday, and even those who stick around aren’t usually contesting Grand Slam finals. In fact, Federer’s Elo rating of 2393 after his US Open semifinal win against Stanislas Wawrinka last week would rank as the sixth-highest peak of all time, behind Lendl and just ahead of Andy Murray.

Here are the top ten Elo peaks for players over 34:

Player         Age   34+ Elo  
Roger Federer  34.1     2393  
Jimmy Connors  34.1     2234  
Andre Agassi   35.3     2207  
Rod Laver      36.6     2207  
Ken Rosewall   37.4     2195  
Tommy Haas     35.3     2111  
Arthur Ashe    35.7     2107  
Ivan Lendl     34.1     2054  
Andres Gimeno  35.0     2035  
Mark Cox       34.0     2014

The 160-point gap between Federer and Jimmy Connors implies that 34-year-old Fed would win about 70% of the time against 34-year-old Connors. No one has ever sustained this level of play–or anything close to it–for this long.

At the risk of belaboring the point, similar arguments can be made for 33-year-old Fed, all the way to 30-year-old Fed. At almost any stage in the last four years, Federer has been better than any player in history at that age [2].  Djokovic has matched many of Roger’s career accomplishments so far, especially on clay, but it would be truly remarkable if he maintained a similar level of play through the end of the decade.

Current Elo ratings

While it’s not really germane to today’s subject, I’ve got the numbers, so let’s take a look at the current ATP Elo ratings. Since Elo is new to most tennis fans, I’ve included columns to indicate each player’s chances of beating Djokovic and of beating the current #10, Milos Raonic, based on their rating. As a general rule, a 100-point gap translates to a 64% chance of winning for the favorite, a 200-point gap implies 76%, and a 500-point gap is equivalent to 95%.

Rank  Player                  Elo  Vs #1  Vs #10  
1     Novak Djokovic         2511      -     91%  
2     Roger Federer          2386    33%     84%  
3     Andy Murray            2332    26%     79%  
4     Kei Nishikori          2256    19%     71%  
5     Rafael Nadal           2256    19%     71%  
6     Stan Wawrinka          2186    13%     62%  
7     David Ferrer           2159    12%     58%  
8     Tomas Berdych          2148    11%     56%  
9     Richard Gasquet        2128    10%     54%  
10    Milos Raonic           2103     9%       -  
                                                  
Rank  Player                  Elo  Vs #1  Vs #10  
11    Gael Monfils           2084     8%     47%  
12    Jo-Wilfried Tsonga     2083     8%     47%  
13    Marin Cilic            2081     8%     47%  
14    Kevin Anderson         2074     7%     46%  
15    John Isner             2035     6%     40%  
16    David Goffin           2027     6%     39%  
17    Grigor Dimitrov        2021     6%     38%  
18    Gilles Simon           2005     5%     36%  
19    Jack Sock              1994     5%     35%  
20    Roberto Bautista Agut  1986     5%     34%  
                                                  
Rank  Player                  Elo  Vs #1  Vs #10  
21    Philipp Kohlschreiber  1982     5%     33%  
22    Tommy Robredo          1963     4%     31%  
23    Feliciano Lopez        1955     4%     30%  
24    Nick Kyrgios           1951     4%     29%  
25    Ivo Karlovic           1949     4%     29%  
26    Jeremy Chardy          1940     4%     28%  
27    Alexandr Dolgopolov    1940     4%     28%  
28    Bernard Tomic          1936     4%     28%  
29    Fernando Verdasco      1932     3%     27%  
30    Fabio Fognini          1925     3%     26%

Continue reading The Case for Novak Djokovic … and Roger Federer … and Rafael Nadal