Michael Eriksson's Blog

A Swede in Germany

Tennis, numbers, and reasoning: Part II

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To continue the previous part:

There are a lot of debates on who is the GOAT—the Greatest Of All Time. While I will not try to settle that question,* I am greatly troubled by the many unsound arguments proposed, including an obsession with Grand-Slam tournaments (“majors”) won. This includes making claims like “20 > 17 > 15” (implying that Federer is greater than Nadal, who in turns is greater than Djokovic, based solely on their counts at the time of writing) and actually painting Serena** Williams (!) as the “she-GOAT”. The latter points to an additional problem, as might the original great acclaims for Sampras, namely a tendency to value “local heroes” more highly than foreigners.***

*But I state for the record that I would currently order the “Big Three” Federer > Djokovic > Nadal (for a motivation, see parts of the below); probably have Djokovic > Sampras > Nadal; and express great doubts about any GOAT discussion that ignores the likes of Borg, Laver, Gonzales, Tilden. I would also have at least Graf > Serena (see excursion), Court > Serena, Navratilova > Serena.

**To avoid confusion with her sister Venus (another highly successful tennis player), I will stick with “Serena” in the rest of this text.

***Relative the country of the evaluator and not limited to the U.S. The U.S. is particularly relevant, however, for the dual reason that authorship of English-language articles, forum posts, whatnot comes from U.S. citizens disproportionately often (measured against the world population) and that U.S. ideas have a considerable secondary influence on other countries.

The fragility of majors won is obvious e.g. from comparing Borg and Sampras. Looking at the Wikipedia entries for “career statistics” (especially, the heading “Singles performance timeline”) for Borg and Sampras, we can e.g. see that Borg won 11 majors by age 25, while largely ignoring the Australian Open, and then pretty much retired*; while Sampras was at roughly** 8 at this age and only reached his eventual 14 some six years later. To use Sampras’ 14 majors as the sole argument for him being greater is misleading, because Borg might very well have won another 3 merely by participating in the Australian Open—or by prolonging his serious career for a few years more.***

*His formal retirement situation is a little vague, especially with at least one failed come back, but it is clear that he deliberately scaled back very considerably at this point.

**I have not checked exact time of birth vs. time of this-or-that tournament, because it is very secondary to my overall point. The same might apply to some other points in this text.

***There are, obviously, no guarantees. For instance, as it is claimed that Borg suffered from a burn-out, he might not have been able to perform as well for those “few years more” (and/or needed a year off to get his motivation back) and playing the Australian Open might have brought on the burn-out at an earlier stage. Then again, what if the burn-out had been postponed by someone telling Borg that “your status among the all-time greats will be determined by whether you have more or less than 14 majors”…

More generally, the Australian Open was considerably less prestigious than the other majors until at least the 1980s, and many others, e.g. Jimmy Connors, often chose to skip it. The 1970s saw other problems, including various boycotts and bans (Connors, e.g., missed a number of French Opens).

Before 1968, the beginning of the “open era”, we have other problems, including the split into amateur and professional tennis, which (a) led to many of the leading pros having lesser counts than they could have had (Gonzales 2!!!), (b) softened the field for the amateurs, leaving some (most notably Emerson) with a likely exaggerated count.

On the other end, we have to look at questions like length of career vs. number of majors, with an eye on why a certain length of career was reached. Federer, for instance, has reached considerable success at an age that would have been considered almost absurd in the mid-1980s, when I first watched tennis—players were considered over the hill at twenty-five and teens like Wilander, Becker, Chang were serious threats.* Is this difference because Federer is that much of a greater player, or is the reason to be found in e.g. better medicine or different circumstances of some other type? Without at least some attempt at answering that question, a comparison of e.g. Wilander and Nadal would be flawed**: Both won three majors in their respective best years (1988, 2010) around age 24. Wilander never won another and ended with 7; Nadal was a bit ahead at 9 already, but has since added another 8***!

*Interestingly, I do recall that there was some puzzlement as to why tennis was suddenly dominated by people so young, when it used to be an “old” man’s sport. Today, we have the opposite situation.

**From a “methodological” point of view. It is not a given that the eventual conclusion would be different, because it is possible to be right for the wrong reason. (Certainly, in this specific constellation, the question is not so much whether Wilander trails Nadal, as by what distance. Is 17–7 a fair quantification or would e.g. 17–13 be closer to the truth?)

***This is written shortly before the 2019 French Open final, which might see yet another added. If so, fully half (and counting…) of his tally came after the age when Wilander dropped out of sight.

Or how about the claimed “surface homogenization”, i.e. that the different surfaces (grass/hard court/clay) play more similarly to each other than in e.g. the 1990s? Is it possible that the Big Three would have been less able to rack up major* wins, with more diverse surfaces? Vice versa, should some of the tallies of old be discounted for being played on fewer surfaces? (Notably, grass was once clearly dominant.)

*Looking past the majors, we can also note the almost complete disappearance of carpet.

Then there is the question of competition faced. For instance, with an eye on the dominance of the Big Three, is Wilander–Nadal a reasonable comparison, or would e.g. Wilander–Murray or Wilander-Wawrinka be more reasonable? Who is to say that Wilander would have got past 3 majors or that Murray/Wawrinka would have been stuck at 3, had their respective competition been switched? What if the removal of just one of the Big Three had given the remaining two another five majors each? (While the removal of some past great would have given his main competitors two each?) The unknowns and the guesswork needed make the comparison next to impossible when two players were not contemporaries.

For that matter, below a certain number of majors won, the sheer involvement of chance makes the measure useless. Comparing Federer and Sampras might be somewhat justified, because they both have a sufficiently large number of wins that the effects of good and bad luck are somewhat neutralized (“you win some; you lose some”)—but why should Johansson (1 major) be considered greater than Rios (none)? (Note that Rios was briefly ranked number one, while Johansson was never even close to that achievement.) How many seriously consider Wawrinka the equal of Murray (both at 3)?

Many other measures are similarly flawed. So what if Nadal has more “masters” wins than Connors? Today, these tournaments are quasi-mandatory for the top players, while they were optional or even non-existent during Connors’ career. Many of the top players of the past simply had no reason (or opportunity) to play them sufficiently often to rack up a number that is competitive by today’s standards. (But, as a counter-point, those who did play them might have had an easier time than current players due to lesser competition.)

Tournament wins (in general) will tend to favor the players of the past unduly, because many tournaments were smaller and (so I am told) the less physical tennis of yore made it possible to play more often—and not having to compete in e.g. the masters allowed top players to gobble up easy wins in weaker competition.

Looking at single measures, I would consider world ranking the least weak, especially weeks at number one. (But I reject the arbitrary “year end” count as too dependent on luck and not comparable to e.g. winning a Formula One season or to the number-one-of-the-year designations preceding the weekly rankings.) However, even this measure is not perfect. For instance, Nadal trails Lendl in weeks at number one, but has a clear advantage in terms of weeks on number two—usually (always?) behind Federer or Djokovic. Should Lendl truly be given the nod? Borg often trailed Connors in the (computerized) world ranking while being considered the true number one by many experts; similarly, many saw Federer as the true number one over Nadal for stretches of 2017 and 2018 when Nadal was officially ahead. Go back sufficiently long (1973?) and there was no weekly ranking at all.

The best way to proceed is almost certainly to try to make a judgment over an aggregate of many different measures, including majors won, ranking achievements, perceived dominance, length of career, … (And, yes, the task is near impossible.) For instance, look at the Wikipedia page on open era records in men’s singles* and note how often Federer appears, how often he is the number one of a list, how often he is one of the top few, and how rarely his name does not appear in a significant list. That is a much stronger argument for his being the GOAT than “20 majors”. Similarly, it gives a decent argument for the Big Three being the top three of the open era; similarly, it explains** why I would tend to view Djokovic as ahead of Nadal, and why I see it as more likely that Djokovic overtakes Federer than that Nadal does (in my estimate, not necessarily in e.g. the “has more majors” sense).

*A page with all-time records is available. While it has the advantage of including older generations, the great time spans and changing circumstances make comparisons less reasonable.

**Another reason is Nadal’s relative lack of success outside of clay. He might well be the “clay-GOAT”, but he is not in the same league as some others when we look at other surfaces and he sinks back when we look at a “best major removed” comparison. For instance, if we subtract his French-Open victories, he “only” has 6 majors, while Federer (sans Wimbledon) still has 12 (!), Djokovic (sans Australian Open) has 8, and Sampras (sans Wimbledon) has 7.

Notes on sources:
For the above, I have drawn on (at least) two other Wikipedia pages, namely [1] and [2]. Note that the exact contents on Wikipedia, including page structure, can change over time, independent of future results. (That future results, e.g. a handful of major wins by Nadal, can make exact examples outdated is a given.)

Excursion on Serena vs. Graf:
Two common comparisons is Federer vs. Sampras and the roughly respective contemporaries Serena vs. Graf. If Federer is ahead of Sampras, then surely Serena is ahead of Graf? Hell no!

Firstly, if we look just at majors won (which is the typical criterion), we find that Graf hit 22 majors at age 29* and retired the same year, while Serena had 13 at a comparable age, hit 22 at age 34/35 and only reached her current (and final?) tally of 23 a year later. By all means, Serena’s longevity is to be praised, but pulling ahead by just one major over such a long time is not impressive. Had Graf taken a year off and returned, she would be very likely to have moved beyond both 22 and 23. In contrast, Federer reached (and exceeded) Sampras tally at a younger age than Sampras—and then used his longevity to extend his advantage.

*Not to mention 21 several years earlier, after which she had a few injury years.

Secondly, most other measures on the women’s open era records page put Graf ahead of Serena, including weeks at number one. This the more so, when we discount those measures where Serena’s longer career has allowed her to catch up with or only barely pass Graf.

Excursion on GOAT-but-one, GOAT-but-two, etc.:
While determining the GOAT is very hard, the situation might be even worse for the second (third, fourth, …) best of all times. A partial solution that I have played with is to determine the number one, remove his results from record (leading to e.g. a new set of winners), re-determining the number one in this alternate world, declare him the overall number two, remove his results from the record, etc. For instance, Carl Lewis is the long-jump GOAT by a near unanimous estimate, but how does e.g. Mike Powell (arguably the number two of the Lewis era) compare to greats like Jesse Owens and Ralph Boston? Bump everyone who lost to Lewis in a competition by one spot in that competition, re-make the yearly rankings without Lewis, etc., and now re-compare. While I have not performed this in detail, a reasonable case could now be made for Mike Powell as the number two of all time.

Unfortunately, this is trickier in tennis than in e.g. the long jump, because of the “duel” character of the former. For instance, if were to call Federer the GOAT and tried to bump individual players in a certain tournament won by him, would it really be fair to give the runner-up the first place? How do we now that the guy whom Federer beat in the semi-final would not have won the final? Etc. (A similar problem can occur in the long jump, e.g. in that someone who was knocked out during the U.S. Olympic trials in real life, might have done better than those who actually went, after the alternate-reality removal of a certain athlete. The problem is considerably smaller, however.)

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Written by michaeleriksson

June 9, 2019 at 12:17 am

Posted in Uncategorized

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  1. […] Two post-scripts to the previous discussions ([1], [2]): […]


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