Elo and goats (part 1)
One way of shedding some light on the GOAT debate in men’s tennis is to look at Elo ratings of players in the professional era. Some who have done this have looked at the highest achieved Elo score. From this point of view, Novak Djokovic is the GOAT: in the first part of 2016 he achieved the highest-ever Elo rating. But there are other ways of looking at Elo ratings that tell more of a story. One story is how Roger Federer seems to have raised the bar for elite men’s tennis in the mid-2000s.
The graph below shows the top 10 largest gaps between the player who achieved the highest average Elo rating in a given year and the player who achieved the second highest average Elo rating.
In 2005, Roger Federer built the largest ever gap in playing strength over his contemporaries, led by Andy Roddick. Federer appears in this list three times for consecutive years from 2005 to 2007. Pete Sampras and Jimmy Connors are the only other players to appear more than once.
In 2005 Federer won ‘only’ two Grand Slams, Wimbledon and the US Open, but he also won four Masters 1000 titles and five lower-level tournaments. His Elo rating partly reflects the playing strength he demonstrated in 2004 (when he won three Grand Slams and 11 titles in total), but he was able to increase it during 2005. The graph below shows Federer’s Elo rating relative to his four closest rivals in 2005.
From 2004 to 2007, Federer maintained a gap in playing strength over his closest rivals, which slowly reduced, first with the rise of Rafael Nadal and later with Novak Djokovic and Andy Murray.
One illustration of what this level of dominance meant is the 2007 Australian Open. Federer’s win at this tournament was the most predictable Grand Slam result in the professional era: at the outset he had a 60 percent chance of winning the tournament. The graph below shows the 10 most predictable Grand Slam results based on a Monte Carlo simulation.
If 60 percent chance of winning doesn’t sound remarkable, consider that to win a Grand Slam, a player must win seven matches in a row. A player that had a 50 percent chance of winning each of those seven matches would only have a 0.8 percent chance of winning the tournament; the same chance as a coin toss coming up heads seven times in a row. A player with a 75 percent chance of winning each match would have a 13 percent chance of winning the tournament. A player with a 90 percent chance of winning each match would still have a less than 50 percent chance of winning the tournament.
To have a 60 percent chance of winning the tournament, Federer had to have been 93 percent favorite to win each of his matches on average. Taking the probabilities implied by the bookie’s odds (which are more accurate win predictors than Elo ratings alone), Federer was indeed the 93 percent favorite on average in his matches, as shown in the table below.¹
The graph below shows the Federer’s probability of winning each Grand Slam he competed in during his period of dominance. The ones he won are highlighted. From 2005, the probability rarely dipped below 40 percent, indicating he had on average at least an 88 percent chance of winning each match.
In the mid-2000s, Roger Federer achieved a greater level of dominance over his contemporaries than the leading players of earlier generations, such as Connors, Borg, McEnroe, Lendl and Sampras.² While this doesn’t necessarily make him the GOAT, it makes what happened next even more extraordinary: not one but two players in the same generation challenged and eventually surpassed him in playing strength. Probably more interesting than the GOAT debate (but also more intractable) is the question of whether Nadal and Djokovic would have achieved what they have without Federer as a yardstick.
¹ The Monte Carlo simulation also takes into account matches that Federer could have played but didn’t. Nadal’s form had been poor (by his standards) towards the end of 2006, but he was still Federer’s closest rival in terms of playing strength. Given their relative Elo scores prior to the tournament, Federer would have had an 80 percent chance of winning had they met.
² This assessment may be unfair to Rod Laver, who won his second calendar Grand Slam in 1969, at the start of the professional era. Since my data starts from that year, the players’ Elo ratings may not have fully reflected their playing strength and Laver’s dominance could have been underestimated.
