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.