Who is the best tennis player of all time? Connors? Borg? McEnroe? Nadal? Federer? As is the case in almost all sports, this is an almost impossible question to answer definitively. Is it the player why was most consistent over their career? The player who won the most majors? The player with the best winning percentage in majors? The most dominant head-to-head player?
And how do you compare across eras? Tennis, like all professional sports, has become more competitive over time, with the result being a general improvement in the quality of the players and the game. A top ten player from today could almost certainy dominate a top player from the 1970s, and possibly even the 1980s. The changes in training, raquets, career length and strategy make the comparisons very difficult.
Further, how do you handle career length? Say someone burst onto the scene, thrashed all the great players for twelve months, then decided to wander the globe, like Caine, and stop playing professional tennis. Are they a great player? How do you weight their brief dominance versus someone whose career was a decade or more, like a Federer, or an Agassi?
A new academic paper tries to answer this “best” question, yet again, by applying a network analytic model. It looks at contacts between players in the top tournaments, and then creates a new measure, called “prestige”, that it uses to re-rank players across decades. Here is the author’s description of how the new measure works:
We consider the list of all tennis matches played by professional players during the last 43 years (1968-2010). Matches are considered as basic contacts between the actors in the network and weighted connections are drawn on the basis of the number of matches between the same two opponents. We first provide evidence of the complexity of the network of contacts between tennis players. We then develop a ranking algorithm similar to PageRank and quantify the importance of tennis players with the so-called “prestige score”.
Here are his results, with Jimmy Connors out front, followed by Lendl and McEnroe. Federer is back in seventh spot, behind players like Edberg and Agassi; Rafael Nadal is further back in 24th place, one ignominious spot behind the flowing mane of Vitas Gerulaitis.
This, of course, entertaining, but an instant argument for anyone who follows tennis. I get that they were more dominant in their era, but is this what we mean by “better”, having Vitas Gerulaitis rank above Rafael Nadal? The latter would have crushed Gerulaitis like a furry bug. Taking a broader view, is Lendl better than Federer? It shows how tricky these inter-generational comparisons can be. Even so, Federer’s 16 wins in the Slams puts him well ahead of anyone else, active or retired, and Connors is nowhere on that list. Granted, Connors has 109 singles titles in total, which Federer will never approach, but those must be hugely discounted against Slams wins.
As an attempt to get around this, the paper closes with another chart. The second one restricts comparison to within individual years, thus avoiding the Gerulaitis/Nadal problem of brief careers in modern era versus long careers in earlier eras.
This chart makes more sense, in that the rankings, while not always matching official ones, are plausible within the year in question. Mind you, I’m not convinced Djokovic was the best player in the world in 2009, so that does seem a little awry, but put that aside and the paper’s “prestige” network analytic model doesn’t do too badly.
All of this leaves us with an open question: Is it possible to do credible inter-generational comparisons in professional sports? This paper leaves, while analytically impressive, wide-ranging and thoughtful, leaves me even more doubtful. [-]
Source: Radicchi F. Who is the best player ever? A complex network analysis of the history of professional tennis. 2011:10. Available at: http://arxiv.org/abs/1101.4028.