Thursday, May 29, 2014

Myth vs. Math: Big Points

This is the fourth 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 three statements in this series were "big servers have a notable advantage in tiebreakers," "Novak Djokovic has the best defensive return in the game right now," and "Rafael Nadal tends to get tougher draws than Djokovic since making his return from injury." The fourth statement that is being put to the test is "The top players play the big points better than their opponents."

The Myth

One of the big mysteries in tennis over the last five years has been what has allowed the big four to dominate the game. Aside from their talent, how have they been able to produce their best tennis week after week? The general agreement is that the top players handle the big moments better, and many take it as far as to say that they play the big points better.

On the surface, it is a statement that makes sense. The Big Four don't win every single point they play, but they always find a way to win. So it's easy to conclude that they play their best when it really matters.

Take this as an example: In 2014, Rafael Nadal, the No. 1 player in the world, has won 55% of all points he has played. However, that is only 9% better than the No. 100 player in the Year-to-date Rankings, Bradley Klahn. So if only nine percent separates No. 100 from No. 1, there must be something more to Nadal's success than just being more talented than his opponents.

To test the claim, I am going to use Novak Djokovic, the best tennis player in the world since the start of 2011, and see how well he does in the big situations in the 2014 season. More specifically, I want to see if he is able to raise his level on the points that determine the outcome of a service or return game.

The Math

The first way I will check this is to look at how Djokovic performs on break points, which are generally considered the most important points in a match before a tiebreaker. Starting with his serve, Djokovic has won 70% of all service points he has played. However, on break points, his percentage drops down to 59%, meaning that his level drops on the big points on his serve.

That is normal to some degree. 13 of the top 20 in the YTD Rankings have do worse when saving break points than on normal service points. However, Djokovic's 11% is the largest of any player in the top 20. However, when given the opportunity to break, the same isn't true. All but four players in the top 20 win a higher percentage of break points than normal return points, which makes sense. If a player is returning well enough to earn a break point, they will likely convert it. Likewise, if a player is serving poor enough to be facing break point, then they are less likely to save it.

But even on return, "the best returner in the sport," does not raise his level when he has the chance to break. Djokovic's winning percentage on break points is identical to his winning percentage on any return point. So on both serve and return, Djokovic's level drops on the biggest points.

The second way I check how Djokovic's level fluctuates on the big points is to compare his expected  games won to his actual number of games won. How to define "expected games won" is where this gets a little tricky. We know that Djokovic has won 70% of all points on his serve in 2014. Therefore, if we pick a random service point that Djokovic played in 2014, there is a 70% chance that we will pick out a point that he won.

Now lets say that if we pick out a winning point, then in an imaginary service game, we are winning 15-0. However, if we pick a losing point, then we are down 0-15. If we keep randomly picking points until someone has won this imaginary game, what is the probability that we will win the game? The answer is the "expected games won." So the EGW metric, essentially measures the percentage of games a player will win if he plays every point at their standard level.

So since Djokovic's standard level is to win 70% of points on serve, his EGW as server is  90.1%. Here is the probability breaks down:
Hold at love: 24.01%
Hold at 15: 28.812%
Hold at 30: 21.609%
Go to deuce: 18.522%
Hold after deuce: 84.483%
Break after deuce: 15.517%
Break with no deuce: 7.047%
Just for fun: The probability of going to reaching deuce No. 9 is 0.02%

When we look at actual games won, Djokovic is at just 88%, so for a third time, the numbers have shown that he does not perform as well in the big points. Same is true on his return. He has an EGW of 33% as a returner, but has only won 32% of return games this year. But how accurate is EGW? If the only stat you have on a player is their percentage of points won, using the formula for EGW is actually the best way to find out approximately how many games they have won. If the sample size is large enough, the two numbers will be almost identical. However, its when looking at smaller sample sizes where you see the variance for each player.

So if we look at individual matches, we can get a closer look at how Djokovic plays the big points. Let's start with Djokovic's loss to Stan Wawrinka in Melbourne. In that match, Djokovic won 68% of service points, so his EGW on serve was 87.6%. That means that in 26 service games against Wawrinka, Djokovic should have held 22.77 times. However, he only held 21 times. On return, he won 37% of points, so his EGW on return was 20.6%. That means he should have broken Wawrinka 5.16 times in 25 tries, but he only broke him four times. In total, Djokovic won 2.93 less games than he should have, which also means Wawrinka won 2.93 more games than he should have. In a match that finishes 9-7 in the fifth set, a 2.93-game swing make a big difference.

For the second match, let's go with Djokovic's win over Nadal in Rome.
Service points won: 65%
Service EGW: 83.4% (11.68)
Service games won: 10
Return points won: 48%
Return EGW: 46% (6.44)
Return games won: 6
Total difference: 2.12 games less than expected

In both of Djokovic's most competitive matches in 2014, he played significantly worse than the numbers expect him to, meaning that Djokovic's level dropped considerably on the big points in two of the biggest matches he has played this year. So not only has Djokovic played poorly in the big points, he is doing it in the big matches.

There is one stat Djokovic has that supports the claim that the top players perform well in the big moments. In tiebreakers this year, Djokovic has won 66.7%. However, Djokovic has only played in six tiebreakers in 29 matches this year, so his ability to win tiebreakers has little to do with his 26-3 record.

Djokovic's success has far more to do with his ability to avoid big points than his ability to win big points. The Serb has played three times as many service games as he has faced break points. Meanwhile, has created 238 break opportunities in 319 return games in 2014. With that many chances to break, he can afford to have a lower conversion rate. So the claim that the top players separate themselves with how they play in the big moments does not hold true, at least for Djokovic.

Also, the fact that Djokovic's actual games won has been significantly lower than his expected games won is good news for his fans. Over the course of his career, Djokovic tends to be about less than a percent below expected on serve and between one and two percent better on return. 

He has been a close second best player on tour in 2014, despite doing so poorly on the big points. It's highly unlikely that the difference between his EGW and actual games won will continue to be so high, so his performances can only get better as we continue in 2014.

Also, if Djokovic can defeat Nadal on the clay in Rome while playing 2.12 games below expected, his chances to beat Nadal in a potential Roland Garros final are very good. Several times, Djokovic lost games where he led 30-0 or 40-0 in Rome. If he can eliminate those, his chances to beat Nadal will be good.

*If you want more information on expected games won or want to discuss anything else in my Myth vs. Math pieces, you can e-mail me at

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