Getting a shoutout from Sports Illustrated

After writing my last post arguing that women should not blindly challenge calls more often in professional tennis, I sent a quick summary to Jon Wertheim at Sports Illustrated.  It sounds like he appreciated my side of the argument, as he published part of my response in his weekly article.  Pretty cool!

Why women should not challenge more in tennis

In last week's Sports Illustrated, Jon Wertheim argues that women should use the challenge system more at Grand Slam tennis tournaments.  Although he includes data in his article to make his case, I'm going to argue that he is misinterpreting the data and show that convincing women to challenge more often might actually hurt the game.  Unfortunately, this article is not available online, so I will begin with a summary and include some direct quotes (*Update - the article is available here).

A little background: "In 2006 tennis instituted a replay challenge system not unlike the NFL's.  Provided the court is equipped with the technology, players can appeal line calls for review."  The rules are the same for men and women; however, men and women have different challenge behavior.  "Men challenge their points 25% more often than women - though their success rates are virtually the same."  For example, at Wimbledon this year, women challenged 2.6% of the points played, while men challenged 3.3% of the time. This trend holds over all Grand Slam tournaments over the past year.  Men won their challenges 27.73% of the time while women won 27.37% of challenges.

Supplied with this data, the author concludes that "men are more prone to question their authority" and "women are more reluctant to challenge and be assertive or confrontational".  Many assume that men are more likely to challenge because they hit the ball harder, so linespersons are more likely to make a mistake.  The author's response: "Sounds logical.  But if this were true - if it were harder for linespersons to trace 140-mph serves, as opposed to 120-mph serves - we would expect to see a disparity in accuracy of line calls".  But because the challenge accuracy is equivalent between gender, the author concludes that women challenge less (and thus accept incorrect calls) because "women are uncomfortable with confrontation and negotiation".  The article concludes with a quote from Martina Navratilova, "Women need to be more comfortable challenging.  Here's one area where there's no reason we shouldn't be like the men."

The author's whole argument hinges on one point: there is no disparity in the accuracy of line calls for men's and women's matches.  I agree that the author's conclusions would hold if the data could show this.  However, we have no way of knowing the accuracy of all linepersons calls from the data - we only know that the accuracy of player challenges is roughly equivalent between genders (27%).  What we cannot know is how many of the unchallenged points contained an incorrect call by a linesperson.  The only way we could figure this out is if someone watching the match (presumably in the TV booth) "challenges" every point to determine how many points contained incorrect calls, then look at how many of these points were challenged by players.  This would allow us to construct the following table for each gender:

	# Points containing all correct line calls	# Points containing an incorrect call
# Points Challenged	A	B
# Points With No Challenge	C	D

From the data presented, we know the values for A and B.  With the Wimbledon 2013 men's data, A = 2.38% of all men's points (3.3% of challenged points x 72.27% of incorrect chalenges) and B = 0.92% of all men's points (3.3% of challenged points x 27.73% of overturned points).  For women, A =  1.89% and B = 0.71% of women's points.

To determine whether or not linespersons make more incorrect calls in men's matches, we need to know D (the total number of incorrect calls is B + D).  Without this knowledge, we cannot determine if more challenges from women would result in more overturned calls.  However, we know that the value of B is larger for men than women by 0.21% of all points played.  For the author's assertion that linespersons are equally as likely to be incorrect for women as for me, D would need to be larger for women than men by 0.21% of all points played.

Let's look at 3 examples using the data from Wimbledon 2013:

1. Assume women got every single wrong call overturned (D = 0).  Therefore, using additional challenges will not get any call overturned.  If women challenge every as frequently as men without any additional incorrect calls, then women's accuracy would drop to 21.56%.  So urging women to challenge more would make them appear to have worse judgement than men (not a good thing when trying to argue for gender equality).
2. Assume the proportion of incorrect men's and women's calls are equivalent (D is equal for men and women).  If this is the case, then you could argue that men and women should both be challenging more.  However, because B+D is still smaller for women than men, their accuracy would decrease if they challenged the same number of times as men.
3. Assume the total number of points containing an incorrect call is equivalent between genders (D is larger by 0.21% of all points for women than men, resulting in B+D being equivalent between men and women).  If this is true, as the author assumes, then his conclusion than women need to challenge more is correct.  However, assuming that women challenge the same number of times as men, their accuracy on the "new" challenges would actually increase from 27.37% to 29.08% if they were to remain as successful as men at getting line calls overturned.  This means that women are currently challenging calls that are less likely to be overturned than the calls that they are are missing (try explaining this to the women players!).

Therefore, we cannot make any assumptions as to whether linespersons miss the same number of calls for women as men.  This also means that we cannot determine whether women can challenge more and still be as accurate as men in getting calls overturned.  So what conclusions can be made from this data?

• Men and women are equally successful at challenging.  This means that one sex does not have better "eyes" than the other.
• Men and women are equally bad at challenging.  On average, less than 1 out of 3 challenges will result in a call being overturned.  This number is likely due to "throw away" challenges when a player knows the call was correct but has challenges to waste at the end of a set (or needs a longer break to catch his/her breath after a long point).
• Assuming that men and women are getting every incorrect call overturned (D=0), linespersons are 29.6% more likely to make a mistake on a men's point than a women's point (0.92% vs 0.71%).

Why Roger Federer (and the entire women's tour) should never hit a second serve

In the 2012 Wimbledon Men's Championship match, Roger Federer beat Andy Murray to win his record tying 7th Wimbledon title and record 17th major overall.  But it was a rough start for Federer, as he lost the first set, which included losing his first 7 second serve points (he won 3/11 overall in the first set).  Federer was having a much easier time with his first serve (as do most players), winning 65% of the points when he made his first serve.  This got me thinking ... does it ever make strategical sense for a player to never hit a slower second serve but always hit a first serve?  The answer may surprise you (although I guess I give it away in the title).

I went through several matches for both men and women at this year's Wimbledon.  Let's use the men's final as an example.  Over the whole match, Federer made his first serve 68.7% of the time, winning 75.6% of those first serve points.  Multiplying these two numbers together, we see that 51.9% of time time Federer made his first serve and won the point (conversely, 48.1% of the time he either made his first serve and lost the point or had to hit a second serve).  Federer won 48.8% of the points when he hit a second serve.  This shows that Federer would have been better off going for his first serve even when hitting a second serve, as he would be expected to win an additional 3.1% (51.9 - 48.8) of second serve points. Federer hit 41 second serves, so he would expect to win an additional (41)*(3.1%) = 1.3 points in the match had he not hit his regular second serve.  This doesn't sound like much, especially since Federer won the match, but it could translate to winning an additional game.

One drawback of only hitting first serves is an increased number of double faults.  Because Federer made 68.7% of his first serves, we would expect him to miss his first serve 31.3% of the time.  If we consider two serves as independent events, the probability that he would miss two in a row and double fault is (31.3%)(31.3%) = 9.8%, resulting in an expected 12.8 double faults (he served 131 points in the match), much higher than the 3 double faults he actually served.  But he would have also been expected to serve an additional 3.75 aces (work not shown, but trust me).  So this turn out to a net decrease of (12.8 expected double faults) - (3 actual df's) - (3.75 additional aces) = 6.05 points.  How can this make sense if I just said that we expect Federer to win a net of 1.3 additional points?  When he does make his first serve, he wins a much higher percentage of those points compared to second serve points (75.6% to 48.8%) that it more than makes up for the double faults.  In other words, the risk of only hitting first serves pays off for Roger Federer.

I decided to look at all men's matches starting with the 4th round of Wimbledon.  Of the 30 matches (or 60 players, some counted more than once), 10 of the players would have expected to benefit by only hitting first serves.  Roger Federer was the only player to show up twice on the list (Finals and QF matches).  Of these 10, 7 lost the match (Federer won both matches and Djokovic won his QF).  In 3 of Andy Murray's 4 matches that I looked at, his opponent would have been better off only hitting first serves (Federer, Tsonga and Cilic), showing how great of a returner Murray is (the other opponent was Ferrer, who doesn't have a big first serve).  The largest expected gain was for Tsonga, who could have expected to win an additional 7.7 points (2 games) against Murray in the semis.

I wanted to look a little more closely at how this strategy may impact the match.  My original thought was that a player probably loses a set when he is serving poorly, so only hitting first serves would result in a lot more double faults and a net loss of points.  I was surprised to see that this was not the case.  Looking at the QF through the Finals, players lost 26 sets.  In 10 of these 26 sets, the player who lost the set would have expected to win more points by serving only first serves.  This definitely supports players only hitting first serves when they lose the set, but I guess this doesn't help much retrospectively.

Looking at sets won, for 19 of 26 sets, the winner would have expected to lose more points by only hitting first serves.  However, only 10 of those 19 would be expected to lose more than 2 points.  Interestingly, Federer could have won more points in 3 of the 9 sets he won by only hitting first serves and never would have expected to lose an additional 2.5 points in the 9 sets that he won.  This shows how great his first serve was working during the Championships.

The players are back at Wimbledon for the next 2 weeks, but this time trying to win an Olympic medal.  My recommendations would be for Federer to only hit first serves, but he is probably the only male player I would recommend this to regardless of opponent.  Plus, this may have the added benefit of screwing up the opponent's game plan.  I would also suggest that all of Andy Murray's opponents to employ this strategy.  But as I said before, no coach will tell their player to use this strategy.  My guess is that this is due to aesthetic reasons - no coach wants to see his player double fault in the double digits even if he would win more points in the long run.

I also performed the same analysis for the women.  To keep things short, every women player should only hit first serves.  Of the final 7 matches (14 players) that I looked at, only 5 players would not have benefited by this strategy.  In fact, 4 of those 5 players who would not have benefited lost the match anyway (the only exception being Serena Williams in the SF).  On average, the women would expect to win an additional 1.1 points per match.  Compare this to the men, who on average would expect to lose an additional 2.5 points.

Will any players employ this strategy at the Olympics?  I'm guessing not.

Wimbledon 2012 wrap-up

Sorry for the long delay in posting - I'm still alive, but have been extremely busy with the new job.  I have also decided to spend more time on "novel" posts where I analyze the data myself to answer new questions, as these seem to get a much better response from readers.  But these posts take more time to write, so I will not be posting as often.  I am finishing up a new analysis with some data from Wimbledon, and I hope to blog about this soon.  For now, I want to give a quick update on my Wimbledon picks (you can read about my picks here).

First the good news: I correctly picked Serena Williams.  The bad news: I picked Novak Djokovic, but he lost to eventual champion Roger Federer.  So I went 1/2, or 3/4 when combining my 2 correct French Open Picks.  When looking at the ESPN expert picks over these past 2 grand slams, only Chris Evert has correctly picked all 4 champions.

Let's hope I can keep up the steam going into the US Open in August/September.

Wimbledon Picks 2012 (Explanation)

With the first week of Wimbledon now a thing of the past, I figured I should actually give my reasoning for my Wimbledon picks.

First, I went with my gut (over data because I didn't have the time) when picking the men's and women's sleepers - players outside the top 10 to go the furthest.  I picked John Isner and Venus Williams who both lost first round.  Guess I shouldn't listen to my gut feeling when making picks anymore.

So let's get to the picks that I actually put some thought into.  I only looked at one stat when choosing my women's champion.  Here are the results of the Williams sisters (both singles and doubles) at Wimbledon since 2000.

Williams Sisters Wimbledon Results 

Year	Doubles Result	Venus Singles	Serena Singles
2000	WON	WON	SF
2001	3RD	WON	QF
2002	WON	RUP	WON
2003	3RD	RUP	WON
2004	-	2RD	RUP
2005	-	WON	3RD
2006	-	3RD	-
2007	2RD	WON	QF
2008	WON	WON	RUP
2009	WON	RUP	WON
2010	QF	QF	WON
2011	-	4RD	4RD

Since 2000, every year that the Williams sisters have played doubles at Wimbledon (highlighted), one of them also wins the singles title (8/8, with both Williams reaching the Final 4 times).  Notice that it doesn't matter how they perform in the doubles, as long as they are playing.  The 4 years that the Williams did not play doubles, often due to one sister being injured, only once did one of them win the singles title (Venus in 2005).  

Serena and Venus entered to play doubles this year (they are currently in the 2nd round).  Looking at past results, the probability that a Williams wins the single title given they play doubles is 1.  So all I had to do was choose between Serena or Venus winning.  I went with Serena because she is the higher ranked and Venus is coming back from injuries.  As of this post, Serena has won her first 3 singles matches and is still alive.

For the men's, I looked at the winner's seed and previous year's performance since 2003 (Federer's first Wimbledon win).

Men's Wimbledon Champions 

Year	Winner	Seed	Previous Result
2003	Roger Federer	4	1st
2004	Roger Federer	1	WON
2005	Roger Federer	1	WON
2006	Roger Federer	1	WON
2007	Roger Federer	1	WON
2008	Rafael Nadal	2	RUP
2009	Roger Federer	2*	RUP
2010	Rafael Nadal	2	-
2011	Novak Djokovic	2	SF

* Federer was the 2 seed, but he was technically the top seed after Nadal withdrew as the number 1 seed with injury before the 2009 tournament began.

Because Federer, Nadal and Djokovic have won 28 of the last 29 major titles, I have eliminated the rest of the field.  I eliminated Federer because it has been one of the top 2 seeds to win every year since 2004.  I went with Djokovic over Nadal because the defending champion has won 6 of the last 9 years (if I consider Federer the defending champ in 2009 since Nadal withdrew and Nadal the defending champ in 2010 since he had not defended his title.**)  Also, Federer and Nadal each defended their first Wimbledon title by winning the following year that they played.  This gives me belief that Djokovic will continue this trend and win his second straight Wimbledon title.  

My men's pick is looking even better after Nadal lost in the second round.  (Still, I'll be cheering for Roger Federer to win the title as he is my favorite player.)

** Under this argument, both Federer and Nadal would have been considered defending champions in 2010, so you could change the fraction to 6/10 defending champs winning. 

MIT Sloan Sports Analytics Conference

I came across a great article today (via Simply Statistics) describing the largest sports analytics (i.e. statistics) conference in the world, held at MIT.  A few points that I found most interesting:

1. The guy that they highlight (Kirk Goldsberry) created the plot of the week last week.
2. They mentioned that they had a panel on tennis analytics for the first time this year, including Pete Sampras and Roger Federer's coach Paul Annacone and former player Todd Martin.  Two great quotes:

On why tennis analytics is lacking: "There's no shared service," says Martin.  "This isn't a team sport with a $500,000 budget for analytics."

"[Analytics] should be a strength of our game.  Tennis is a game of patterns." - Craig O'Shannessy

This conference could be worth a vacation next year.  Might depend on whether I have one or two great blog posts to report on.

Wimbledon 2012 predictions

Wimbledon starts on Monday and I wanted to announce my picks (I was 2/2 for the French Open).  

I am going to follow ESPN's format for their picks (which you can see here):

Men's winner: Novak Djokovic

Men's sleeper (someone outside of the top 10 to go the furthest): John Isner

Men's toughest road (top 10 player to lose earliest): Janko Tipsarevic

Women's winner: Serena Williams

Women's sleeper: Venus Williams

Women's toughest road: Samantha Stosur

Things are very busy for me, so I do not have the time to justify my picks right now - but I hope to later in the week.

French Open Picks: Follow Up

A few weeks ago, I made my picks for the 2012 French Open champions (Part 1 and Part 2).  Using my statistical wizardry (ok, more like logic and process of elimination), I correctly picked Rafael Nadal as the men's champion and Maria Sharapova as the women's.

Compare this to the ESPN expert picks: 11 of the 12 correctly picked Nadal, but only Chris Evert picked Sharapova.  Maybe if I keep this up for Wimbledon and the US Open, ESPN will start knocking on my door.

Djokovic and Federer: Semifinal Attraction

For the past 20 grand slam tournaments (5 years, including this French Open), Federer, Nadal and Djokovic have been ranked/seeded in the top 3.  Nadal has been either the #1 or #2 seed in all of these tournaments, meaning that either Federer or Djokovic has been the #3 seed.  A majority of the time, Murray has been the #4 seed, but there are some exceptions (Soderling, del Potro, Ferrer, Davydenko, Roddick).

Nadal Getting Lucky with Grand Slam Draws?

In tennis, the placing of seeded players in the draw includes some randomness.  That is, half the time the #1 seed will draw the #3 seed in the semi-finals, and the other half of the time will draw the #4 seed.  This is different from basketball and other tournaments, where the semis will always consist of #1 vs #4 and #2 vs #3 (barring upsets).  This means that Federer and Djokovic would expect to be in the same half of the draw (i.e., scheduled to meet in the semis) in 10 of these 20 Grand Slams.  In actuality, Federer and Djokovic have been placed in the same half of the draw 15 times (actually playing 7 times in the semis, with Djokovic leading 4-3).  This means that Nadal has been scheduled to play the #4 seed in 15 of the last 20 Grand Slams, giving him the easier path to the final.  In fact, 5 of the 7 majors won by Nadal in this time span were won when Federer and Djokovic were both on the other side of the draw (only defeating both players in the 2008 French Open).  Does this supply evidence that the draw is rigged in favor of Nadal, thus increasing his chances of winning?

This problem can be rephrased in terms of flipping a coin.  If we flip a coin 20 times, how likely is it that we see 15 heads (i.e., Fed and Djokovic are on the same half of the draw)?  Coin flips are independent, so we can easily calculate the probability of 15 heads to be 0.0148, or about a 1.5% chance.  This is very unlikely, but not completely unexpected.

To better illustrate the point, I ran 10,000 simulations where I flip a coin 20 times and record the number of heads, shown in the following graph.  These simulations show that we expect to see at least 15 heads about 2% of the time (proportion to the right of the red line), which is similar to the theoretical value of 1.5%.

Nice to See You Again...

Another interesting pattern is that Federer and Djokovic were placed in the same half of the draw for 7 straight Grand Slams (2008 Wimbledon - 2010 Australian Open).  How likely is this occurrence?  That is, how likely is it to see 7 heads in a row when flipping a coin 20 times?  The theoretical calculation is more complicated, so I again ran 10,000 simulations of 20 flips and recorded the maximum number of heads to appear in a row.

The probability of seeing a run of 7 heads (i.e., 7 heads in a row) or more is 0.1112, or about 11%.  This means that if you flip a coin 20 times, you will see a run of at least 7 heads 11% of the time, which is probably much more common than you might expect.

There was another stretch of 6 grand slams where Fed and Djokovic were again on the same side of the draw (2012 Wimbledon - 2011 US Open; combined with the previous run of 7, Federer and Djokovic were on the same half of the draw 13 out of 14 grand slams!).  What's the probability that the second longest run when flipping a coin 20 times is at least 6?  It's about a 1% chance, which is much less common than seeing a run of 7.

Will it Ever End?

While a run of 7 grand slams in a row is not very uncommon, having a second run of 6 or being placed on the same side of the draw 15 out of 20 tournaments is not very likely.  I do not actually believe that the draw is rigged, but the frequency of Fed and Djokovic meeting is only expected to occur about 1% of the time.

The Law of Large Numbers tells us that, eventually, we expect Djokovic and Federer to be on opposite sides of the draw 50% of the time.  However, as neither player will be playing infinitely many more grand slams, this does not impact the probability at the next Grand Slam.  That is, assuming the rankings stay the same, there is still a 50% chance that Federer and Djokovic will be placed on the same half of the draw at Wimbledon, the next Grand Slam tournament.

French Open Bracket Challenge

The French Open draws came out today.  For the past few years, I have been filling out grand slam brackets online with my family for bragging rights.  Normally we all make awful picks, but one of my parents manages to crush me.  This year, I thought that I would open up our family pool to all of my blog followers.  To enter your brackets, follow the links, then create an account and your ready to go! Note that the entries must be received by Sunday May 27 at 5 AM.

Men's bracket:
http://www.tourneytopia.com/RacquetBracketFrenchOpenWTA/nosweatstats/Default.aspx

Women's bracket:
http://www.tourneytopia.com/RacquetBracketFrenchOpenWTA/nosweatstats2/Default.aspx

If you are having any difficulty, leave a comment and I will try to help you figure it out.  You can also enter the main pool, which will allow you to win some prizes if you finish first.  Winners will get a shout-out in a future post.

Don't forget to check out my picks for the winners.

French Open 2012 - Part 1

It's already the middle of May, which means that the French Open is right around the corner.  In this week's posts, I will make my predictions for the men's and women's 2012 French Open Champions.  I will be looking at the results since 2000 to determine the player who I think is most likely to win.  Let's start by looking at the seed for the winner:

French Open Champions

Year	Men's	Seed	Women's	Seed
2000	Gustavo Kuerten	5	Mary Pierce	6
2001	Gustavo Kuerten	1	Jennifer Capriati	3
2002	Albert Costa	22	Serena Williams	3
2003	Juan Carlos Ferrero	3	Justine Henin	4
2004	Gaston Gaudio	44	Anastasia Myskina	6
2005	Rafael Nadal	5	Justine Henin	10
2006	Rafael Nadal	2	Justine Henin	5
2007	Rafael Nadal	2	Justine Henin	1
2008	Rafael Nadal	2	Ana Ivanovic	2
2009	Roger Federer	2	Svetlana Kuznetsova	7
2010	Rafael Nadal	2	Francesca Schiavone	17
2011	Rafael Nadal	1	Li Na	6

10 of the past 12 men's champions have been seeded 5 or higher.  Using this as our cutoff, this leaves the following players as possible winners this year (by current world ranking):

1. Novak Djokovic
2. Roger Federer
3. Rafael Nadal
4. Andy Murray
5. Jo-Wilfried Tsonga

Djokovic, Federer, and Nadal have won 27 of the past 28 Grand Slam tournaments (Del Porto won the 2009 US Open), but we won't eliminate Murray and Tsonga quite yet.

11 of the past 12 women's champions were seeded in the top 10.  Using the current world rankings, this leaves the following players:

1. Victoria Azarenka
2. Maria Sharapova
3. Agnieszka Radwanska
4. Petra Kvitova
5. Samantha Stosur
6. Serena Williams
7. Marion Bartoli
8. Carolina Wozniacki
9. Li Na
10. Vera Zvonareva

Also note that Kuerten, Nadal, and Henin are the only players since 2000 to have won the French Open as the number 1 seed.  Each time, they were the defending champion.  Since it looks like Djokovic and Azarenka will receive the number 1 seeds and neither won the French Open last year, we will eliminate them from out list.

Now let's look at each champion's performance in that year's Australian Open (the most recent Grand Slam).

French Open Champions

Year	Men's	AO Result	Women's	AO Result
2000	Gustavo Kuerten	1R	Mary Pierce	4R
2001	Gustavo Kuerten	2R	Jennifer Capriati	Win
2002	Albert Costa	4R	Serena Williams	DNP
2003	Juan Carlos Ferrero	QF	Justine Henin	SF
2004	Gaston Gaudio	2R	Anastasia Myskina	QF
2005	Rafael Nadal	4R	Justine Henin	DNP
2006	Rafael Nadal	DNP	Justine Henin	F
2007	Rafael Nadal	QF	Justine Henin	DNP
2008	Rafael Nadal	SF	Ana Ivanovic	F
2009	Roger Federer	F	Svetlana Kuznetsova	QF
2010	Rafael Nadal	QF	Francesca Schiavone	4R
2011	Rafael Nadal	QF	Li Na	F

None of the past 12 men's champions had won the Australian Open in the same year.  Assuming this same pattern holds, this eliminates the 2012 Australian Open Champion, Novak Djokovic (who we had already eliminated). Our updated men's list looks like:

1. Novak Djokovic (#1 seed but not defending champ, AO Winner)
2. Roger Federer
3. Rafael Nadal
4. Andy Murray
5. Jo-Wilfried Tsonga

Each of the past 12 women's champions either did not play (DNP, ocurred 3 times in the past 10 years) or reached at least the 4th round if they did play.  This leaves us with the following women:

1. Victoria Azarenka (#1 seed but not defending champ)
2. Maria Sharapova
3. Agnieszka Radwanska
4. Petra Kvitova
5. Samantha Stosur (1R)
6. Serena Williams
7. Marion Bartoli (3R)
8. Carolina Wozniacki
9. Li Na
10. Vera Zvonareva (3R)

The next post will look at how important previously winning a Grand Slam or winning a clay court warm-up tournament is.

Plot of the Week 1

Today is the first installment of Plot of the Week.  I am planning on posting a sports-related plot every week.  Some weeks I will interpret the plot; other weeks I hope that you will help post what you find interesting about the plot.

This is a scatterplot of athletes' win percentage in Majors vs. win percentage at other non-Major tournaments.  

• I have plotted male golfers (Tiger Woods pre-scandal, current Tiger Woods, Phil Mickelson, Jack Nicklaus) and female golfers (Yani Tseng, Annika Sorenstam) in black and male tennis players (Pete Sampras, Roger Federer, Rafael Nadal, Novak Djokovic) and female tennis players (Venus and Serena Williams, Martina Navratilova, Chris Evert, Steffi Graf) in red.
• Annika Sorenstam and Novak Djokovic are tough to read due to overplotting in the middle of the plot.
• The solid line represents the 45-degree line (y = x) and the dashed line is the least squares regression line.

Here are the most interesting features in this graph (to me, at least):

• Phil Michelson does not win tournaments (Majors and non-Majors) as frequently as the other athletes.
• Graf won much more often than anyone else - over 50% of non-Major tournaments and 40% of Major tournaments.  From this view, it seems that Graf is clearly the best female tennis player, with Evert and Navratilova not too far behind.
• Athletes close to the solid line win Majors at the same frequency as non-Majors.  This seems to represent the set of athletes who are not intimidated by the pressure at the Majors.
• Yani Tseng is the only athlete much farther above the line - she seems to over-preform at the Majors.  It is still very early in her career, so I would not be surprised if she moves closer to the diagonal line as her career progresses.
• The athletes below the line tend to under-perform at the Majors compared to other tournaments. But this set contains some of the best athletes ever, so this is not quite a fair assessment (Venus has 7 majors and Evert and Navratilova 18 each). Maybe it is more fair to say that they over-perform at non-Majors.
• Federer and Nadal have very similar winning percentages.  Since Federer is 5 years older than  Nadal, it will be interesting to see if Nadal can keep this same pace for the next 5 years to catch up to Federer in terms of tournaments won.

Do you notice anything else interesting that I missed?

A New Tennis Statistic: BGO

In an earlier post where I ranted about baseball statistics, I said that all good statistics should be two things: simple and easy to understand/interpret.  I'm proposing a new statistic that the tennis folk should start using.  It's a modification of the break point conversion.  For those of you not familiar with tennis, a break point is when you have an opportunity to break your opponent (win a game when your opponent is serving).  Consider two scenarios where Player A loses:

Scenario 1: 1/7 (14%) break point conversion

Scenario 2: 1/7 (14%) break point conversion 

These two scenarios are the same, right?  WRONG!!  Suppose that we have a bit more information about the scenarios:

1. 1/7 break point conversion.  Each break point occurred in a different game.
2. 1/7 break point conversion.  All 7 break points occurred in the same game (many deuces), a game which Player A eventually won.

Remember that tennis is scored in games and sets, and that the player who wins the most points doesn't always win the match.  In scenario 1, had Player A won every break point, he would have broken his opponent 7 times and maybe would have won the match.  In scenario 2, Player A only had the opportunity to win one game on his opponent's serve.  Winning the first break point would increase his break point conversion and may have saved a lot of hard work, but it would not have changed the outcome of the match as he didn't have any more return games with break point opportunities.

I am proposing a new statistic, Break Game Opportunities (BGO)*, which is the percent of times that a player breaks (wins the game) when he has the opportunity (at least one break point in the game).  If this percentage is high, even if the break point conversion is low, then a player takes advantage of his opportunities to break.  If this percentage is low, then the (un-opportunistic) player lost a lot of games in which he could have broken.  This means that the score and outcome could have been very different.

*[Part of developing good statistics is coming up with a catchy name.  Previous statistics that I developed for my PhD research are SWISS and ReQON (pronounced recon).  Feel free to comment if you have any better naming suggestions before ESPN scoops me.]

Returning back to the earlier example, the BGO of scenario 1 is 1/7 (14%) and the BGO of scenario 2 is 1/1 (100%).  Thus, the scoreboard would not have been different had the break point conversion increased in scenario 2 (as he converted in all games with break opportunities), but could be very different in scenario 1.

On the ATP website, they report players' break point conversion and number of games in which they broke their opponent.  This gets close to the idea, but not exactly.  Here are 2 interesting cases.  

1. Novak Djokovic, the number 1 ranked singles player: 
• converts 47% of break points - ranked 9th this year on tour
• wins 37% of return games (opponents' service games) - ranked 2nd
2. Marty Fish, toped ranked American at #9
• converts 48% of break points - ranked 8th
• wins 24% of return games - ranked 36th

So while they both have equal break point conversion, Djokovic breaks a lot more often.  This means one of two things: 

• either Djokovic has more opportunities to break (which would give Fish a higher BGO), or 
• Djokovic has more opportunities in each game (which would give Djokovic a higher BGO).  So while it takes Djokovic more chances to finally break, he is successful in more of those games.

It is impossible to calculate BGO from the data available from the ATP.  But my hope is that BGO catches on so that the TV announcers don't solely blame a low break point conversion as the reason a player is losing.