Using Slam Scores: Difficulty of Final

Last time out, we used Slam Scores to evaluate which players might be overrated or underrated by conventional wisdom. This time, we’ll be… doing something almost identical, actually, but in a different way. It’s easy to find the players who’ve won the most Grand Slams, but it’s rare that anyone puts systematic consideration into the question of who was beaten in the process of winning them.

So let’s find out – which players have faced the toughest slates of opponents in Grand Slam finals?

First, as always, we have to decide how we’re going to answer the question that’s being asked. The basic method I’m using is simply “average total Slam Score of opponent.”

There are any number of adjustments that could be made to this. For instance, it will disregard the obvious fact that player quality evolves over time, so playing Novak Djokovic in the final of the US Open in 2007 (as Roger Federer did) is not the same as playing Djokovic in the Wimbledon final in 2014 (which Federer also did). It will also ignore that facing Rafael Nadal in a final at the French Open is a very different proposition from playing him anywhere else (not that he's an easy task on any surface).

Leaving out those considerations will keep this from being a fully comprehensive consideration of the question at hand – but there’s still a significant amount of information to glean here, because we can still capture the basic truth that there’s a big difference between facing Federer in a Grand Slam final and facing… well, anyone else.

On that note, it’s no great surprise that the three players at the top of the list for “toughest average opponent” are the three who played Federer in their lone Slam finals: Juan Martin del Potro (2009 US Open), Fernando Gonzalez (2007 Australian), and Marcos Baghdatis (2006 Australian). Up next is Robin Soderling (faced Federer in one French Open final and Nadal in another), followed by Andy Roddick (five total finals, four of them against Federer). The theme continues with Andy Murray (eight finals – three against Federer, five against Djokovic), then finds a variation with a four-way tie between one-time finalists who faced Nadal: David Ferrer (2013 French), Tomas Berdych (2010 Wimbledon), Stan Wawrinka (2014 Australian), and Mariano Puerta (2005 French).

You can see a secondary issue coming up here, which is that one-time finalists fare unreasonably well in the rate metric. The same is true on the other side of things to an even greater extent; the bottom 28 in average difficulty of final are all players who made 3 finals or fewer. There should be a way to combine volume and rate – and there is, but we have to normalize it somehow, because just looking at “total of all final-opponent Slam Scores” is going to be ridiculous.

The answer is to compare the players’ opponents to the average Grand Slam finalist. There have been 188 Slam finals in the Open Era, and the average participant in one of those finals has gone on to amass a career Slam Score just over 11 (that is, roughly Mats Wilander quality). So the extent to which one’s average opponent exceeds 11 should be a good measure of difficulty compared to average, right?

Actually, not quite – because it fails to account for the impossibility of playing oneself in a final. Roger Federer has played in 25 Grand Slam finals – almost exactly 2 out of every 15 in the Open Era. In none of those finals has he played himself, because that is not allowed. It hardly seems fair to penalize him because his set of potential opponents is weaker than everyone else’s.

The solution is to adjust for the impossibility of a reflexive final by removing the player himself from the average to which his opponents are compared. For most people, this makes very little difference; taking the Slam score of the median finalist (Andres Gimeno) as an example, removing his two finals made and total score of 2.86 from the equation shifts the average from 11.05 all the way to… 11.10.

For the top guys, however, the change is more noteworthy. Removing Ivan Lendl’s 19 finals at a total of 17.24 drop the average from 11.05 to 10.72. Eliminating Nadal (20 finals, 18.79) lowers it to 10.62. And Federer (25, 25.34) takes it all the way down to 10.03 – a decrease that puts Federer’s slate of opponents above the average rather than below it.

I also took the extra step of calculating standard deviations from the adjusted average (compensating for the fact that the standard deviation over a larger sample will be smaller) rather than simply total distance from average, because that’s a more useful quantity. Here, then, is the final list of the players who have faced the toughest sets of Grand Slam finalists to date:

Rank	Player	Finals	Avg Opponent	Std Dev
1	Rafael Nadal	20	16.07	3.47
2	Andy Roddick	5	21.10	3.18
3	Andy Murray	8	18.91	3.14
4	Novak Djokovic	15	15.06	2.30
5	Robin Soderling	2	22.07	2.21
6 (tie)	Juan Martin del Potro Fernando Gonzalez Marcos Baghdatis	1	25.34	2.03
9	Cedric Pioline	2	18.66	1.52
10	Todd Martin	2	17.41	1.27
11	Miloslav Mecir	2	17.24	1.24
12	John McEnroe	11	13.59	1.22

Yes, I intentionally extended the list to 12 just to get McEnroe on it. As soon as Djokovic takes the court in his next Slam, McEnroe will become the best player whose average final opponent was better than him, as 9 of his 11 finals were against Lendl, Connors, or Borg.

The top 3 on this list are very far ahead of everyone else – and they’ve all had their primes within the last decade. What’s more, they’re likely to continue putting distance between themselves and the rest of the pack even if they don’t make any more finals (which two of them very well might), as many of the players they faced in their finals are still active and effective. It is a very good time to be watching Grand Slam finals.

The easiest sets of opponents in finals:

Rank	Player	Finals	Avg Opponent	Std Dev
1	Gustavo Kuerten	3	2.32	-2.17
2	Juan Carlos Ferrero	3	2.98	-2.01
3	Johan Kriek	2	1.30	-1.97
4	Jan Kodes	5	5.23	-1.88
5	Sergi Bruguera	3	4.28	-1.69
6	Alex Corretja	2	3.66	-1.50
7	Steve Denton	2	4.15	-1.40
8	Richard Krajicek	1	1.27	-1.40
9	Marin Cilic	1	1.30	-1.39
10	Gaston Gaudio	1	1.44	-1.37

There really were not a lot of excellent clay court players between, say, Lendl and Wilander in the late ‘80s and Nadal in the mid-2000’s. Or maybe it’s more correct to say that there were not many great players who were especially good on clay during those times. This isn’t the first time we’ve seen the French Open in the ‘90s and early 2000’s give several players a prominent place on an unfavorable list. Throw in the Australian Open from the ‘70s and ‘80s (Kriek and Denton faced each other in back-to-back Australian finals, and neither ever made it to another final in any Slam), and you’ve got the same result in yet another form.

The most interesting part of the bottom of the list is actually outside the bottom 10; it comes in the person of the finalist who faced the 18^th-most-clearly below average set of opponents, and the worst of anyone who played more than 5 finals. That person is Pete Sampras, whose average opponent in a final would go on to assemble a score of 8.62, 1.24 standard deviations below the expected average.

Since they’ve both won 14 Slams to date, Sampras and Nadal make a natural comparison, so let’s compare them. Sampras played in 18 finals, Nadal 20 (so far). Here is the breakdown of the seeds of their opponents in title matches:

Seed	Sampras	Nadal
1-2	4	13
3-4	6	3
5-8	2	2
9+	6	2

About 2/3 of Nadal’s foes in Slam finals have been seeded 1 or 2; Sampras faced such competition roughly a quarter of the time. Fully 80% of Nadal’s opponents were seeded in the top 4; barely half of Sampras’s were.

You can also look at most common opponents in finals. Sampras opposed Andre Agassi in five finals over the course of 12 years (going 4-1); his other multi-final rivals were Goran Ivanisevic and Cedric Pioline, occurring twice each.

The Agassi matchup is undeniably impressive, but Nadal can beat it. He has famously faced Roger Federer in eight Slam finals (6-2), and Novak Djokovic in a further seven (4-3). Fully three quarters of Nadal’s finals have come against two players who are going to end up ranked among the top 10 players of the Open Era at worst; Sampras’s best opponents after Agassi are more along the lines of Stefan Edberg and Boris Becker (once each, 1-1), who were fine players but not historic titans on the same level.

Given that Nadal’s basic level of achievement in Slams is effectively identical to Sampras’s, and further that he has reached that level against tougher competition and still has time to add to his trophy case, it seems pretty inescapable that Nadal has been the more impressive player over the course of their respective careers.