Posts Tagged ‘GOAT’
Follow-up V: Djokovic as GOAT? (III) and COVID distortions
As I have argued repeatedly in the past (cf. [1], [2], [3], [4]), Djokovic is the true number-one player in the world, only failing to be so officially due to artificial restrictions placed upon him. Moreover, these restriction have skewed various measures of GOAT-ness, including weeks-at-number-one (his lead artificially shortened) and majors-won (temporarily trailing Nadal, when he might well have been one or a few ahead).
Looking at the official ATP rankings, Djokovic began the day with at least three artificial strikes against him: he had not been allowed to compete in the 2022 Australian Open and U.S. Open, and his victory at Wimbledon had not brought him any ranking points—a penalty of potentially 6,000 points.* With today’s final of the 2023 Australian Open, a mere one of these artificial strikes were removed, as Djokovic won—and this is still enough to allow him to return to the official number-one position on Monday (when the next official rankings are released).
*An enormous amount. Compare this with e.g. the overall numbers given in [4].
Looking at his last 12 months, he has won three out of the five largest tournaments (2023 Australian Open, 2022 Wimbledon, 2022 ATP Finals), reached the quarter-finals in one (2022 French Open),* and been artificially barred from one (2022 U.S. Open). As a comparison, this would have been a banner year even for someone like Pete Sampras and it exceeds the career best of any active player except for Djokovic, himself, and Nadal.
*Losing against eventual champion Nadal. A negative side-effect of the knock-out format is that someone unlucky enough to meet the eventual champion early might go out in a, in some sense, “too early” round, and a quarter-final is best seen as the lower limit of the accomplishment. I note that Djokovic was the defending champion and likely is the second best clay player (after Nadal) among the currently active players. (But this is the same for everyone and moves on a very different level from the other issues.)
Looking at the Australian Open, this was Djokovic’s 10th (!) victory, and it comes in a series of three straight victories (2019–2021), one missed tournament (2022), one victory (2023). Now, had Djokovic not been artificially barred in 2022, what are the chances that Nadal would still have won? That Djokovic would have won instead? This is impossible to say in detail, but giving Djokovic a better than 50% chance borders on the cautious, in light of both his success at the Australian Open and at such tournaments that he was allowed to play during the surrounding year. Nadal, then, correspondingly well below 50%, as he does not just have to fend of Djokovic but also has to consider the risk of losing against someone else as the events are reshuffled.*
*Note e.g. [5] and how strongly chance plays in for any player who is not highly dominant.
Looking at the overall majors won, Djokovic has now caught up with Nadal at 22, but should likely be a few ahead. Just turning last year’s Australian Open would make it 23 to 21; with a 22 to 21 resulting from a partial change (Nadal does not win, but neither does Djokovic). Ditto replacing a 2020 scrapped Wimbledon and a Nadal-victory in the French Open with a scrapped French Open and a Djokovic-victory in the Wimbledon. A 2022 U.S. Open victory for Djokovic would have made it 23 to 22. All taken together, 25 to 20.* (And I might well have forgotten some artificial disadvantage for Djokovic.)
*But note that the probability of all is much smaller than the probability of at least one, and that the latter is all that it takes to put Djokovic in an outright lead.
Follow-up IV: Djokovic as GOAT? (III) and COVID distortions
To further make my point from yesterday, the new ATP rankings are in.
First, to revisit an older rankings discussion, we then had a ranking that made Djokovic a strong candidate for the true number one (see there for argumentation):
The official ATP ranking currently* has a top-7 of:
*Note that this page is regularly updated. Data used represent the current state.
1 Carlos Alcaraz 6,740 2 Casper Ruud 5,850 3 Rafael Nadal 5,810 4 Daniil Medvedev 5,065 5 Alexander Zverev 5,040 6 Stefanos Tsitsipas 4,810 7 Novak Djokovic 3,570
Today, the same official ranking has a top-5 of:
| 1 | Carlos Alcaraz | 6,820 |
| 2 | Rafael Nadal | 6,020 |
| 3 | Casper Ruud | 5,820 |
| 4 | Stefanos Tsitsipas | 5,550 |
| 5 | Novak Djokovic | 4,820 |
Djokovic is now exactly 2000 points from a tied number one—and this is exactly the points that were withheld from him for his Wimbledon victory.* Alcaraz, too, has some points missing from his Wimbledon exploits, but far fewer, and even with this lone adjustment, Djokovic would be a clear number two and nabbing at Alcaraz’s heals. However, Djokovic was unfairly denied a chance at both the Australian Open and the U.S. Open, and even a very sub-par effort at even one of them would have been enough to bring him to number one.**
*Intended as a punishment of Wimbledon, not Djokovic, but he is the one who might see the largest negative effect.
**Alcaraz, in turn, missed the ATP Finals due to injury. However, injury is something relating to the player, e.g. in that a player who trains harder and plays more often has a larger injury risk (and might, therefore, have avoided the injury by earning less points in the past). Moreover, the maximum payout at the ATP Finals is 1,500 points to 2,000 for each of Djokovic’s missed majors.
Conclusion: in a fairer world, Djokovic would right here and right now be the number one on the ranking, and, as this is the final ranking of the year,* Djokovic would have just earned his 8th (!) end-of-the-year top spot, thereby extending his lead in the ATP era. (Sampras 6, Federer/Nadal/Connors all 5. Cf. Wikipedia on ATP number ones.) It would also make him highly competitive with the likes of Pancho Gonzales from the pre-ATP era.** (I caution that I, personally, do not give the end-of-the-year ranking a greater weight than the weekly ranking; however, many others consider it important—especially, for comparisons with the pre-ATP era.)
*At least in terms of top players and movements between them. There might or might not be other changes through lesser tournaments.
**Rankings from these times are often disputed and comparisons tricky.
Combine this with the artificial damage done to counts of majors-won and weeks-at-number-one, and it is clear that the last few years have been a travesty (cf. earlier texts), which makes just going by numbers impossible—but where it is to be feared that most future judges will just go by numbers.
Follow-up III: Djokovic as GOAT? (III) and COVID distortions
In the previous follow-ups (cf. [1], [2]), I noted that “The arguably best tennis player in the world, right here, right now, is Djokovic.”, with further remarks on how he was artificially disadvantaged and how he, among other consequences, might miss the ATP Finals through these artificial disadvantages.
As it happens, Djokovic just won these ATP Finals, even be it in the absence of Carlos Alcaraz, the injured number one on the world ranking, giving further support to my assessment. To wit: out of the five most important tournaments of the year, Djokovic won two (Wimbledon and the ATP Finals), lost against the eventual winner in the French Open (Nadal), and was artificially barred from both the U.S. Open and the Australian Open. In contrast, Nadal won the Australian Open and French Open, the first in the absence of Djokovic. (And flopped badly in the ATP Finals.) The sole other winner, Alcaraz had “only” the U.S. Open—again, in the absence of Djokovic.
The existence of the ATP Finals is, of course, yet another reason to discount the “majors won determines the GOAT” idea: While the relative value of the ATP Finals and the majors can be discussed back and forth, neglecting the former is silly. Looking at this year, Djokovic went undefeated* in five matches against players all in the top-9 of the world-ranking. Winning a major, seven matches against players in the top-128, or so,** is standard, and beating even one top-9 player is not a requirement—beating more than two is rare. If we look at totals of majors and ATP Finals for the “Big Three”, we find Djokovic at 21 + 6 = 27, Federer at 20 + 6 = 26, and Nadal at 22 + 0 = 22. (Yes, Nadal has never won.)
*Unlike the majors, the ATP Finals are divided into two round-robin groups, followed by semi-finals and finals. Correspondingly, it is possible to win the overall despite an imperfect record in the group phase.
**There are 128 slots for each major, but some are filled with wild cards, qualification players, and the like, that are not necessarily in the top-128 ranking-wise.
In a correction to my earlier claims: My fears that Djokovic would miss the ATP Finals were a little misguided, as there is a wild-card rule for those who have won one of the four majors during the year. Due to this rule, it would have taken a very unfortunate constellation for him to be excluded (barring more COVID-nonsense, of course).
Follow-up: Djokovic as GOAT? (III) and COVID distortions
As a follow-up to an earlier text on Djokovic and COVID distortions:
The arguably best tennis player in the world, right here, right now,* is Djokovic. He was a single match away from winning a Grand Slam in 2021 and he has lost only one match in the majors this year (and that against Nadal in the French Open).
He still is no better than 6th on the world ranking; Nadal, his long-time rival, might retake the number one position on the world ranking presently; and Nadal might outdo him 3 majors to 1 for the year by the end of the ongoing 2022 U.S. Open. (Currently, 2 to 1.) To boot, Nadal might outdo him 23 to 21 overall. (Currently, 22 to 21.)
*Time of writing: September 3rd, 2022.
What is wrong with this picture? Well, firstly, looking at this year, Djokovic has been unfairly banned from two out of four majors (Australian Open,* U.S. Open) where he would have been the favorite** (and Nadal won the Australian Open in his absence, might do the same to the U.S. Open). Secondly, Djokovic’s Wimbledon victory gave him not one single point on the ATP ranking.*** All this for reasons of politics—not tennis.
*My original text, written during this tournament, speaks of the “on-going 2022 French Open”. This should, of course, be the “on-going 2022 Australian Open”.
**Very clearly so for the Australian Open; more narrowly for the U.S. Open.
***However, as unfortunate as this is for the sport of tennis, letting Wimbledon get away with blocking Russians (individual players are not party to the war) and Belorussians (even the country is not party to the war) because of the Russian invasion of the Ukraine would be a greater evil. Also note that the Wimbledon issue has a different cause than the other problems discussed.
(I have not looked into the non-majors, but there is a possibility that Djokovic has been similarly mistreated in other tournaments too. It can certainly not be ruled out that the unnecessary chaos, stress, and lost time has negatively affected him. Moreover, there is a non-trivial risk that he will be either unfairly banned from or unfairly fail to qualify for the ATP Finals, which would ruin his ranking further.)
Looking at the overall count of majors, this is partially caused by the disparities of 2022; however, these problems began earlier: the 2020 Wimbledon, where Djokovic was a clear favorite,* was canceled, while the French Open, won by Nadal, was merely postponed.
*He had won the two previous editions—and has gone on to win the two following.
I have written in detail about why the “majors won” heuristic for GOAT-hood and player comparisons is flawed ([1]). The extreme distortions over the last few years cement this—in a slightly different reality, Nadal might have two resp. three majors less (2020 French Open, 2022 Australian Open; 2022 U.S. Open), while Djokovic might have two resp. three majors more (2020 Wimbledon, 2022 Australian Open; 2022 U.S. Open). In this alternate reality, we would then see the current 22/23 vs. 21 change to 20 vs. 23/24.*
*With other alternate realities showing numbers in between. The point is that the current 22/23 vs. 21 is a clear and artificial distortion of historical greatness through the issues of the last few years.
The much more sensible “weeks at number one” heuristic is still clearly Djokovic’s, but his number is artificially diminished,* understating how great his career has been, while Nadal’s might soon be inflated, potentially giving him an unfair leg up against the likes of Sampras, Lendl, Connors.**
*Twofold: once for the reasons discussed here, which have caused him to be out of the top position when he likely otherwise would have held it; once through an earlier rankings’ freeze, where he did lead but his lead did not count in official statistics.
**But, to avoid misunderstandings, I would tend to give Nadal the nod over these past greats in a more holistic evaluation. Even a good heuristic is still a heuristic.
Excursion on different types of distortions:
Note that these distortions are not comparable with what misfortunes might take place through sheer bad luck (tends to even out over time; you win some, you lose some) and what is rooted in the person of the player (e.g. being disqualified for yelling at an official, being injury prone). Here we have distortions imposed by others, and in a manner that systematically disadvantages one player (or one group of players) relative the other players.
And, no, the bans based on vaccination status can not be put on Djokovic with an imbecilic “He should just get the vaccine! Then he could play!”: Apart from basic human decency and the right to medical self-determination, Djokovic’s decision is perfectly rational and reasonable, and he should be lauded for standing up for what is right: he already has immunity through prior COVID, a man of his age and fitness would be at minimal risk through COVID (as would the other players), and the risks of the vaccines are not trivial for an elite athlete. (Moreover, we know by now that the risks of COVID, in general, are far smaller than were claimed in 2020, and that current strains are even less dangerous than the early ones. Many measures that might have seemed reasonable in 2020 cannot be considered so in 2022.)
Djokovic as GOAT? (III) and COVID distortions
I have repeatedly mentioned Djokovic as the potential GOAT of tennis, including in at least [1] and [2].
Last time around ([2]), I wrote that:
Should Djokovic add this [2021] year’s U.S. Open, winning the Grand Slam, this would probably close the debate for me. If he does not, I suspect that the developments over the next one or two years will leave the same conclusion. (But let us wait and see.)
While Djokovic was “only” the runner-up, I see it as time to close the books on the current* candidates: Djokovic is the GOAT of at least the Open Era.**
*What future candidates might achieve is yet to see.
**For reasons discussed in older texts, a comparison outside the Open Era is even trickier, but there are precious few candidates that are even on the table as superior, even should we drop the “Open Era” restriction.
This for two reasons:
- Djokovic has torn ahead on my main proxy criterion, weeks at number one, and has an overall record in almost any other category that matches the best of the best, including Federer.
Specifically, he now stands at a massive 356 weeks (Federer 310; no-one else above 300) and counting. This despite being shortchanged 22 weeks due to a COVID freeze.* True number, then, 378 or well over 7 (!) years. (Cf. Wikipedia.)
*At the time of other texts on the topic, I was under the impression that these weeks had counted in his favor. Note that he would almost certainly have had the same set of weeks at number one even had there been no freeze.
- The arbitrary removal of Djokovic from the on-going 2022 French Open makes any future comparison with Federer and Nadal flawed. Djokovic has now missed two majors, in which he would have been the favorite, for reasons external to him.* He has already lost the chance of taking the Grand Slam this year and he risks an unfair and premature end to his time at number one, as he has been given a severe points handicap. Unless one of the other two achieves far more than is currently likely, any edge that they might gain in some criterion (especially, majors won**) would be unfair. This especially should such a gain be made when Djokovic is unfairly absent and would have been favored to win, e.g. a gain through a Nadal*** win at the on-going French Open.
*To be contrasted with e.g. missing a major due to injury, as there is a trade off—train and compete harder and increase the injury risk or reduce the injury risk and risk less success while healthy.
**And note that the low usefulness of “majors won” was an early motivation behind my writings on tennis—even before the current situation arose.
***Federer is not participating due to an injury.
Worse, there have been rumors that Djokovic might be prevented from competing at other tournaments too, including the other majors of 2022 or some of the future Australian Open tournaments. I have yet to hear a final word on this, but it would turn a severe distortion into a catastrophic one.
Djokovic as GOAT? (II) / Follow-up: Tennis, numbers, and reasoning
As I suggested earlier this year, a strong case can be made for Djokovic as the GOAT of tennis. As he now has added another two majors, for a three-way tie with Federer and Nadal, even those obsessed with the flawed proxy of majors won (Cf. [1]) should slowly be caving.* This especially as his Wimbledon victories in 2019 and 2021 (this year) point to his being a clear favorite for 2020, had there been a tournament. In a reality just a little different, with Wimbledon postponed and the French Open canceled, Djokovic might lead 21 to 20 to 19 over Federer and Nadal.
*Except that tennis fans are often religious and might change criteria after the fact.
As to my own main proxy, weeks at number one, he has built a lead on Federer (while Nadal is not a factor) and will necessarily extend it further after his Wimbledon defense.
Moreover, as I wrote in [1]:*
*Footnotes removed for brevity.
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).
Look at the same page today, roughly two years later, and note how the distance between Federer and Djokovic has grown smaller or even reversed in various measures.
Should Djokovic add this year’s U.S. Open, winning the Grand Slam, this would probably close the debate for me. If he does not, I suspect that the developments over the next one or two years will leave the same conclusion. (But let us wait and see.)
Excursion on Federer as GOAT:
Now, if I were to argue Federer as GOAT, which is a position closer to my heart, I would probably rely on two things. Firstly, rivalries tend to favor the younger player, and will almost certainly have done so in the case of players this long-lived. This would give Federer a greater handicap from competing with the other “Big Three” than it does Djokovic and Nadal. Secondly, the great slowdown of surfaces has certainly favored the immensely strong defensive players and runners that are Djokovic and Nadal over Federer, who has a faster and more attacked based game. The downside of this argument, is that we cannot know how other players would have fared without a slowdown—and maybe all three would have seen their success diminished relative some even more attack based, and/or younger, and/or more canon-serving players. (Maybe, for instance, we would have had a four-way tie with Sampras at 14 in terms of majors won, with Sampras still leading in weeks at number one?)
Djokovic as GOAT? / Follow-up: Tennis, numbers, and reasoning
In light of Djokovic now being set to overtake Federer in weeks-at-number-one and having just taken his 18th major, while Nadal has caught up with Federer at 20, it is time to briefly revisit a text on how to determine the tennis GOAT (Part II in a series)—or rather on why doing so is next to impossible.
As this blog is closed-ish, I will not dig deep into details or re-analyze what is said in the old text, but I do note that:
- I still consider weeks-at-number-one the best of the “easy” proxies. If we apply this proxy, Djokovic would (in just a few weeks) be the GOAT (of at least the Open Era). This especially as he is a fair bit younger than Federer (and a-year-or-so* younger than Nadal).
*Here and elsewhere, note that I will not do any fact checking either. There might be minor errors here and there, but nothing that changes the “big picture”.
- I would still rate Federer’s career as the better overall, but not by that much and, again, Djokovic is the younger. Certainly, while Federer’s longevity is (was?) extreme, it appears that both Nadal and Djokovic are similar—possibly, even better.
- Federer’s dominance at his height was almost unsurpassable, and that might in the end be the strongest argument pro-Federer in a GOAT discussion and/or in a discussion of who was the best among the “Big Three”.
- Nadal’s fatal flaw remains that he has achieved too little (relatively speaking!) outside of clay and that he has mostly been second to either Federer or Djokovic at any given time. I can still see no true case for Nadal being more than the “Clay GOAT”. My old estimate of “Federer > Djokovic > Nadal” might now be “Federer = Djokovic > Nadal”, or Federer marginally ahead of Djokovic or Djokovic marginally ahead of Federer.
However, Nadal has improved in the comparison of feats that formed Part III of the aforementioned series. The comparison made there was based on 12 French-Open titles, while he now stands at 13. (On the other hand, Djokovic reaching 9 Australian Opens, at a lesser age and on a more competitive surface, weakens the accomplishment in comparison.)
- The already tricky comparisons are made trickier by the effects of COVID, which include several weakened playing fields, including for Nadal’s 13th French Open and, maybe, the current/2021 Australian Open for Djokovic; a canceled Wimbledon (Djokovic reigning champion; Federer a strong victory candidate, had he played*); and a long period where the ATP ranking** was frozen or otherwise used exceptional rules.
*Independent of the COVID issue, Federer appears to have taken portions of 2020 off for an injury break or operation or similar. I have not followed tennis in enough detail after 2019 to say for certain.
**But I suspect that Djokovic would have remained at number one even with the regular rules, and would still be set to take over in weeks-at-number-one.
Skimming through the articles of the series, I note at least one faulty math statement (others might very well be present):
In Part I, I say that “For instance, the probability that the sum of two fair and six-sided dice exceeds* seven is 5/12 a priori but 5/6 given that we already know that one of the dice came up six.”, which is correct in the first half but not in the second: I had my mind on a scenario where one die (dice?) is thrown, it comes up six, and then the other die is thrown. As the order is not specified, another view is necessary. To this, there are 11 (independent) outcomes with at least one six, viz 1–6, 2–6, …, 5–6, 6–6, 6–5, .., 6–2, 6–1. Of these, all but two (6–1, 1–6) exceed seven and the true probability, barring other errors on my behalf, should be 9/11. Looking at the difference, 9/11 – 5/6 = (54 – 55) / 66 = – 1 / 66, making the new result slightly smaller. (The difference is an implicit, faulty, double-counting of 6–6, which unlike e.g. the 5–6/6–5 pair only appears once.)
*Used in the “strictly greater” sense. Another weakness is that this formulation could be interpreted as “greater or equal”. In the latter case, both the old and the new “given that” probability is 1, as the event is unavoidable. (The probability for the first half of the statement would rise to 7/12.)
Tennis, numbers, and reasoning: Part II
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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