while true live

Musings on the fatality of infinite loops and other stuff.

Historical Elo Tennis Rating

Recently I’ve come across that fivethirtyeight article comparing the female tennis all-time greats by means of an Elo rating variant (originally known from chess). It concludes that Serena Williams does not have the highest rating in history, although she is frequently considered as the greatest player of all time nowadays. Obviously, I wondered what’s the situation like in the men’s tennis world. Have Roger Federer’s record 17 Grand Slam wins led to the highest Elo rating as well? What about players like Borg and McEnroe? Anyway, I have found surprising results.

Technical approach

This is where I got the match data on ATP matches from 1968 onwards providing the source of the Elo evaluation in yearly CSV files. I have adopted the mathematical details of the computation from the Elo rating Wikipedia page, while I took the recommendation for the computation of the K-factor from fivethirtyeight. In addition, I valued Grand Slam tournament matches higher than other matches (because of the longer and more challenging best-of-5-sets distance) by increasing the rating changes resulting from those matches by 10%. Anyway, I wrote an R script which can be found here.

The top 10 highest tennis Elo ratings

Obviously, the main question is: Who has acquired the highest Elo rating? The answer is: Novak Djokovic in May 2015! That’s the top 10:

12335Novak Djokovic
22310Bjorn Borg
32304John McEnroe
42274Rafael Nadal
52254Roger Federer
62253Ivan Lendl
72191Jimmy Connors
82168Boris Becker
92159Andy Murray
102132Pete Sampras

Interesting to see that Borg, McEnroe and Lendl (dominating the 1980s) rank in between the likes of Djokovic, Nadal and Federer who have dominated the last decade.

Anyway, you might be surprised to see 14-time Grand Slam winner Pete Sampras only in 10th place. In my opinion, his case demonstrates a practical requirement to get to the top of the above list – or rather a lack thereof: High-ranked opponents.


Everything is relative – being the best, too!?

No matter how good a professional tennis player you are, you will lose sooner or later “because you are human” (this is obviously controversial and Elo does not account for this). When the defeat happens it is better to lose against higher Elo-rated opponents since you then lose less points. To put it bluntly: When you have an hypothetical Elo advantage of 1000 points with regard to the next-best player at the start of the season and you win 99 of 100 matches, you will most likely have a worse rating in the end of that wonderful season due to that one devastating loss! Consequently, it could be said that Sampras might have lacked high-valued contemporaries to make an even deeper run. In contrast, Djokovic has benefited from the high ratings of Nadal and Federer to get to the very top. (Apart from that, Elo inflation might be a reason for higher ratings nowadays, too.) Similarly, Borg, McEnroe and Lendl have benefited from the strong competition in boosting their respective peaks. That’s why I have looked for a way to abstract the performance from absolute ratings: I have compared the margins that the above best players could amass in comparison to the next-best player at their ratings’ peaks. Thus, it can be analyzed by what margin a player has been able to set oneself apart from the competition, which I consider as an indicator as significant as the maximal Elo rating.

225Roger Federer
194Ivan Lendl
181Bjorn Borg
172Novak Djokovic
154Pete Sampras
148John McEnroe
61Rafael Nadal

In February 2007 Federer reached his rating peak and the next-best player at that time, Rafael Nadal, trailed 225 Elo points. That event has marked the biggest gap of the Elo rating’s leader and the rest of the world; a difference of 225 Elo points means a winning chance of 78% for the higher-ranked player. Well, two months later Federer lost to Nadal in the 2007 French Open final, nevertheless.



No matter whether you ‘prefer’ the first or the second table – both tables shows the current top players count among the best of all times, however, they don’t really outperform the likes of Borg, McEnroe and Lendl! The R source code for my analysis can be found here.