Grand Slam Scores 2: The other weighting option

We’ve previously introduced Grand Slam scores as a simple-yet-effective method for evaluating players through tennis history through a lens that conventional wisdom can understand. The initial method used was to award 1 point for a title, and split that in half for each round further from the title that the player was eliminated. While that’s a mathematically satisfying way of handling things, there’s no reason to insist on it as the only possibility. And as it happens, there’s a readily-available alternative, one that’s already in use in a well-known venue.

Here are the proposed weights, as compared to those of the odds-based method:

Round	Alt Weight	Odds Weight	Difference
R128	.005	.0078125	-.0028125
R64	.0225	.015625	+.006875
R32	.045	.03125	+.01375
R16	.09	.0625	+.0275
Q	.18	.125	+.055
S	.36	.25	+.11
F	.6	.5	+.1
W	1.0	1.0	0

In simple terms, the proposed weightings value a final at 60% of a title, and a semi at 60% of a final, as opposed to 50%. From there, the values are reduced by 50% in each round until you get back to a first-round loss, which is cut down significantly.

There is less inherent sensibility to these numbers, but they aren’t my own arbitrary invention either; they originate from the way the ATP rankings award points for Grand Slams. (Just multiply each entry by 2000 and you get the value of each round.) And they have the benefit of putting somewhat less weight on titles above all else, while simultaneously downgrading first-round losses in comparison to every other result.

So let’s see what happens to the overall rankings when examined through the same lens as the world rankings, as compared to the one through which we’ve already looked:

1. Roger Federer 27.97 (Also first in the odds-based system)

Given that he was clear of the next-best score under the first system by over 30%, it’s not too shocking to see him stay in the top spot. I suspect he’ll be there no matter how you look at it – at least in terms of career totals.

2. Jimmy Connors 20.25 (6th in the odds method)

3. Pete Sampras 20.19 (2t)

4. Roy Emerson 20.00 (4)

5. Rafael Nadal 19.99 (2t)

6. Ivan Lendl 19.95 (5)

All right, can I just say how much I like this group? It is so tightly packed that if Nadal makes the semis in Australia, he’ll jump from fifth to second (in fact, his first round win will have pushed him past Emerson once it’s entered). Not only that, it features players whose careers were focused in the 1960s, ‘70s, ‘80s, ‘90s, and 2000s, which is historically pleasing.

Analytically, you can also see the obvious change from the last option, as Connors jumps from sixth to second and Nadal falls from second to fifth. You may recall that Nadal’s Slam career has been title-heavy, while Connors complements his wins with a huge number of finals and semis. Let’s see how that change affects things further down the list…

7. Andre Agassi 18.84 (7)

8. Ken Rosewall 17.64 (8)

9. Rod Laver 16.46 (9)

10. Novak Djokovic 16.30 (11)

11. Bjorn Borg 15.51 (10)

Yeah, career-focused measures are not Borg’s closest friends. They do seem more fond of Djokovic, however, as he’ll pass Laver if he makes the quarters in Melbourne, and he’s lasted at least that long in 22 consecutive Slams.

12. John McEnroe 14.38 (12)

13. Stefan Edberg 14.26 (14)

14. John Newcombe 14.12 (13)

15. Boris Becker 13.26 (15)

16. Mats Wilander 12.53 (16)

17. Guillermo Vilas 10.32 (17)

18. Arthur Ashe 9.96 (18)

19. Andy Murray 9.54 (20)

20. Jim Courier 8.99 (19)

21. Tony Roche 8.79 (21)

This group predominantly stays the same, with only a couple of exceptions – most notably in the person of Andy Murray. Just like Djokovic, Murray does a bit better here – which makes sense, because both of them have made a lot of semis and finals. And they’ve lost in those rounds because of the guys they’ve had to play there (including each other). This system puts a bit more weight on consistently deep runs than on a couple of titles that may have come against weaker fields (especially if they’re won by someone who doesn’t make those consistently deep runs in other events). That’s one of the things I like about it.

22. Lleyton Hewitt 7.92 (22)

23. Andy Roddick 7.85 (23)

24. Michael Chang 6.60 (26)

25. Ilie Nastase 6.38 (25)

26. Jan Kodes 6.30 (24)

27. Goran Ivanisevic 6.27 (27)

28. Stan Smith 6.02 (28)

29. Marat Safin 5.87 (29)

30. Yevgeny Kafelnikov 5.83 (30)

31. Vitas Gerulaitis 5.46 (32)

Now here we have some movement. Chang, winner of only one Slam, flies past Nastase (2) and Kodes (3). And a bit further down the list, Vitas Gerulaitis also advances past a close competitor, who we’ll see shortly…

32. David Ferrer 5.46 (36)

33. Patrick Rafter 5.26 (31)

34. Juan Carlos Ferrero 5.19 (35)

35. Johan Kriek 5.07 (33)

36. Roscoe Tanner 4.95 (37)

37. Todd Martin 4.78 (41)

38. Michael Stich 4.77 (38)

39. Gustavo Kuerten 4.56 (34)

More shifting around here, of the same type. Two-time Australian Open champion Kriek and two-time US Open champion Rafter slide, while second-best-non-Slam winner Martin climbs. But the biggest climber and tumbler, respectively, deserve a bit more attention, and we’ll give that to them in a moment.

In the interest of vastly oversimplifying things, these two sets of coefficients seem to present us with a variation on the classic sports analysis debate: Peak or career? That debate can probably be encapsulated in the persons of the biggest riser and faller from the last group: Gustavo Kuerten and David Ferrer.

The decision between the two players seems obvious; Kuerten not only won three Slams to Ferrer’s none (so far), but also held the top spot in the rankings for a full year, while Ferrer has never ascended past #3.

On the other hand, Ferrer has made six Slam semis to date, while Kuerten never made one outside of the three he won. He’s also nearly doubled Kuerten’s total in quarterfinals (15-8), and has more than doubled him in R16 appearances (23-11). Ferrer also has an extra 250 wins on tour (608-358 as of his first-rounder this week), which is no small advantage; if he lasts a few more years, he could double Kuerten’s total there as well.

If you look at the ATP rankings, the story is much the same. Kuerten placed in three consecutive year-end Top 5’s from 1999-2001 (5, 1, and 2, respectively); his next-best efforts were 14 (1997), 16 (2003), and 23 (1998). Ferrer, meanwhile, has finishes of 3 (2013), 5 (2007, 2011, 2012), 7 (2010), 10 (2014), 12 (2008), 14 (2005, 2006), and 17 (2009); despite the lower peak, he has more top-5 finishes than Kuerten, and twice as many years in both the top 10 and top 20 (and counting, possibly).

So who’s better? Really, as it usually does in peak-vs.-career arguments, it comes down to personal preference. Conventional wisdom is likely to lean in Kuerten’s favor; I would tend to go the other direction. But either way, it’s a fun discussion to have, and providing another way to look at this kind of debate is one of the best uses for a metric of this type.

Just as I prefer Ferrer to Kuerten, I also prefer the results of the rankings-based weights for Slam scores, rather than the odds-based alternative. The next few posts, however, will still focus on the odds-based method, partly because it remains more mathematically compelling, and partly because I have over 170 Excel worksheets that would have to have formulas replaced in order to switch versions. Moreover, the effect of the change would be minimal for the topics I'm moving toward next: Slam-by-Slam breakdowns and scores per Slam played.