Ranking tennis players: Motivation

When introducing a statistical system in sports, it’s always worth considering what purpose the system will serve. In this case, since the system is a ranking of tennis players, assessing the rankings used by the ATP, the main officiators of men’s tennis, is a natural starting point in determining whether a new system intended for the same purpose can be of use.

In brief, the ATP rankings consider two things: the tournaments you play, and how far you advance in them. With a few exceptions (which are laid out in other sources and are not especially relevant here), the tournaments are generally assigned a certain point value (Grand Slams are 2000; ATP World Tour events are either 1000, 500, or 250; lower-level events have correspondingly lower values). The winner of the tournament earns its full value in ranking points, the runner-up gets 60% of the winner’s score (for instance, 1200 in a Grand Slam), the semifinalists get 60% of the runner-up’s score (36% of the winner’s, 720 points in a Slam), and the points are reduced by 50% for each additional round earlier.

This proves to be a relatively effective system, especially because ATP ranking points themselves are an end pursued by the players. As a result, the fields at the Grand Slams and 1000-point Masters events, which are weighted most heavily by the rankings, also attract the best players, making victory in these events a more impressive feat (and thus deserving of the additional weight).

There are some issues, however. Consider the case of the 2011 French Open.

John Isner (ATP rank of 39 at the time) lost his first round match. One bracket line away, so did Santiago Giraldo (ranked 63^rd). As a result, both players were awarded 10 ATP ranking points, the amount allotted to first-round losers in Grand Slams.

Their performances, however, were quite different. Isner’s match lasted 5 sets and just over 4 hours, with a score of 6-4, 6-7 (2), 6-7 (2), 6-2, 6-4. Had it been a best-of-3 match and played out the same way, Isner would have emerged victorious. As it was, the match was quite closely contested. Giraldo, meanwhile, was swept aside by a comparatively perfunctory 7-6 (5), 6-3, 6-3 score; it wasn’t an utter blowout, but he failed to take a set. Isner’s performance appears more impressive, and it would be reasonable for a tennis ranking system to account for the closeness of his match as compared to Giraldo’s.

There is, of course, one other factor that was not mentioned in the preceding paragraph: the identities of the players’ opponents. Giraldo was beaten by Pablo Andujar, ranked 48^th at the time of their contest.

Isner’s opponent? Rafael Nadal, #1 in the world and very nearly unbeatable on the clay courts of Roland Garros. Isner was only the second player to take two sets from Nadal in a match at the French Open, and Nadal would go on to lose a total of one set in his remaining six matches as he romped to the sixth of his eight titles (to date) at the event.

At this point, considering Isner and Giraldo’s matches as equivalent simply because both of them lost simultaneously ceases to look sensible. Isner taking Nadal to five sets was one of the more impressive feats achieved by anyone at the French Open that year, and it seems unfair to penalize him just because the luck of the draw put that match in the first round.

This is hardly the only case of this type. Florian Mayer has lost to Novak Djokovic at each of the last two Wimbledons, both times in straight sets. In 2012, Mayer’s 6-4, 6-1, 6-4 defeat came after a run to the quarterfinals; in 2013, his loss was closer (6-3, 7-5, 6-4), but also earlier (the first round), and Mayer’s ranking dropped 12 places as a result.

In the week of February 18, 2013, there were two hard-court tournaments played – one in Marseille, the other in Memphis. The field at Marseille included four players ranked in the top 10 at the time (Tomas Berdych, Juan Martin del Potro, Jo-Wilfried Tsonga, and Janko Tipsarevic); the top seed in Memphis (Marin Cilic) was ranked #12. One might expect Tsonga’s victory in Marseille (in an excellent final in which Berdych held a match point before succumbing) to be valued more highly than Kei Nishikori’s simultaneous Memphis title (over then-#47 Feliciano Lopez), but the ATP designated Memphis as a 500-point event and Marseille as a 250, thus placing more weight on Nishikori’s less impressive victory.

Again, the ATP ranking system does a relatively decent job picking out the best players (although it should be pointed out that this is not typically a monumentally difficult task). But it also comes with a number of issues, particularly the arbitrary nature of the scoring system and the failure to account for closeness of match and strength of opponent, and it is at least worth investigating what would result from accounting for those factors.

Hence the ranking system that will be laid out here. It will ask the same two questions, over and over: How did you play, and who did you play?