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.

Advertisement

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:

1. 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.

2. 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:

1. 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”.

2. 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.
3. 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”.
4. 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.)

5. 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.)

Interesting sports events

There have been a few recent sports events that have been more interesting to me outside of sports than within:

Firstly, the European Championships in handball: During the time when I was the most interested in sports (late teens or so), Sweden was one of the world’s leading handball nations, often dueling it out with Russia. These days are long gone, and the world has changed sufficiently that Sweden’s smaller neighbor Denmark, an absolute nobody back then, is the reigning Olympic champion—something that teenage me would likely have considered an absurdity, even an insult, seeing that Sweden has racked up four silver medals without ever reaching the gold.

In the first game of the European Championships came the ultimate blow: A humiliating loss against dwarf country Iceland… I wrote off the rest of the Championship, reflecting on how sadly similar things had happened in tennis and table tennis, and noting how well this matched some of my thoughts on how short-lived traditions actually often are and how the world can change from what we know in our formative days. (Cf. my Christmas post.)

Today, Sweden played in the final of the same Championships against Spain, even having a half-time lead and an apparent good chance at victory. (Before, regrettably, losing badly in the second half. Still, a silver is far beyond what seemed possible after the Iceland game and a very positive sign for the future.) The road there was very odd, including the paradox of an extremely narrow semi-final win over Denmark, the aforementioned Olympic Champions, and another embarrassing and unnecessary loss against a smaller neighbor in Norway. Funny thing, sports.

Secondly, the immensity of Roger Federer’s 20th Grand-Slam title. A year ago, he and Nadal met up in the final of the Australian Open for what seemed like their last big hurrah—one of them was going to get a last title before age or injuries ended their competitive careers. Since Federer’s narrow win, we have seen another four Grand-Slam tournaments—with the winners Nadal, Federer, Nadal, and (with this year’s Australian Open) Federer. Indeed, where a year ago I was thrilled over the (presumed) last win, I was now slightly annoyed that Federer narrowly* missed going through the tournament without a loss of set. This is a very good illustration of how humans tend never to be satisfied, to ever want more or better**, and of how our baseline for comparisons can change.

*He entered the final without a lost set, won sets one and three, and only missed the second in a tie break. One or two points more and he would have had it. Such a result is extremely rare. (The oddity of 2017 notwithstanding, where it actually happened twice, making the year the more remarkable: Nadal in the French Open and Federer a few weeks later in Wimbledon.)

**Whether this is a good or bad thing will depend on the circumstances and on whether this tendency leaves us unhappy or not. At any rate, humanity would hardly have gotten to where it is without this drive.

An interesting lesson is the importance of adapting to new circumstances: Apparently, Federer has spent considerable time modifying his approach* to tennis in order to remain reasonably healthy and competitive even at his ancient-by-tennis-standards age of 36. Those who stand still fall behind (generally) and we all do well to adapt to counter aging (specifically).

*In a number of areas including style of play, racket size, and yearly schedule.