I would like to say that Filippo Radicchi is nuts. I’d like to, but I’m not sure. He might be a genius.
Radicchi, a chemical and biological engineering professor at Northwestern University, likes to play tennis. Like many of us, he has gotten into the argument over who is the best player of all time. It’s one of those arguments that has no answer really.
Radicchi, as a scientist, doesn’t see things that way.
He set out for proof.
So he conducted a study using a diffusion algorithm – I’m already confused — punching in results of over 133,000 matches from 1968 to 2010. And who was the greatest of all time, or at least since 1968?
I don’t agree, but Connors isn’t the crazy part. This was: Rafael Nadal was No. 24. At No. 18?
Eddie Dibbs. I mean, nothing against Eddie Dibbs, exactly. But, uh. . .
So I called Radicchi, and he explained:
“Maybe Eddie Dibbs had an advantage by the fact he played against other good players, more than Nadal,’’ Radicchi said. “Everything’s relative.
“In this case, it’s important to win against other top players. Everything determined by the algorithm is that it’s important to win against other guys who win a lot of matches. It’s if your opponents are very good, and opponents of your opponents are very good.’’
OK. But Eddie Dibbs?
Well, Radicchi’s system had Connors No. 1, followed by Ivan Lendl, John McEnroe, Guillermo Vilas and Andre Agassi. Roger Federer was 7, Pete Sampras 8, Bjorn Borg 10.
And Michael Chang, Roscoe Tanner, Dibbs, Harold Solomon and Vitas Gerulaiits were all ahead of Nadal. (Rod Laver is not in the top 30, as much of his success came before 1968.)
“If you beat players better than you, that’s something not counted by the ATP in its rankings,’’ Radicchi said. “They just do it based on round.’’
Yes, the tour gives players a certain number of computer rankings points based on what round they reach in tournaments.
Radicchi explains, if I understand, that his method works as a web connecting all matches played. Somehow he established a Prestige Value for players.
Let’s call a player ED (the first name, as well as the initials of Dibbs). ED has a value. If he loses to a player we’ll call RN, then some of ED’s prestige flows in the algorithm to RN. Meanwhile, RN gains prestige.
Well, pull the camera back to all the players ED and RN played in a tournament, and then in every tournament. And pull it back farther to see all the opponents of their opponents, and then the opponents of the opponents of the opponents. And so on.
You see the interconnectivity, and the prestige flows in all different directions.
“Particularly relevant results are those regarding: the robustness of networks under intentional attacks,’’ Radicchi said. “(T)he spreading of viruses in graphs; synchronization processes, social models and evolutionary and coevolutionary games taking place in networks.’’
Did we just switch subjects? Nope. That was part of the clear explanation in his study.
And I thought it was about who had the best serve and return. I’m getting the same headache I get when trying to understand the BCS and RPI computers.
This is exactly why I don’t care for computers and over-reliance on stats in sports. These things should not be what decides which teams play in the national college football game, for example.
“We represent the data set as a network of contacts between tennis players. . .’’ Radicchi wrote. “A single match can be viewed as an elementary contact between two opponents. Each time the player plays and wins against a player, we draw a directed connection from (one player to the other). (Then) we adopt a weighted representation of the contacts.’’
It almost makes sense.
What he’s saying is that Connors played in an era with better players than Federer and Nadal did. Radicchi also said that Connors’ longevity helped his score in this study, and that Nadal’s will rise as he spends more years on tour.
“According to our ranking technique,’’ Radicchi wrote, “the relevance of players is not related to the number of victories only, but mostly to the quality of these victories. In this sense, it could me more important to beat a great player than to win many matches against less-relevant opponents.’’
Look, I’m trying to get this. I prefer judging footwork and backhands over algorithms. I’m not even comfortable spelling “algorithm.’’ There’s no y in there? The study actually included several mathematical formulas.
So Radicchi, trying to break it down, sent me a mini-scaled version of his study, looking only at players who won at least two majors. In the case of this mini-version, Radicchi considered only results from majors. (That’s the chart above).
Players had different-sized circles next to their names. Radichhi referred to those circles as nodes.
“Players are more or less ordered according to their appearance in Slams (left older, right younger),’’ he said. “The size of the nodes is proportional to the number of Slams won (i.e., Federer is the largest) and arrows connect players according to the results of their matches.
“The width of the edges is proportional to number of victories, and edges point toward the winner. Arrows can go in both directions, of course.’’
Of course. So there you have it.
But Dibbs vs. Nadal? Seems to me as if Nadal would have won 6-0, 6-0 based on power and speed.
According to science, though, while Nadal had a bigger node, Dibbs had more prestige.
Top 30 players, according to the study:
1) Jimmy Connors 2) Ivan Lendl 3) John McEnroe 4) Guillermo Vilas 5) Andre Agassi 6) Stefan Edberg 7) Roger Federer 8) Pete Sampras 9) Ilie Nastase 10) Bjorn Borg
11) Boris Becker 12) Arthur Ashe 13) Brian Gottfried 14) Stan Smith 15) Manuel Orantes 16) Michael Chang 17) Roscoe Tanner 18) Eddie Dibbs 19) Harold Solomon 20) Tom Okker
21) Mats Wilander 22) Goran Ivanisevic 23) Vitas Gerulaitis 24) Rafael Nadal 25) Raul Ramirez 26) John Newcombe 27) Ken Rosewall 28) Yevgeny Kafelnikov 29) Andy Roddick 30) Thomas Muster