Who is the least deserving world #1 tennis has ever had?
The answer will barely move you. But the accompanying results are cool.
What this blog is all about: Love All
The dataset being used: Note on the Datasets
Earlier this week, I received this A2A on Quora: What is the least number of points that any male tennis player has achieved in order to be number one in the ATP rankings?
In its simplest form, this is a fairly straightforward question to answer. I only need to check the Rankings table for the smallest value of pts where pos is 1. However, the result can be misleading. This is because ranking systems in tennis haven’t exactly been consistent. In 2009, the entire points system was changed, and points available were doubled for a lot of the events.
You can probably sense the real sentiment behind this question though, which is to find the player who became world #1 ‘most easily’. To find who this least deserving candidate really is, I shouldn’t be looking for the player who became #1 with the lowest absolute total points, but rather the one who held the lowest fraction of all available points, and was still able to make it to the top with that fraction.
To do this, for every week, we sum up the points held by all the players on the tour, down to the last guy who holds just one point. This total is the number of points that were ‘up for grabs’ at this stage. We then take the points held by the player ranked #1, and divide it by the earlier total. This tells us what fraction of the available points is held by the top ranked player, and consequently gives us a metric for how effectively he has ‘cleared the field’. We now have our ‘deservedness’ function, for a given week:
D(w) = {points held by world #1}/{total points held by all players}
With this modified query (which you can find here) the results are slightly different. Here’s a list of the players who were #1 in the ‘least deserved’ weeks tennis has ever seen*.
* - Since 1990. I don’t have reliable point totals from before that. Sorry.
Least Deserved Weeks at #1
Yevgeny Kafelnikov holds the record for lowest fraction of available points held, whilst ranked #1. Kafelnikov won 2 Slams in his career, the ‘96 French Open and the ‘99 Australian Open. This latter title helped give him the world #1 ranking for 6 weeks, from 3rd May to 7th June. These 6 weeks top my list of ‘least deserved’ weeks, with Kafelnikov holding between 1.79 and 1.81% of available points.
Next on the list is Pete Sampras, who on dozens of occasions (33) during his career, held less than 2% of available points. This shouldn’t actually come as a surprise. Sampras was ranked #1 in the world for 286 weeks, so the volume alone should ensure that he’s well represented in his list. That said, the highest percentage Sampras ever held was still just 3.19%, which ranks 659th on my (inverted) list of most dominant weeks.
Carlos Moya, who was #1 for 2 weeks in April ‘99 rounds up my bottom 3, holding just 1.84% of available points.
Incidentally, the 17 least deserved weeks ever all took place in ‘99, between April and June. Terrible year for tennis. Or was it the best year?
Now that I’ve already written the query to get the full list of such weeks, it only makes sense to flip it over and find the players who were correspondingly ‘most deserving’ of their #1 ranking. The answer will shock no one.
Most Deserved Weeks at #1
Unsurprisingly, Djokovic tops the list of highest percentage of available points ever held by one player, with a staggering 6.79% of points held in June 2016. Remarkably, the second best week (6.61%) isn’t from the same run, but from October 2015, meaning Djokovic actually peaked twice in this regard, nine months apart.
That isn’t all. Have a look at the list itself.
Djokovic so utterly owns this list, that the first time any name other that his appears in it is all the way down at week #49, where we see Nadal’s peak of 5.86% in February 2014.
So, the top 48 most dominant weeks of all time don’t just belong to the same person. They belong to the same person during very different times of his career. You can see weeks from all over his 2015 and 2016 seasons, and by the time we’ve made it to #40, we’ve already crossed a few weeks from late in his 2011 season. He’s far ahead of his competition, being the only man to have held more than 6% (and 6.5%) of the available points.
Further down the list, Nadal’s name becomes slowly more frequent, mostly from his 2013 season. Until #200, there’s still no sign of anyone other than these two. Finally, at #217, Federer’s 2012 season comes through, during which he held 5.02% of points in October. Murray’s peak 4.94% comes at #235, from December 2016.
Parting Notes
I like that Murray showed up on the list. I suspect that he’d also have been the third distinct name on a list of players who held the highest percentage of points, irrespective of rank, even if you checked this before he was #1 himself. Essentially I think he held a higher fraction of points as #2 than most players before him did at #1.
Aditya Ramani pointed out that since the points held by ATP players come from different sources, i.e. tournaments at different levels, it’s wrong to say that all these points are ‘available’ to the player. On the other hand, how does one measure the number of points actually available to a player? One half-decent way of optimising the results is this: only consider points held by the top 50 ranks. This way we’d actually be measuring what fraction of the top 50 players’ point stash is held by the #1 ranked player, and since they’re all likely to have played a lot of the same tournaments (giving priority to Slams and top Masters events), you can assume all points are roughly ‘from the same pie’. I added this condition to the query, and got…exactly the same results. I mean, sure, the fractions were different, but Kafelnikov, Sampras, Moya, and 50 appearances of the word ‘Djokovic’ were exactly where you’d expect them to be. Djokovic’s 2016 season shone a little more brightly than his 2015 season. Nadal was pushed back to week #52, and Federer showed up at week #135, and Murray broke into the top 200 weeks, at #194. The first appearance of a non-Big 4 name was that of Ivan Lendl, all the way down at week #600. Oh well.
This is obviously only one way of trying to ascertain how much a player deserves his #1 rank. Other, equally acceptable ways could be number of titles won, number of significant titles won, etc. Fodder for a future post perhaps.
Since the percentage of points you can hold is largely dependent on the points your opponents are capable of keeping from you, this whole metric is very reminiscent of the ‘era’ discussion in tennis. Djokovic is so far ahead of competition here that you could accuse him of playing during a weaker era than most. On the flip side, Federer’s most successful seasons show him retaining the #1 ranking with less than 4% of the points, leading one to question what a ‘weak era’ really is.
The weak era argument is a subject for a whole other post though.
All images in this post are from Creative Commons.
