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

 

Conclusion

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.

Australian Open Week 1 Preview

The Australian Open draw came out today with a stacked top half full of exciting matchups. Here is a look at the most anticipated matches during the first week of the first slam of 2014.

1st Round: Before the draw came out, I was looking at how many quality players were going to be unseeded, and I thought there would be plenty of exciting first round encounters. I was dead wrong about that. The most dangerous unseeded players like Querrey, Dolgopolov, Istomin, and Cilic avoided playing seeded players in the first round. Then Ivo Karlovic, who actually did draw a seeded player, got 32-seed Ivan Dodig. However, there are two matches that will get my full attention when they are on.

The first is No. 24 Andreas Seppi (Ita) vs. Lleyton Hewitt (Aus). If I had to bet that any match would go five sets, this would be the one. At the last five grand slams, Hewitt has played 11 matches. Four of them went five sets, and five of them were four sets. Seppi's numbers knack for long matches is even more impressive. He has played 11 five-set matches in his last 19 completed slam matches. Even in Davis Cup play last year, he had a five-set match. If you aren't convinced yet that this match is going the distance, let me tell you about their head-to-head record. In six matches, the record is tied 3-3. Although they have never played a best-of-five match, each of their first three encounters were determined in a deciding set. Many fans would argue that Hewitt always plays his best in Australia is playing too well right now to need five sets to beat Seppi. However, when they met merely three months ago, Seppi won 6-4, 6-2. Seppi also has already defeated Hewitt once in Australia with a 4-6, 7-5, 7-5 win in Sydney 2006. I am picking Hewitt to win though.

The second is No. 1 Rafael Nadal (Esp) vs. Bernard Tomic (Aus). Nadal will likely win this one in straight sets, but it should still be fun to watch. The two also met three years ago in Melbourne in the third round, where Nadal won in three sets, so it will be interesting to see how much Tomic's game has improved since he was just 18.



2nd Round: This is the last round before the seeded players begin to play each other, so this round also lacks some really intriguing matchups. Marin Cilic does have a chance to take out a seeded player when he plays against Gilles Simon. Also, Fernando Verdasco will take on red-hot Sergiy Stakhovsky for the right to play Roger Federer, who Stakhovsky beat in Wimbledon last year. As someone who used to attend the tournament in Los Angeles each year, a potential matchup of former champions Ernests Gulbis and Sam Querrey will be interesting.

3rd Round: This is where the fun begins. This is the kind of day where you want to have different matches being played on your computer, tablet, and phone all at once. Thankfully, at the slams each round takes two days.

Gael Monfils and Nadal should meet in a rematch of the Doha final, which went three sets. Kei Nishikori versus Lleyton Hewitt would be an instant sellout in the Asia/Pacific Slam. Then Milos Raonic and Grigor Dimitrov would be a matchup between the two best young players on tour. Dimitrov would be in search of his first trip to the second week of a slam. Juan Martin del Potro will get his first test in the third round, where he will likely play Benoit Paire, who upset him in Rome last year.

Then we get to go through the awkwardness of Judy Murray being at a "Deliciano" Lopez match, when he takes on her son, Andy Murray. Jo-Wilfried Tsonga will either face his countryman Gilles Simon or former top 10 player Marin Cilic, who is trying to climb the rankings again. Then, as mentioned before, we could see Stakhovsky get his rematch against Federer. All of those matches are just in the top half of the draw, so they will all be played on the same day. Thankfully Monfils is in one of the matches, so he and Dustin Brown likely won't play in doubles that day too.


However, there is one match that I left out, which I think will be the best out of all of them. That is the matchup between No. 21 Philipp Kohlschreiber (Ger) and No. 13 John Isner (USA). The pair met just yesterday, when John Isner came back from down a set to win in three tiebreak sets. Isner leads the head-to-head 4-2 now, but has never beat Kohlschreiber in a best-of-five match. Only one match between the two hasn't gone to a deciding set. That was a four-set match that the German won at the US Open, which was the second time Kohlschreiber has beaten the top-ranked American at his home slam. Needless to say, Isner would love to get some revenge.

Federer no stranger to facing a home-favorite

Federer d. Hewitt 6-2, 6-3, 6-4 in R16 of 2010 Australian Open

In a few hours, Roger Federer will play against Lleyton Hewitt in the 2014 Brisbane final. It is the pair's 27th meeting, tying them with Stefan Edberg and Ivan Lendl for ninth most meetings between two players in the Open Era. It will be the fifth meeting in Hewitt's home country of Australia. However, none of the previous meetings were in a final.

Federer, who will be playing in his 114th career final, has become accustomed to meeting the home-favorite in finals. This will be his 19th meeting against a player who represents the country that the tournament is held in. In the previous 18 finals, Federer holds a record of 13-5, including a nine-match winning streak that spanned from 2003 to 2009.

However, Federer's recent record in these finals should give Hewitt some hope. Federer has won just one of the last three, which includes his straight-set loss against Andy Murray in the Gold Medal match in London.

Here is a look at all of the finals in Federer's career against players on home soil:

No.	Year	Tournament	Opponent	Result
1	2002	Milan	Davide Sanguinetti	L 6-7(2), 6-4, 1-6
2	2002	Miami	Andre Agassi	L 3-6, 3-6, 6-3, 6-4
3	2003	Halle	Nicolas Kiefer	W 6-1, 6-3
4	2003	Masters Cup	Andre Agassi	W 6-3, 6-0, 6-4
5	2005	Cincinnati	Andy Roddick	W 6-3, 7-5
6	2005	US Open	Andre Agassi	W 6-3, 7-6(0), 4-6, 6-3
7	2006	Indian Wells	James Blake	W 7-5, 6-3, 6-0
8	2006	US Open	Andy Roddick	W 6-2, 4-6, 7-5, 6-1
9	2007	Cincinnati	James Blake	W 6-1, 6-4
10	2008	Halle	Philipp Kohlschreiber	W 6-3, 6-4
11	2009	Madrid	Rafael Nadal	W 6-4, 6-4
12	2010	Madrid	Rafael Nadal	L 4-6, 6-7(5)
13	2010	Cincinnati	Mardy Fish	W 6-7(5), 7-6(1), 6-4
14	2011	Paris	Jo-Wilfried Tsonga	W 6-1, 7-6(3)
15	2012	Indian Wells	John Isner	W 7-6(7), 6-3
16	2012	Halle	Tommy Haas	L 6-7(5), 4-6
17	2012	Wimbledon	Andy Murray	W 4-6, 7-5, 6-3, 6-4
18	2012	London Olympics	Andy Murray	L 2-6, 1-6, 4-6
19	2014	Brisbane	Lleyton Hewitt	??

One of reasons that Federer is so great for the sport of tennis is that he is internationally loved. However, this table shows that there are several countries that maybe shouldn't love him as much as they do. Federer has spoiled the United States' hopes of having a winner from their country nine times. He has done the same twice in Germany and one time in Italy, Spain, France, and Great Britain. Today, Federer will try to add Australia to that list for his 78th career title, which by the way, will put him ahead of John McEnroe for career titles won, moving him into third place in the Open Era.

 

100 Predictons for 2014 ATP World Tour

These are my 100 predictions for the upcoming season. I only got 47 right last year, so I'm hoping I can do a little better this year. All of my grand slam predictions for finalists are at the end. I let the fan inside me come out for those predictions. I'll defend my picks a little bit at the end. Federer will finish the season in the top 10

Federer will not reach a grand slam final

Federer will win one or less 1000 event

Federer will win multiple titles

Nadal will not be No. 1 after the US Open

Nadal will defend one or less hard court title

Nadal will get at least 10,000 ranking points

Nobody besides Nadal and Djokovic will be No. 1 or 2

Nadal and Djokovic will combine for at least 3 slams

Nadal and Djokovic will combine for at least 16 finals in slams and masters

Nadal and Djokovic will combine for at least 26,000 ranking points

Djokovic will win a title in at least four of the first five months of the year

Djokovic will win multiple titles in tournaments not played on hard courts

Djokovic will win multiple titles in North America

Djokovic will have more ranking points than Wawrinka and Murray combined

Ferrer will drop out of the top five

Ferrer will earn at least 600 ranking points at one or less tournaments

Ferrer will not win his 600th career match in 2014

Ferrer will win multiple titles for the fifth consecutive year

Murray will not win a grand slam

Murray will finish with less than 8,000 ranking points

Murray will reach one or less semifinals at clay tournaments

Murray and Nadal will meet each other one or less times

Murray will get at least six top 10 wins

Del Potro will be a top four seed at Wimbledon

Del Potro will reach multiple slam semifinals

Del Potro will reach a final in a 1000 or slam before by the end of US Open

Del Potro will win more clay matches than Murray

Del Potro will earn at least $4,000,000 in prize money

Del Potro won't win a five-set match against Nadal, Djokovic, or Murray

Berdych will win a title

Berdych won't win a five-set match against Nadal, Djokovic, or Murray

Berdych will reach the semifinals of at least eight events again

Berdych will end the year ranked higher than Ferrer

Berdych will set a personal record for titles in a season

Berdych, Tsonga, and Federer will not win a grand slam

Wawrinka will never be ranked higher than seven

Wawrinka will fail to reach the quarterfinals in at least two slams

Wawrinka will not beat Djokovic or Nadal

Wawrinka will not finish in the top eight

Gasquet will reach one or less slam quarterfinal

Gasquet will not finish in the top 10

Gasquet will win a title in France

Gasquet will win a five-set match

Gasquet will win at least 42 matches

Tsonga will finish the year as the top-ranked Frenchman

Tsonga will reach the second week in Roland Garros and Wimbledon

Tsonga will defeat three former grand slam champions

Tsonga will win multiple titles

Tsonga will get at least five wins against top 10 opponents

Raonic will finish the year in the top 10

Raonic will win a title without dropping serve

Raonic will lead the tour in aces

Raonic will win at least 10 matches on grass and clay combined

Raonic will reach the quarterfinals in at least eight tournaments

Haas will drop outside the top 20 before Wimbledon

Almagro will win at least 40 matches

Almagro will win a title in South America

Isner will hit at least 900 aces

Fognini will crack the top 15 before the end of February

Anderson will drop out of top 20 before end of March and won't return

Janowicz will finish the year in the top 13

Janowicz will earn at least 500 ranking points from one event

Dimitrov will not win  title

Dimitrov will reach the top 15 for the first time in his career

Dimitrov will reach the fourth round at a slam

Gulbis will reach a career-high ranking before March

Paire will have more double faults than any player in the top 20

Pospisil will reach the top 28 by the end of Wimbledon

Cilic's year-end ranking will be at least 15 spots better than at the start of July

Tomic will not reach the top 20 at any point in the season

Dolgopolov will lose in the first or second round in at least two slams

Between Hewitt, Haas, and Robredo, at least one will retire

Nobody younger than Jiri Vesely will finish the year ranked higher than him

Vesely will win a grand slam match

Harrison will reach a final

Klahn and Young will both be in the top 10 for left-handed players

Sock will earn $500,000 in prize money

Lajovic will crack the top 100

Giraldo will make more in prize money than Seppi

Lopez will hit more aces than Karlovic

Simon's winning record will be better than his percentage of points won

Istomin will hit more aces than he will face break points

Brands will have more break points on his return than on his serve

Brands will reach a final and have a winning record

Matosevic will win a grand slam match

Verdasco will not get more than 300 points at a single tournament

Querrey & Istomin will combine for more ranking points than Haas & Seppi

Exactly four players from Spanish speaking countries will finish in the top 20

At most, 15 different countries will be represented in the top 20

Spain will have  most players in top 15, but France will have most in top 25

At least 20 tournaments will be won by players from that country

The United States will have more players in the top 100 than Germany

No player will reach the top 10 for the first time

The finalists at each slam will be players who have already reached a final

Djokovic will beat Nadal in the Australian Open final

Djokovic will beat Nadal in the Roland Garros final

Djokovic will beat Del Potro in the Wimbledon final

Djokovic will beat Murray in the US Open final

Djokovic will finish the year No. 1 in the world As I thought about my picks for the grand slams, I tried to think about which slam I thought Djokovic wouldn't win, and I couldn't think of any slam that he wouldn't win. He owns the Australian Open, and who will beat him? Murray is coming off an injury and Djokovic owns the rivalry with Nadal on hard courts since the US Open. For Roland Garros, that is going to be Djokovic's biggest goal of the year. He proved he is good enough to win it last year. I think this is the year that he finally gets it done. Wimbledon will be the tough one for Djokovic. Federer and Nadal proved that they won't ever win another Wimbledon with their disappointing performances last year, so it comes down to Djokovic, Murray, and Del Potro. It will be easier to predict a winner when the draw comes out, but a repeat would be difficult for Murray, and Del Potro has a poor five-set record in his career. At the US Open, Djokovic has always done well. His first slam final was at the US Open and he has reached four consecutive finals there. I also predicted Djokovic would win all four in 2013 and I was wrong of course. I would be shocked if Djokovic actually does win the calendar slam, but I'm not sure which one he will lose. This is certainly going to be a fun season at the slams.