Friday, April 25, 2014

Myth vs. Math: Rafa, Nole, and Draws

This is the third installment in a five-part series called Myth vs. Math. In this series, I am taking a look at five widely-accepted statements that tennis writers, analysts, fans, and commentators frequently make. I'm checking to see if these statements hold up against the numbers. The first two statements in this series were "big servers have a notable advantage in tiebreakers" and "Novak Djokovic has the best defensive return in the game right now." The third statement that is being put to the test is "Rafael Nadal tends to get tougher draws than Djokovic since making his return from injury."

The Myth
It's the worst excuse in the book, but it's still the most common complaint amongst tennis fans of every player. Since the dawn of draws tennis fans have complained that their player always gets the hardest draws and that all of their rivals always get the easy draw.
Draws are a fascinating thing in tennis. The randomness of draws can make the ceremony almost as exciting as a real tennis match, and the anticipation for when the draw is released can be as great as the anticipation of the slam itself. After the draw is released, tennis fans have one or two days to analyze and predict what is in store for the days ahead. And regardless of what the draw says, there is a 100% chance that someone will claim their favorite player has a harder draw than someone else.
It happens at every major tournament in tennis history, but since the 2014 Australian Open men's singles draw was released, the Rafael Nadal fans have made an inordinate amount of griping about the difficulty of Novak Djokovic's draw. However they took it as far as to exaggerate that Djokovic always gets easier draws.
It has gotten to the point where Nadal fans have said it so much that even Djokovic fans have begun to believe it. On the ATP website, a Nadal fan accused Djokovic of cheating to which a Djokovic fan replied "He does typically get the easier draws, but that is out of his control." So does Djokovic really tend to get significantly easier draws? Are Djokovic's opponents easier than Nadal's? Are the matchups created by the draw really better for Djokovic?
The Math
I'm going to do the math on tournaments since the start of the 2013 season, since that is when the complaints have really picked up from Nadal fans (there wasn't much to complain about when Djokovic and Roger Federer were on the same side of the draw at 13-of-15 slams). When looking at specifically the slams, I will focus on just the last four since Nadal didn't play in the 2014 Australian Open.
There is special attention paid to the draws at the slams, and rightfully so, since that's where the most is at stake. However, I first want to look at strength of schedule overall. Since the start of 2013, Nadal, who has played four more matches, has had to play against top 10 opponents three less times and top 20 opponents five less times.
Overall, Nadal's average opponent had a ranking of 45.1, while Djokovic's average opponent had a ranking of 35.8. However, Nadal did have a match against a player ranked 570, and a player ranked 570 isn't much easier than anyone else outside the top 100 for Djokovic and Nadal. If we change the ranking of every player outside the top 100 to exactly 100, Djokovic still has had to face tougher opponents with a new mean rank of 32.5 compared to 37.7 for Nadal, which is still higher than Djokovic's original rank.

Now, if we created a bar graph for the ranking of their opponents faced, both players would have a graph that skews towards the higher ranking, with the mode at the low ranking. For graphs like that, the median is a much more telling summary statistic than the mean. However, Djokovic has a tougher median-ranked opponent as well. The median rank of his opponents is 23, while Nadal's is 29.

If rankings in tennis were done like they are in college football or college basketball in the United States, there could be a case to be made that Djokovic is the rightful world No. 1 right now, because his strength of schedule is clearly superior to Nadal's over the last 15 months. However, what about the majors? Is Nadal's strength of schedule week only because he plays a lot more tune-up events than Djokovic or does the same hold true at the biggest tournaments in the game?
To find the toughness of draws, I looked at the 20 seeded players that Nadal and Djokovic each would have played if seeds held at each of the last four majors. However, instead of looking at how high those players were ranked, I want to look at how tough of a matchup each player is based on previous head-to-head records.

Nadal held a 69.2 win percentage against his scheduled opponents, compared to Djokovic, who had the tougher path with 61.5 win percentage against his opponents. However, Nadal does have a higher win percentage against his opponents, partially because he does well against everyone. So if we compare each players' win percentage against an average opponent to their win percentage against their should-be opponents, we can see how tough the matchups that their draw created really were.
Rafael Nadal's path at last four majors Novak Djokovic's path at last four majors
Head-to-Head Head-to-Head
Slam Seed Opponent Wins Losses Win% Seed Opponent Wins Losses Win%
AO 25 Gael Monfils 10 2 0.833 30 Tursunov 1 0 1
16 Kei Nishikori 6 0 1 15 Fognini 7 0 1
5 Juan Martin Del Potro 8 4 0.667 8 Wawrinka 15 3 0.833
4 Andy Murray 13 5 0.722 3 Ferrer 11 5 0.688
2 Novak Djokovic 22 18 0.55 1 Nadal 18 22 0.45
USO 27 Fernando Verdasco 13 1 0.929 25 Dimitrov 3 1 0.75
13 John Isner 4 0 1 16 Fognini 7 0 1
7 Roger Federer 23 10 0.697 6 Del Potro 11 3 0.786
4 David Ferrer 21 5 0.808 3 Murray 12 8 0.6
1 Novak Djokovic 22 18 0.55 2 Nadal 18 22 0.45
W 25 Benoit Paire 2 0 1 28 Chardy 8 0 1
11 Stanislas Wawrinka 12 1 0.923 13 Haas 6 3 0.667
3 Roger Federer 23 10 0.697 7 Berdych 15 2 0.882
2 Andy Murray 13 5 0.722 4 Ferrer 11 5 0.688
1 Novak Djokovic 22 18 0.55 2 Murray 12 8 0.6
RG 27 Fabio Fognini 4 0 1 26 Dimitrov 3 1 0.75
13 Kei Nishikori 6 0 1 16 Kohslschreiber 3 1 0.75
7 Richard Gasquet 12 0 1 8 Tipsarevic 5 2 0.714
1 Novak Djokovic 22 18 0.55 3 Nadal 18 22 0.45
2 Roger Federer 23 10 0.697 2 Federer 16 17 0.485
Average Opponents 679 132 0.837 Average Opponents 559 134 0.807
Opponents in Path 281 125 0.692 Opponents in Path 200 125 0.615
Bolded Opponents 105 61 0.633 Bolded Opponents 123 84 0.594
* Opponents in bold are ones that reached the round in which they would've met
The opponents Nadal would have faced if the seeds held at each of the last four majors were 14.5% harder than average opponents for him. For Djokovic though, his opponents were 19.2% tougher than his average opponents. So if both players played against who they should have according to the draw, Djokovic had the much tougher draws overall.

Even with Nadal's easy draws, things got even easier for him. Of those 20 opponents that he should have faced, only eight of them actually got far enough in the tournament to have to play against Nadal. And those eight that got far enough were only 16.4% tougher matchups than average opponents. Djokovic, on the other hand, had 11 opponents, who got far enough to play against Djokovic. Those 11 opponents were 21.3% tougher than average opponents.
So since Nadal's return, he has gotten to face lower-ranked opponents than Djokovic, gotten more favorable potential matchups in the majors, and seen more of his opponents bow out before he even had to play against them.

Flaws in the Math

The flaws in the math  is that the math doesn't take into consideration how hard each player's draw should  have been. The way the draws work is that there is no difference in who the No. 1 seed and who the No. 2 seed could play against in each round. Both of the top two seeds are guaranteed to be on opposite sides of the draw and any other player can wind up on either  half of the draw. Players who are seeded three or lower start seeing more difficult draws, and even more so for the players outside the top four.
Since Nadal's return, Djokovic has always been ranked in the top two, meaning he should be getting the easiest draws possible at every tournament he plays in. Nadal, though,  was ranked no higher than three for the first seven months of his comeback and even dropped as low as five for several 1000 events and Wimbledon. So Nadal really deserved to have the tougher draws, but instead wound up with even easier opponents than his higher-seeded rival.

Nadal fans that complain that Djokovic tends to get the easier draws are wrong. Even though Djokovic deserved to get easier draws, he was the one who had to face tougher opponents and was set up to have tougher matchups.
Nadal fans will remember how stacked Nadal's top half of the draw was at Australian Open and how Nadal had a potential meeting set up in the Wimbledon quarterfinals with Federer. However, in both cases, Nadal's expected opponents were victims of major upsets and Nadal's draw opened up. Meanwhile, Djokovic had the tougher matchups at each of the other two slams, and actually had to go against them.

Also, when Nadal was ranked outside of the top two, there was the possibility that both players could wind up on the same half of the draw. Since Nadal was chasing Djokovic for the world No. 1 ranking, opportunities to play Djokovic earlier in tournaments was good for Nadal. Instead of having to wait until the final to play Djokovic, playing him earlier meant he had the chance to prevent him from earning ranking points.

So even though having to face the world No. 1 before a final made Nadal's strength of schedule seem better, it was actually a benefit for him in the race for No. 1. It's normal for fans to think that their player always gets the toughest draws, but Nadal couldn't have asked for it to be much easier as he overtook Djokovic in the rankings.

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