# Federer has outperformed everyone on grass - including himself

With his haul of 8 titles, Roger Federer has triumphed at Wimbledon more than anyone else. But how does 8 titles compare with how many we could have expected him to win given his level—and his competition—over the years? And which title was his most impressive? [Authored by Graeme Spence]

Since he won his first Grand Slam at Wimbledon in 2003, Federer has been one of the most impressive performers ever at the All England Club. Federer first matched Björn Borg by winning five consecutive titles, and then last year—after a four year drought—he claimed a record 8th title to surpass Pete Sampras for the most Wimbledon Championship wins in the Open era.

With a chance of adding a 9th title in the coming weeks, it’s timely to ask how incredible has his haul at Wimbledon been?

Federer has been the No. 1 seed at Wimbledon 6 times, which might suggest a fair number of his wins were expected. But can we analyse these expected titles more accurately given his level and the competition he’s faced since his Wimbledon debut in 1999? And can we use the data to judge which of his titles was the most impressive?

### Tournament simulations

To help us answer these questions, I simulated each Wimbledon Men’s Singles draw since Federer’s debut 5,000 times using the players' grass-weighted Elo ratings to give us match win probabilities. By extracting the title probabilities for each year and aggregating over all the years 1999-2017, I obtain the expected number of titles for each player during this period.

The table below shows the expected and actual number of titles since 1999 for players who’ve lifted the trophy in that period or who the prediction model assigns an expected number of 0.2 titles or greater.

Player Expected titles since 1999 Actual titles since 1999 Titles above expectation
Roger Federer 4.50 8 +3.50
Novak Djokovic 2.47 3 +0.53
Rafael Nadal 1.82 2 +0.18
Andy Murray 1.29 2 +0.71
Lleyton Hewitt 1.04 1 -0.04
Andy Roddick 0.85 0 -0.85
Pete Sampras 0.71 2 +1.29
Andre Agassi 0.61 0 -0.61
Tim Henman 0.30 0 -0.30
Goran Ivanisevic 0.02 1 +0.98

Federer certainly stands out with his 8 titles since 1999 compared with an expected 4.50 titles. He has excelled at Wimbledon with an additional 3.50 titles than could have been expected using Elo ratings—one of the most reliable methods for predicting elite match results.

Interestingly, all of the ‘Big Four’ (Federer, Nadal, Djokovic and Murray) and Sampras have gathered more titles than expected by our simulations. Does this hint at an additional ‘champion’ performance factor displayed by all of these great players?1

It’s unsurprising that Ivanisevic had a low title probability in 2001—his win as a wild card could not have been expected by anyone!

## Which of Federer’s titles was the most impressive?

Federer’s 8 titles clearly outperforms even his own high levels on grass. Can we use the data to judge which title was his most impressive?

### Title probabilities

By looking at the individual years in our tournament simulations, we can pull out Federer’s title probability for each year. Based on these probabilities, Federer’s debut title in 2003 was the most impressive as he started the tournament with only a 9% probability of the title. This compares with a peak of 53% in his 2007 championship year. In 2003, he was third favourite behind previous winners Hewitt and Agassi, and our Elo ratings made him the underdog in his quarter- and semi-finals (against Sjeng Schalken and Andy Roddick) and only marginal favourite in the final (against Mark Philippoussis).

### Opponent strength

These title probabilities take into account Federer’s level through his own Elo rating at the time. But we could also judge his most impressive title purely by the quality of his opposition, by looking at their Elo ratings. This throws other years into the mix for consideration:

Highest rated opponent: 2005

When Federer faced Andy Roddick in the 2005 final, Roddick’s grass-weighted Elo was 2178 - the highest rated opponent Federer has ever faced at Wimbledon.

Highest average opponent rating: 2006

Looking across all seven rounds, 2006 could be considered his toughest overall with the highest mean opponent rating. This was mainly due to a tough early draw—he faced Richard Gasquet and Tim Henman in first 2 rounds.

Highest rated back-to-back opponents: 2012

In 2012, Federer dispatched Novak Djokovic in the semi-final and broke British fans' hearts in the final by beating Andy Murray. It’s difficult to think of a harder last two rounds, reflected in Djokovic’s and Murray’s Elo ratings—the 3rd and 4th highest faced by Federer at Wimbledon.

Top rated opponents

Opponent Match Opponent Elo Federer’s Elo
Andy Roddick 2005 Final 2178 2210
Andy Roddick 2004 Final 2112 2139
Andy Murray 2012 Final 2101 2231
Novak Djokovic 2012 Semi-final 2092 2218
Andy Roddick 2009 Final 2087 2307

### Title number 9?

As we can see, it’s hard to pick between Federer’s 8 Wimbledon titles. So it’s up to Federer fans to decide which is their personal favourite. With this year’s Wimbledon just days away and the number 1 seeding his again, can Roger make the selection harder by adding another title to his haul?

1. Perhaps the greatest example of a champion performing above expectation is Rafael Nadal at Roland Garros. Simulating all the French Open Men’s Singles draws since Nadal’s debut in 2005 gave Nadal an expected 4.5 titles. Compared with his incredible 11 actual titles, that’s more than 6.5 titles above expectation. ↩︎