Head Over to HeavyTopspin.com

It was only a matter of time before I started a dedicated tennis blog.

My archived tennis studies will remain here, but from now on, I’ll be publishing tennis commentary (and additional research) at my new site, HeavyTopspin.com.

Click on over, tell your friends, and learn more than ever wanted to know about men’s tennis.

Lefties in Tennis: Doubles and Prize Money

A few days ago, I offered some numbers on the prevalence of lefties in men’s tennis.  It turned out that, in the top 300 of the ATP singles rankings, lefties don’t show up much more than you would expect them to.

A reasonable follow-up question would be: What about doubles?

Being left-handed may not make one a better doubles player, but being left-handed does have the potential to make one part of a better doubles team.  Case in point: Five of the eight doubles teams that earned a spot in the ATP Tour Finals last year were a righty/lefty duo, including the top two teams in the year-end rankings.

And indeed, it turns out that left-handers are more prevalent in the top ranks of men’s doubles.  As we’ve seen, in November 2010, five of the sixteen players (31 percent) included in the ATP Tour Finals were left-handed.

The most current ATP doubles rankings tell a similar, if less extreme, story.  Of the top 100 ranked doubles players, 18 are left-handed.  That’s considerably higher than the 12 of 100 at the top of the singles rankings.  (Both top 100s include Rafael Nadal, who plays left-handed but was born right-hand dominant.  These calculations consider him left-handed.)

Prize money

The majority of players participate in both singles and doubles, at least on occasion.  To determine some general level of “success” for ATP players, we could look at total prize money.  This weights singles much more heavily.  An advantage is that it is a reasonable measure of a sustainable career in professional tennis.

So, do left-handers have a better chance at making money in tennis than we would expect, given their prevalence in the general population?

It doesn’t look like there is any substantial advantage.  Of the top 100 money-winners, 13 are left-handed, including Nadal.  The top 100 does include four doubles specialists, out of only 13 total doubles specialists in the top 100.

If we go further, we find an additional five lefties from 101 to 150, and six more from 151 to 200.

Left-handers do seem to have a better chance than right-handers of reaching a certain level of success in men’s doubles.  Beyond that, there is little in the way of a handedness advantage.  Whatever the advantages of playing tennis left-handed and the challenges of facing a lefty, they don’t translate into an overwhelming number of left-handers at the top of the professional game, or a disproportionate level of success for left-handed professionals.

The Prevalence of Lefties in Men’s Tennis

Many people, in and out of tennis, believe that left-handed players have an advantage of some kind.  The perceived advantage may just be one of unfamiliarity; a junior or club-level player doesn’t see many lefties, so he is unaccustomed to the angles and spins that come of a left-hander’s racquet.

In any event, we need some hard data.  Are lefties overrepresented in the top ranks of professional men’s tennis?

The short answer: Not really.

There’s no universal consensus on the prevalence of left-hand dominance in the general population.  You’ll frequently see the figure 10 percent, or a range between 8 and 15 percent.  How does that compare to the number of lefties in the ATP rankings?

Here is a breakdown of lefties in the ATP rankings of 7 Feb 2011:

• Top 10: 2 (20%)
• Top 20: 3 (15%)
• Top 50: 6 (12%)
• Top 100: 12 (12%)
• Top 200: 29 (14.5%)
• Top 300: 40 (13.3%)

An interesting case is Rafael Nadal, who was born right-hand dominant, but was taught to play left-handed.  So if we are looking at the success rates of left-hand dominant players, we could subtract one from each of the raw totals above.  Of course, there may be other players who were taught to play with their non-dominant hand.

(An odder case is that of Guillermo Olaso, who is listed on the ATP site as ambidextrous.  Other resources show him as right-handed.  I saw him play a couple of years ago and don’t remember anything unique about his game, so I left him in the righty category.)

The advantage, if any

A perspective that I’ve heard (I have no idea from where) is that lefties can take advantage of the unfamiliarity advantage early in their careers, giving them a foundation of success that earns them more matches, more support, more coaching, and the like.  The left-handedness doesn’t make them a better player, exactly, but it causes other things that lead to an improvement in their play.

Depending on how long that advantage persists, we might expect to see a “bulge” in the number of lefties somewhere in the rankings.  There’s a bit of a blip in the 101-200 range, and there’s a bigger one if we narrow our focus to 151-200, where 10 of the 50 men play left-handed.  Perhaps unfamiliarity helps them get to some level, but when they start meeting opponents at higher levels, the unfamiliarity advantage is not enough.

The blip between 101 and 200 might not mean anything; perhaps if we went further down the rankings, or even into the national or junior rankings, we’d see something more pronounced.  Alas, it was hard enough to get handedness for the top 300 players, so any larger project will have to wait for another day.

Quantifying the Bias of an ATP Draw

ATP tennis draws are biased in favor of top-ranked players.  If you’re ranked in the top four, you won’t face another top-16 player until the round of 16, you won’t face a top-8 player until the quarters, and you won’t face a fellow top-4 player until the semis.  If you’re unseeded (out of the top 32 in slams, 16 or 8 in smaller tourneys), you’ll probably have to face a top-16 player just to get into the round of 16 … and you might draw a top-4 player in the first round.

This is the way it is, and it’s not going to change anytime soon.  Since it’s the nature of the beast, we should better understand the effects of this system.

In short: The more highly ranked you are, the easier it probably will be to win the first few matches of a tournament.  The further you go in the draw, the more points you earn, and the higher your ranking stays.  A higher pre-tournament ranking–regardless of actual skill!–increases your odds of a better performance.

Thus, the rankings lag behind changes in skill level, creating a bias against rapidly-improving youngsters and players returning from long absences.

An example

Let’s play around with this a bit.  Before the Australian Open started, I published the odds that each player in the main draw would reach any given round.  From that, we can calculate “expected points,” which gives us a way of directly comparing each player’s chances, given his skill level and his draw.

For instance, Nadal’s expected points were 1056, Federer’s were 857, and 11th-seed Jurgen Melzer’s were 227.

What happens if swap two players’ positions in the draw?  Let’s try #4 and the top-ranked non-seed.  Going into the tournament, #4 was Robin Soderling, and Phillip Kohlschreiber was #34, unseeded.  In the draw as it actually happened, Soderling’s expected points were 515 and Kohlschreiber’s were 56, thanks in part to a 2nd round matchup against Tomas Berdych.

If we exchange Soderling’s and Kohlschreiber’s draw positions and run the simulation, we get very different results.  Soderling’s expected points are 353 (down 31 percent) and Kohlschreiber’s expected points improve to 103 (up 84 percent).

Randomization

The Soderling/Kohlschreiber swap may be an outlier.  We can do better, and besides, I don’t want to type “Kohlschreiber” anymore.

Let’s try a new simulation.  For each run, we’ll randomize the draw positions, so Nadal has an equal chance of drawing Marcos Daniel, Roger Federer, or anybody else in the first round.

The differences in the results are substantial.  Nearly 75 percent of players have their expected points change by more than 10 percent.  39 of the 128 players see their expected points decrease with randomization, and those players are disproportionately seeds.  The seeds are disproportionately high seeds.

Two types of players seem to benefit from the status quo:

• High seeds.  They are guaranteed non-seeded opponents for at least two rounds, and lower-seeded opponents for a round or two after that.
• Marginal players who get lucky draws.  The player who the Aussie Open draw benefited the most was wild card Benoit Paire.  He was one of the weakest players in the field, but in the first round, he drew Flavio Cipolla, one of the few competitors who was even weaker.

Of the 39 players who do better under the original draw, 19 are seeds and 9 are WCs or qualifiers, mostly in situations like Paire’s.  That leaves only 11 middle-of-the-pack, unseeded players who weren’t disadvantaged by the draw.

If the draw had been randomized, half of the field (mostly unseeded players) would have seen their expected points increase by more than 10 percent.  52 players would have jumped by 20 percent or more, 37 by more than 30 percent, and 22 by more than 50 percent.

Season-long bias

To some extent, the bias is mitigated over the course of a season.  Players like Kohlschreiber are disadvantaged by the draw so long as their ranking stays in the unseeded-but-good 33-50 range for slams, but in smaller tournaments, such a player is often seeded.

And, of course, by playing 20-30 tournaments, the draws are randomized for some players.  Paire got lucky by drawing Cipolla in Melbourne, but he could just as easily have found himself pitted against a top seed.

As is intuitively obvious, draws are biased in favor of the top players, and that is one thing that isn’t mitigated by a year’s worth of tournaments.  The top 12 seeds all did better in the actual draw simulation than in the randomized simulation, and I expect that would be true for the vast majority of tournaments.

If some players are consistently “winning” through draw bias, there must be losers.  As we’ve seen, lower-ranked players can win big or lose big in a draw, but it stands to reason that, over the course of the season, they lose a little bit.  At least until they overcome and disadvantage and become top-ranked players themselves.

Python code for WPA stats

A long time ago I put together a python version of the win expectancy/volatility calculations contained in Studes’s WPA spreadsheet.  Those were the days–if we wanted a post-game WPA graph, we had to do it ourselves :).

I’ve brushed off the cobwebs and published the code.  Click here to see it.

All this does is calculate the win expectancy and volatility (~leverage) in any situation.  It doesn’t calculate WPA on the play.  Of course, if you’re running this on a play-by-play log, it’s trivial to compare the WX of one play and the next.

‘Volatility’ is the difference between the win expectancies that would result from a home run and from a strikeout.  To normalize it so that the average volatility is 1.0, I have this code divide the result by 0.133.  Depending on your dataset, that might not be quite right.  There are more sophisticated ways to measure leverage, though this one is adequate for many purposes.

Thank you Studes, Tango, and others for publishing all that you have.  As is so often the case, I’m just the code monkey.

Home Court Advantage Run Amok

This week in Johannesburg is the only time of year that an ATP tour-level event goes to South Africa.  Accordingly, all the South Africans take part, the wild cards are generally awarded to South Africans, and a disproportionate number of entries in the qualifying draw are South Africans.  And they performed unexpectedly well.

Thus, of the main draw of 32, 6 players were South Africans.  They included 4th seed Kevin Anderson (ranked 59th), wild cards Fritz Wolmarans (261), Rik de Voest (183), and Izak van der Merwe (170), along with qualifiers Raven Klaasen (307) and Nikala Scholtz (662).

It isn’t uncommon to see someone ranked as low as Anderson win a 250-level tournament; for example, another local player, 84th-ranked Crotian Ivan Dodig took the title in Zagreb this week.  But rarely do home favorites make such comprehensive work of a draw.

Anderson won the tournament–though he’s not all that pertinent to our theme, since he outranked every one of his opponents.  All five other South Africans exceeded expectations.

The qualifiers, Klaasen and Scholtz, didn’t win a main draw match, neither would have been expected to come through qualifying.  Scholtz had to beat Pierre-Ludovic Duclos and Thiago Alves, ranked 443rd and 178th, respectively.  Klaasen had to get past Rajeev Ram, currently ranked 188th but ranked inside the top 80 only a year ago.

Of the wild cards, only Wolmarans failed to reach the quarters.  He did win his first round match against Igor Sijsling, who outranks him by 130 places.

Rik de Voest defeated Stefano Galvani (ranked 321) and 8th seed Michal Przysiezny (81), one of his best ATP-level results.  And van der Merwe made it to the semifinals, beating Stephane Robert, Dustin Brown, and Simon Greul, all players who have spent substantial time in the top 100.

It is tempting to wonder if some locations lend themselves to a greater home court advantage.  South Africa, in particular, is one of the more far-flung spots on the ATP map.

But it would be foolish to draw any conclusions based on one tournament.  After all, last year, South Africans won a grand total of two matches in the Johannesburg main draw.  This results of this year’s event are at least partly due to an usually weak field: only the top four seeds were among the world’s top 65.  Some challenger-level events may be similarly competitive.

In any event, this week’s results are certainly a boost for tennis in South Africa; maybe the draw will be stronger next year.