The whole purpose of professional sport is to find out one thing. Football leagues, cup competitions and all sports tournaments around the globe are set up to answer the question that motivates the entire sporting world: “who is the best?”.
As a consequence of all of this interest in ranking, and not just in sport, there has been much research in the scientific community on developing mathematical and statistical models to rate things. These rankings models are perfectly suited to sport. Of course, in a league system (such as football) there is little need for a model to obtain a rankings list – the final table will suffice.
However, if the sport is not organised into a league, or if the contestants took part in different eras, one needs a mathematical model to obtain rankings. And as it is the time of year for strawberries and cream, it is tennis that concerns us.
Crunching the numbers
To find the greatest tennis player, we fed the results of every Grand Slam tennis match since 1968 into our model. This covers the entire “open era” - the period since the sport was professionalised. And one man came out on top: Jimmy Connors.
The result of each match was recorded in set scores. The model is weighted so that a 6-0, 6-0, 6-0 victory is rated as better than a 7-6, 7-6, 7-6 victory, and a victory against a top player is rated as better than a victory against a lesser player. The results are in the table below.
The model gives us the estimated “strength” of each player in each year, which can vary over the course of his career. The strength is given a number and is relative to the average strength of all players over the entire time period.
The nice thing about the model is that the strengths can be used to estimate the probability of one player beating another player in a match. For example, using the numbers from the third column of the table, Jimmy Connors of 1976 has a 64.5/(64.5 + 49.56) = 56.5% chance of beating Roger Federer from 2005.
How do you measure greatness?
Even the most rigorous mathematical model requires some human interpretation, and there are various ways of judging the best player according to the model. For example, you could take the one-year maximum strength of a player (the first four columns of the table) as your rankings list and leave it at that.
However, there are alternative measures of greatness. You may want to assess excellence over a longer period of time, say for 10 years – this is the rankings list given in the middle two columns of the table. A third alternative is to measure strength over the lifetime of the player, as given in the final two columns of the table.
Jimmy Connors tops all three rankings lists, with Bjorn Borg a constant in second place. Roger Federer fans, myself included, may be surprised by this. After all, the Swiss has won the most Grand Slam titles.
However, a little digging reveals why Connors is ranked so highly. He was banned from the French Open for a few years during his peak, saving him from potential losses on clay, his worst surface. And Connors only entered the Australian Open twice: winning it one year and getting to the final the only other year. Like Federer he was a serial finalist and winner in his pomp in the mid-1970s.
Where’s Pistol Pete?
A surprising omission from the rankings is Pete Sampras. Again, there are sound reasons why he does not fare well here. First, the model rewards big victories, but Sampras had a different strategy. He would play for one break of serve before holding his serve to win a set 6-4, or even 7-6. Thus he was involved in lots of tight matches. Second, he performed well only on certain surfaces, reaching the semi-final of the French Open on clay only once.
It also appears that Sampras played during a particularly weak era. Connors’ big rivals – Borg, John McEnroe and Ivan Lendl – rank second, seventh and tenth. Federer, Rafael Nadal and Novak Djokovic all appear in the top six. The quality of these two eras really stands out. Among the 1990s-era that Sampras figured in, only Andre Agassi makes it into the top ten.
The maths say that Jimmy Connors is the best player of the open era. However, these rankings should not be viewed as an attempt to end the discussion. Rather, I hope they act to increase the debate. So, who do you think is the greatest of all time?