Appreciating the Big Four in Tennis (Or is it the Big Three?)

By Carlos Pena-Lobel

With the men’s semifinals starting up tomorrow, all eyes will turn to the action at Wimbledon, tennis’ oldest tournament.  One of the biggest storylines of the tournament was Rafael Nadal making an early exit, while Federer made it through with relative ease.  Federer is 2/3 in break points saved, whereas Djokovic is 17/21 and Murray is 17/24.  In fact Federer hadn’t had his serve broken in over 100 service games (Gilles Simon broke Roger yesterday, ending his streak at 116 consecutive holds).

However, it wasn’t long ago that these roles seemed to be reversed.  Federer had dropped to number 6 in the ATP rankings by July 2013, and people were questioning how long he could keep going.  During this time, Nadal beat Djokovic to win the 2013 US Open, then lost in the finals of the 2014 Australian Open to Stanislas Wawrinka, before winning the 2014 French Open once again over Djokovic.  This was his 14th major, tying him with Pete Sampras for 2nd most majors of all time, and his 9th French Open (for comparison, the record for most Australian Opens, US Opens, or Wimbledon’s any player has won are 6,7, and 7 respectively).   In fact, this 538 article (which was published shortly before Nadal won his 14th major) gave Nadal practically a 2/3 chance of reaching 16 or more majors.  Furthermore, Nadal was given a 1 in 20 chance to reach 20 or more titles.  Since that French Open, Nadal went out in the 4th round at Wimbledon, withdrew from the US Open, only made it to the Quarterfinals in both the Australian and French Opens, and now fell in the second round to Bob Marley (Dustin Brown).

While Federer is no longer the favorite, he is back up to 2nd in the rankings and still has a chance of reaching an 18th title at this Wimbledon.  Current odds have Djokovic and Murray as runaway favorites at Wimbledon, with Federer in a distant 3rd and then Richard Gasquet.

Which brings us to the topic of this post.  Since winning his first major at the 2005 Australian Open, Nadal has never gone 5 majors without winning one.  Basically, he has never performed this poorly in his career, so it isn’t unreasonable to think that the Big 4 (or was it a big 3?) are seemingly done atop the rankings.  Thus, it is good to look back to remember how dominant they really were.  From the 2005 French Open to the 2013 US Open, the Big 4 won 34 of 35 majors, and both Olympic gold singles medals.  Since then they are 3-3 in majors, with Wawrinka doubling the combined total of Murray, Federer, and Nadal.

Since ATP rankings have changed their point’s distribution, in order to measure how dominant the Big 4 were I looked at the amount of time these players were at the top of the rankings rather than just the player scores.  For each ranking, I looked at the top n players irrespective of order (so days with Federer first and Nadal second were combined with days Nadal was first and Federer second), and calculated how many days they appeared at the top of the rankings.  This was done for tuples of size 2-10 (since a tuple of size 1 is just the number of days a player was ranked #1).  Ties in rankings were based on order of appearance on the ATP website (there were only a handful, and some were later dropped because of missing data).

There was also a lot of missing data, (rankings with players missing, or rankings with only 1 player) with all of it occurring before 1984.  There was no rhyme or reason to what or why something was missing so it would’ve been too hard to fix the data.  Thus, I took 2 approaches.  First, I dropped all data before and up to December 12, 1983 (the most recent missing data point).  The other approach I took, is to drop all data points with incomplete data, and calculate everything as if they just never existed.  This is of major importance because the late 70’s and early 80’s was the era of the other “Big 4” of McEnroe, Lendl, Connors, and Borg.  Also during the 70’s and 80’s, there are less frequent rankings.  Prior to the “dead period” as I’ll call the time before Dec 12, 1983 (the date for which there was no longer any missing data), there were rankings separated by 721, 273, 202, 182, 181, and 177 days.  After the dead period, the longest gap between rankings was 48 days.  Thus I will present both, but each needs to be taken with a grain of salt.

To visualize how awful the data was prior to 1984, I’ve created histograms showing the days between rankings for the Dead Period and Post Dead Period.  You’ll notice that the longest gap between rankings lasted nearly 2 years, 721 days to be exact.  The beneficiary of this was the quartet of, in order, Borg, McEnroe, Connors and Vilas.  These were great players, but it is highly unlikely that they held such a stranglehold on the rankings for almost 2 years, and this it is hard to accurately measure how dominant they actually were during this time.

Days Between Rankings

Now for the tables comparing the best duo, trio, and quartet.  For each image a ranking including the Dead Period is on the left and one without the Dead Period is on the right, and bold text marks the tuple that is currently accruing days.  (Data is updated as of the French Open (5/25/2015)).  The order of names appearing is alphabetical based on first names.

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Finally, I created a plot to compare across time how long different groups of players have been at the top.  Can you guess which group of 2 is Federer and Nadal?  How about Federer, Nadal, and Djokovic? And Murray?  Besides showing how dominant the Big 4 are, it shows how beneath them there hasn’t been a consistent 5th place person below them.  If you don’t understand the graph, each line represents a group of players.  The height is how many days up to that date, they had been ranked at the top.

Days at Top vs Days Elapsed
While this shows how dominant each group has been, it doesn’t show how good each member in the group is.  Thus, it doesn’t answer who is better Federer, Nadal or Djokovic, rather that we are lucky to have witnessed probably the best tennis of all time.

The data used for this analysis can be found here.

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  • We have found several big names in the tennis world, especially in men’s category players like Rafael Nadal ( king of clay courts), Roger Federer, Novak Djokovic, and Andy Murray are the big popular names of the tennis world. We have been watching them from the very beginning and in different big tournaments, we have witnessed their performance. While watching their games, we are also able to understand some basic techniques of tennis.

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