the federer bureau of investigation

A couple of thoughts after watching a bit of the men's Australian Open tennis final the other day. Firstly, I should lay my cards on the table and say that I'm delighted that Roger Federer won, as I'm a big fan and I'd like to see him stay ahead of Rafael Nadal at the head of the overall list of Grand Slam singles title winners. I have no beef with Nadal, I should add, as he is wholly admirable and gives every indication of being a lovely bloke, but it seems right to me that Federer, the best all-round tennis player I've ever seen (not that I am any kind of expert) stays at the top of the list. Even the most ardent admirer of Nadal, and there are many (including a substantial contingent of The Ladies, if you know what I mean, and doubtless a few of The Guys too), would have to admit his tennis is a bit more based on power, supreme fitness and bloody-minded persistence and perhaps doesn't have the aesthetic grace and finesse of Federer's. Plenty of overused clichés are available:  the open-topped sportscar versus the Sherman tank, the rapier versus the broadsword, the sgian-dubh versus the shillelagh, if you want something a bit more Brit-centric.

Another reason is that despite both players having achieved the career Grand Slam, Nadal's Grand Slam singles record looks a bit more uneven than Federer's as it's more skewed towards the tournament he's won the most, the French Open. Ten out of his sixteen titles were won here, compared with eight out of Federer's twenty being at Wimbledon. So it occurred to me to wonder: what if we built a list of Grand Slam winners ordered by how many singles titles they'd won that were not at their favourite event? The idea is that this would be some crude measure of their versatility across different tournaments, different surfaces, different times of year, all that stuff. So here's the starting list (shamelessly stolen from Wikipedia): everyone who's won more than five Grand Slam men's singles titles.

Player	Total	Australian Open	French Open	Wimbledon	US Open
Roger Federer	20	6	1	8	5
Rafael Nadal	16	1	10	2	3
Pete Sampras	14	2	0	7	5
Roy Emerson	12	6	2	2	2
Novak Djokovic	12	6	1	3	2
Rod Laver	11	3	2	4	2
Björn Borg	11	0	6	5	0
Bill Tilden	10	0	0	3	7
Fred Perry	8	1	1	3	3
Ken Rosewall	8	4	2	0	2
Jimmy Connors	8	1	0	2	5
Ivan Lendl	8	2	3	0	3
Andre Agassi	8	4	1	1	2
Richard Sears	7	0	0	0	7
William Renshaw	7	0	0	7	0
William Larned	7	0	0	0	7
René Lacoste	7	0	3	2	2
Henri Cochet	7	0	4	2	1
John Newcombe	7	2	0	3	2
John McEnroe	7	0	0	3	4
Mats Wilander	7	3	3	0	1
Laurence Doherty	6	0	0	5	1
Tony Wilding	6	2	0	4	0
Jack Crawford	6	4	1	1	0
Don Budge	6	1	1	2	2
Stefan Edberg	6	2	0	2	2
Boris Becker	6	2	0	3	1
Frank Sedgman	5	2	0	1	2
Tony Trabert	5	0	2	1	2

And here's the re-ordered list if you exclude the one they won the most:

Player	Favourite tournament	Number of titles	Corrected number
Roger Federer	Wimbledon	8	12
Pete Sampras	Wimbledon	7	7
Rod Laver	Wimbledon	4	7
Rafael Nadal	French Open	10	6
Novak Djokovic	Australian Open	6	6
Roy Emerson	Australian Open	6	6
Björn Borg	French Open	6	5
Fred Perry	Wim / US	3	5
Ivan Lendl	French / US	3	5
Andre Agassi	Australian Open	4	4
Ken Rosewall	Australian Open	4	4
John Newcombe	Wimbledon	3	4
Mats Wilander	Aus / French	3	4
René Lacoste	French Open	3	4
Don Budge	Wim / US	2	4
Stefan Edberg	Aus / Wim / US	2	4
Bill Tilden	US Open	7	3
Jimmy Connors	US Open	5	3
Henri Cochet	French Open	4	3
John McEnroe	US Open	4	3
Boris Becker	Wimbldeon	3	3
Frank Sedgman	Aus / US	2	3
Tony Trabert	French / US	2	3
Jack Crawford	Australian Open	4	2
Tony Wilding	Wimbledon	4	2
Laurence Doherty	Wimbledon	5	1
Richard Sears	US Open	7	0
William Larned	US Open	7	0
William Renshaw	Wimbledon	7	0

Obviously this is very satisfying to me as it places Federer head and shoulders above the others. It also shunts a lot of the oldsters down to the bottom of the list as back in the day travelling from your home country to other parts of the world was a ridiculously time-consuming undertaking and so a lot of people didn't bother. So Bill Tilden drops from 10 to 3 and the serious one-tournament wonders like Sears, Larned, and Renshaw drop to zero. It's harsh, but fair. Let's try another formula - multiply everything together! Hang on, though, anyone who hasn't done the career Grand Slam will get a product of zero; we'd better add one to everything first, just to be fair. So someone who's won all the Grand Slams once will get a Grand Slam Factor or GSF of 16, whereas someone who's won one of them four times will end up with a GSF of 5. That sounds about right; consistency and versatility is what we're trying to reward here.

Player	Total	Aus	French	Wim	US	GSF
Roger Federer	20	6	1	8	5	756
Rafael Nadal	16	1	10	2	3	264
Roy Emerson	12	6	2	2	2	189
Rod Laver	11	3	2	4	2	180
Novak Djokovic	12	6	1	3	2	168
Pete Sampras	14	2	0	7	5	144
Fred Perry	8	1	1	3	3	64
Andre Agassi	8	4	1	1	2	60
Ivan Lendl	8	2	3	0	3	48
Ken Rosewall	8	4	2	0	2	45
Björn Borg	11	0	6	5	0	42
Jimmy Connors	8	1	0	2	5	36
René Lacoste	7	0	3	2	2	36
John Newcombe	7	2	0	3	2	36
Don Budge	6	1	1	2	2	36
Bill Tilden	10	0	0	3	7	32
Mats Wilander	7	3	3	0	1	32
Henri Cochet	7	0	4	2	1	30
Stefan Edberg	6	2	0	2	2	27
Boris Becker	6	2	0	3	1	24
John McEnroe	7	0	0	3	4	20
Jack Crawford	6	4	1	1	0	20
Frank Sedgman	5	2	0	1	2	18
Tony Trabert	5	0	2	1	2	18
Tony Wilding	6	2	0	4	0	15
Laurence Doherty	6	0	0	5	1	12
Richard Sears	7	0	0	0	7	8
William Renshaw	7	0	0	7	0	8
William Larned	7	0	0	0	7	8

The biggest casualties are the two-Slam wonders Borg and Tilden, while the consistent three-Slam guys like Rosewall and Lendl get a leg-up. Once again the oldsters get shunted to the bottom of the list, but, I mean, come on, guys, make an effort - if you can't be bothered to live in the right era of history with high-speed travel and communications, not to mention sports psychologists and Lucozade, then I've no sympathy for you.

That said, I expect if you come up with some suitably contorted formula you can probably work your guy to the top of the list. There's a challenge for all you Laurence Doherty fans out there.