Friday, March 28, 2014

Myth vs. Math: Big Servers in Tiebreakers

This is the first installment in a five-part series called Myth vs. Math. In this series, I am going to take a look at five widely-accepted statements that tennis writers, analysts, fans, and commentators frequently make. I'm going to take these statements and see how they hold up against the numbers. The first statement in this series is "big servers have a notable advantage in tiebreakers."

The Myth

In tennis, the serve is an absolutely essential part of every player's game. It's the shot that starts every point. Having a big serve like Goran Ivanisevic, Andy Roddick, or Ivo Karlovic can be a huge weapon for getting out of trouble. However, having a weak serve means working a lot harder to win service games.

Anytime one of the big servers reaches a tiebreaker against a player, who relies more on other parts of their game, someone is bound to claim that the bigger server has the advantage. Before tiebreakers, when a commentator asks the other who they are picking to win the tiebreaker, the response is often something along the lines of "John Doe has the bigger serve, so I would have to give him the advantage in this tiebreaker."

And these kind of statements seem to make sense. Sets involving big servers have a higher probability of reaching a tiebreaker, so the big servers have more experience in those situations. Also, taking care of the points on serve is particularly crucial when one mini-break can determine a set.

However, does that mean the big servers actually have an advantage? Every point in a tiebreaker matters, whether it is on serve or not. And the big servers tend to be weak returners. So is being a big server really an advantage in a tiebreaker, or does it just make up for a weak return game?

The Math

The statistical mark of any big server is aces. So what I want to see is how high the correlation between aces and tiebreak win percentage is. If there is a high correlation, then the claim is true, but if there isn't a notable correlation, then the math

The ATP began tracking aces back in 1991. Since then, 42 players have played at least 600 tour-level matches. I used those 42 players as my sample to create this scatterplot.

On the x-axis is the players' aces per match, while the y-axis is each players' win percentage in tiebreaks multiplied by 50. I multiplied it by 50 simply to make the range of the two sets of data equivalent to each other. Each 'x' on the scatterplot represents one of the 42 players. The line through the middle of the data is a linear least squares fit. It shows for an average player how much an increase in aces per match will increase the chance of winning a tiebreaker.
To make this a little more tangible, let's look at how individual players fit on the scatterplot. The 'x' furthest to the right of the graph is Goran Ivanisevic, who won 58.9% of his tiebreakers, which is better than expected for a player with over 13 aces per match. The 'x' is the upper-left is Rafael Nadal, who strikes an average of just under three aces per match, but still wins 63.8% of his tiebreakers. At the bottom of the graph is Vincent Spadea, who won just 41.9% of his tiebreakers, while hitting 3.5 aces per match. The 'x' that is closest to sitting perfectly on the line is Tim Henman, who hit 5.9 aces per match, while winning 53.6% of his tiebreakers.
The slope of the linear regression is very mild, indicating that while there is a connection between aces and winning percentage in tiebreakers, it is very week. The correlation coefficient is merely .277, which means that aces per match are just 7.69% predictive of the outcome of a tiebreak.
Flaws in the Math
First, the scatterplot does nothing to account for differences in surface. This scatterplot treats all surfaces as equal. If it were broken down by surface, we may find that the statement is more true on a particular surface than another. However, the plot does show that overall, the connection is hardly impressive.

Second, in every point, there are two kinds of serves: 1st and 2nd serve. However, aces are primarily a first serve statistic since aces are so rare off the second serve. The biggest servers though are able to get a substantial amount of unreturned serves on the second delivery. A comparison of unreturned serves to tiebreak win percentage would produce a more accurate scatterplot. However, stats on unreturned serves aren't tracked at every match.
Third potential flaw is the sample size. Since I only looked at players with over 600 career matches played, I looked only at players who won often enough to play 600 matches. As a result, the majority of the players in the scatterplot had a winning record. In fact, the average win percentage in tiebreakers of the 42 players 54%. A look at more players with a losing record in tiebreakers could create a more complete scatterplot
Math seems to disprove the claim that "big servers have a notable advantage in tiebreakers." Having a big serve does seem to be a slight benefit in tiebreakers, but it is not much of a factor in determining the winner of a tiebreaker.
Supporters of the claim will often point to John Isner, who averaged exactly 16 aces per match after reaching the semifinals in Indian Wells and has a 65% winning mark in tiebreakers. However, the data shows that Isner's stats are an outlier and not indicative of other players. So perhaps the reason for Isner's success in tiebreakers has to do with something more than just having a monstrous serve.
So the widely-accepted claim that having a big serve is an advantage in tiebreakers should be a rejected claim.

Monday, March 17, 2014

3/17/14 YTD Country Power Rankings

These are the rankings of how each country has done since the end of the 2013 tennis season. Rankings are based mainly on the year-to-date ranking of the individuals from that country

1. Spain- For the first time since 2004, not a single Spaniard reached the quarterfinals in Indian Wells. However, the Spaniards aren't going anywhere. It's only March and they have basically clinched the No. 1 ranking as a country in 2014 already. France is the only country that has enough tour-level players to challenge Spain, but France lacks a top player like Rafael Nadal or David Ferrer. In total, Spain has 13 players, who have already accumulated 100 ranking points this year and the clay season hasn't even truly began.

2. Switzerland- This one is going to upset some fans. The top two spots in the year-to-date rankings are both occupied by a Swiss man, so how is Switzerland not in the No. 1 spot? The short answer is that there is no other Swiss in the top 180 of the YTD rankings. The other explanation is that the top of the men's game is weak right now. Nadal, Andy Murray, Juan Martin del Potro, David Ferrer, and Novak Djokovic have all had very slow starts. Stan Wawrinka and Roger Federer fell into the top two spots by default and they don't hold significant leads over the rest of the field. When the top is soft, depth is what matters in these rankings, and that is what Switzerland is missing.

3. France- Despite having the most players with 100 ranking points in 2014 at 15, France is even farther behind Switzerland than it was three weeks ago. That is largely because of what Federer did in Dubai and Indian Wells, earning a total of 1100 ranking points. However, it also has a lot to do with a lack of a top player for the country. Jo-Wilfried Tsonga just dropped out of the top 10 again and Richard Gasquet could be the next to go. Gael Monfils is the highest ranked Frenchman in the YTD rankings at No. 15 with just 535 ranking points to his name this year, and has won just won of his last three matches since winning in Montpellier.

4. United States-  There is a fairly large gap in tennis right now between the No. 3 nation and the No. 4, which is likely the highest the United States will get this year. John Isner just reentered the top 10 after reaching the semifinals in Indian Wells, and Americans are still waiting for Sam Querrey to produce. The United States has a lot of depth, but their No. 2 player in 2014, Steve Johnson, is still playing on the Challenger Tour. If the United States finish 2014 at No. 4 it will be a good year. Between Switzerland, Serbia, and the United States, only two of those countries can be in the top four.

5. Germany- When the rankings came out on Monday, Tobias Kamke was the lone German in the top 100 to see his ranking go in the positive direction, moving a whole two spots. It hasn't been a good three weeks for Germany, who is now even further behind the United States. Philipp Kohlschreiber's struggles have continued with a first round exit in Indian Wells, but Tommy Haas had a solid tournament before running into Roger Federer. Germany has the Czech Republic and Serbia breathing down its neck. Let's see how long Germany can stay in the top five.

6. Czech Republic- Lukas Rosol won in Irving last week, which is one of the highest level challenger tournaments in the world. However it wasn't enough to make up for Tomas Berdych's early exit to Roberto Bautista Agut in Indian Wells. Radek Stepanek ran into another tough draw in Indian Wells, but had opportunities to upset the world No. 1 before eventually falling in three sets. With Serbia on the rise again, it will be tough for the Czechs to ever get back into the top five, but it is still doable.

7. Serbia- Janko Tipsarevic and Viktor Troicki who? More like Dusan Lajovic and Illiya Bozoljac. Even Filip Krajinovic, who was Djokovic's doubles partner in Indian Wells is getting in on the fun. However, the real reason Serbia jumped five spots since the last rankings came out is thanks to Djokovic's title in Indian Wells. After disappointment followed by disappointment for Serbia, whether in Melbourne, Davis Cup, or Dubai, things are finally turning around for the Serbs in March. Even in Miami, Krajinovic and Lajovic have already notched wins. If Tipsarevic can get healthy, Serbia could be knocking on Switzerland's doorstep soon.

8. Argentina- Depth is the only thing going for the Argentines at this point. It is one of only four countries with at least three players in the top 35 of the YTD rankings. However, there isn't a single Argentine in the top 20. In fact, it is the only country in the top 13 of my rankings without a player in the top 20.

9. Croatia- Marin Cilic is still on fire. He reached the last 16 in Indian Wells before he nearly took out the eventual champion. Ivo Karlovic and Ivan Dodig have also notched a few impressive results this season themselves. They will remain in the top 10 as long as those three keep playing like this.

10. Italy- Fabio Fognini is like a fish out of water when he switches from the clay to hard courts. It hasn't been pretty, but he has done just enough to keep Italy in the top 10. Paolo Lorenzi though, is the one that is mainly responsible for Italy's ranking. At 32-years old, Lorenzi not only reached his first tour-level semifinal, but won it to reach the final of Sao Paulo, which is probably Portuguese for Saint Paolo... or something.

11. Ukraine- You never know what to expect from Alexandr Dolgopolov. After starting the season 4-5, he has won 11 matches in his last three tournaments, including victories over Ferrer and Nadal. That effort has boosted Ukraine four spots in the rankings. Illya Marchenko even made a nice run in Irving, reaching the quarterfinals as a qualifier.

12. Japan-  It has been a team effort for Japan to get to this spot. Kei Nishikori and his Memphis title is a big reason why they are where they are, but Japan also has four other players with at least 100 ranking points in 2014.

13. Great Britain- Murray has company this year from his fellow Brits, but he hasn't made the most of it. Daniel Evans, Daniel Smethurst, and James Ward are all on the brink of the top 100 to help Great Britain's ranking, but Murray has had a brutal start to 2014. He is in danger of dropping outside of the top 10 after Wimbledon if he has a clay court season like last year's.

14. Australia- I've said it before, I'll say it again. The farther we get from January, the lower Australia will be in the rankings. The have dropped from No. 8 to 11 to now 14. They had an incredible start to the season, which would have been impossible to continue. It doesn't help that Bernard Tomic is injured.

15. Russia- This has been a nightmarish start to the 2014 season for Mikhail Youzhny. He and Nikolay Davydenko have held up the countries tennis hopes for years. Now they are both over 30 with Dmitry Tursunov and Alex Bogomolov Jr. as well, and Teymuraz Gabashvili isn't far behind. Russia doesn't have a player 27 or younger in the top 100 right now.

16. Bulgaria- The word in bold may as well say Grigor Dimitrov. Baby Federer is the only player representing Bulgaria anywhere near the top 100 and he has been stellar. He claimed the title in Acapulco and is producing hot shots in every match he plays.

17. South Africa- Kevin Anderson handed Wawrinka his first loss of the season and is now one of the hottest players on tour. The winning has been consistent since the start of the first grand slam, but if he could go just one round further in any tournament, he could significantly boost his ranking.

18. Latvia-  This is the third straight country with just one player representing it. Ernests Gulbis defeated Dimitrov in Indian Wells and Dimitrov beat Anderson in Acapulco, so logically, Latvia should be on top. However, Gulbis's early exit to Querrey in Melbourne is still hurting him.

19. Colombia- Alejandro Gonzalez is having a phenomenal season, which continued in Indian Wells with his first two tour-level victories. He even took a set off of Djokovic. Alejandro Falla and Santiago Giraldo have been solid as well.

20. Canada- Milos Raonic played in just his second tournament of the year in Indian Wells and reached the quarterfinals to help Canada. The Canadians are still far from where they want to be.

21. Kazakhstan
22. Chinese Taipei
23. Austria
24. Netherlands
25. Brazil
26. India
27. Slovenia
28. Uzbekistan
29. Poland
30. Finland
31. Slovakia
32. Tunisia
33. Dominican Republic
34. Lithuania
35. Portugal
36. Israel
37. Belgium
38. Turkey
39. Luxembourg
40. Romania
41. Bosnia and Herzegovina
42. Hungary
43. Belarus