Methodology follows the first table.
GOAT list - all surfaces (active players are highlighted in green):
Methodology:
The focus was to try and be as objective as humanly possible.
1. Screening: only players who have won at least 1 grand slam, or 1 Masters 10000, an ATP finals title, or an Olympic Gold Medal are screened in.
2. Criteria were decided such that they were 1) generally recognized as important records, and 2) unambiguously positive/good (example: number of weeks in 2nd place doesn't count as unambiguously good, because 2nd place isn't as good as first), 3) not too nichey (number of slams won without losing a set is somewhat nichey), 4) not based on timing at all (e.g. no number of consecutive titles, or CYGS) and 5) in the Open Era.
3. Two lists are compiled with all the criteria, and each player's score.
4. There are 5 GOAT lists (a total one, and one for each surface, as well as one BOAT list:
GOAT lists: The first list, which I am calling the "GOAT" list, measures players' greatness mostly based on their achievements, putting a lot of weight on Grand Slams and other big titles. This is done by surface - so there are 5 of these lists. There is one overall list, and one for each surface (hard courts, clay, grass, and carpet)
BOAT list: The aim is measure who the best player of all time was. Compared with the GOAT list, the BOAT list puts far less emphasis on achievements, and more on statistics. Here, I use Principal Component Analysis (PCA) to compute a score for each player. The theory here is that the first principal component captures the biggest common factor that makes a player excel in all the criteria.
Criteria for GOAT list:
Number of Grand Slams: 50 points
Number of World Tour Finals: 25 points
Number of Olympic Gold Medals: 25 points
Number of Masters 1000: 10 points
Number of ATP 500 tournaments: 4 points
Number of ATP 250 tournaments: 2 points
Peak Elo rating: 50 points per every standard deviation above the minimum (approximately 50 GOAT points per 135 Elo ranking points above the minimum of 1910)
Winning percentage in Grand Slams: 50 points per standard deviation above the minimum
Winning percentage against Top 5 players: 50 points per standard deviation above the minimum
Total weeks at Number 1: 1 point per week
Number 1 bonus: 50 bonus points to any player who has ever been Number 1
PS: note that for the lists by surface, there are a couple of methodological differences compared with the overall GOAT list. First, there are no ATP rankings by surface, so to compute the weeks at number 1 by surface, I use the Elo rankings provided by Ultimate Tennis Statistics - Rankings Table. The second difference is that instead of using the winning percentage in Grand Slams, I use the winning percentage in Big Titles - that's mainly because the Carpet surface never had a Grand Slam, so I wanted to keep things consistent.
Here are the tables by surface:
HARD COURT GOAT:
CLAY COURT GOAT:
GRASS COURT GOAT:
CARPET COURT GOAT:
And now for the BOAT list,
Criteria:
Number of Big titles (GS, WTF, Masters, Olympic Golds)
Peak Elo rating
Winning percentage in Grand Slams
Winning percentage against Top 5 players
A very interesting compilation of lists, nice work, given the limitations of working in the open era of course its hard to judge where Laver, Rosewall etc. truly sit unfortunately.
My criteria is that to be on the list, you have to win a big title (Grand Slam, Masters, Olympic gold, or ATP finals), and he just hasn't won a big title on clay yet. Probably next year...
But I agree he deserves to be on the list and is already much better than many players that are on it.
I do appreciate the hard work behind statistics of this sort. With that said, I do have complaints. As for the ranking by surface, well, that is okay if not perfect, so I'll concentrate on the ranking system for all surfaces - the so-called BOAT list.
The readers of MTF are wise to assume that anyone posting regarding such a subject has an agenda. In my case, I might be a hidden Federer-tard or Nadal-tard being displeased with Djokovic occupying the top spot. I don't think I can prevent anyone from having such a belief, but let me say this: When all is said and done, I would not be surprised if Djokovic's claim to GOAT-hood is more persuasive than that of Nadal and/or Federer. Even as of today, a case can be made that the Serb is the best of the three, although I wouldn't go so far myself. However, I'm not here to argue who is the GOAT (or BOAT for that matter), rather my point is that the all-surface list is not based on very relevant statistics.
So, what is the problem with the all-surface list? Well, I don't have all day, so I'll just point out some of the more obvious problems:
1) The title-count only focuses on "big titles" for the all-surface list. When doing the surface ranking, the OP realizes not all big titles are equal. In the surface rankings, the slams give 330, the WTF 160, and the masters 65 points. These exact point values can be debated, of course, but in any case, slam titles should be weighted well above masters and WTF.
2) The huge weight that is given to "Peak ELO", where Nole crushes his big three fellows. Okay, but what is wrong with this? Why shouldn't Nole be given due credit for soundly beating his rivals? Well, to some extent he should, of course, since he did earn the Nole slam fair and square (I think it is safe to assume that it was during this period Nole got his "peak ELO"). However, we are trying to evaluate whole careers against each other. Giving huge weight to something like "peak ELO" is strange, for at least two reasons. Firstly, it measures the relative strength between players during a short period of time, when it is the whole careers we are trying to measure. Secondly, you get a high ELO rating as much due to your own strength as due to the weaknesses of your main opponents. To me, Nole was more impressive in 2011, when he defeated really strong versions of Nadal and Federer, than he was during 2015-2016 when his "peak ELO" was generated.
3) The only column where slams are given extra weight (compared to masters and WTF) is the "slam win percentage". This is a really strange way to measure things. To see this, let's look at an example: Let's say that Federer struggles for much of 2020; lose in the second round in AO, the first round in RG, and the third round in Wimbledon. Some say age has finally caught up with him, others think he struggles with injury. It does not really matter, because Federer gets to triumph Sampras-style by winning USO in his last ever tournament. That would be somewhat of a fairy-tale-end for Federer. I think everyone would be hugely impressed by him winning USO at such an old age. Even some of Federer's detractors would grudgingly agree that he has improved his case as a GOAT-contender this way. Now let us see how such an imaginary turn of events would affect the all-surface list: Well, to start with, Federer would get one more big title (the same as if he had won Miami instead) and improve slightly in the first column. However, looking at the whole of 2020, the slam statistics would be worse than at the start of the year. With three losses and ten wins, the win percentage would be 77 % for 2020, lowering the previous value of 86 % somewhat. One of Federer's most triumphant years would be viewed as more of a setback when this list is compiled, and the old man would have been better off had he retired at the end of 2019. This argument has nothing to do with Federer specifically, and similar examples could have been made for Nole, Rafa or anyone else.
Conclusion: Well, as Mark Twain famously said: There is lies, damned lies, and statistics.
I do appreciate the hard work behind statistics of this sort. With that said, I do have complaints. As for the ranking by surface, well, that is okay if not perfect, so I'll concentrate on the ranking system for all surfaces - the so-called BOAT list.
The readers of MTF are wise to assume that anyone posting regarding such a subject has an agenda. In my case, I might be a hidden Federer-tard or Nadal-tard being displeased with Djokovic occupying the top spot. I don't think I can prevent anyone from having such a belief, but let me say this: When all is said and done, I would not be surprised if Djokovic's claim to GOAT-hood is more persuasive than that of Nadal and/or Federer. Even as of today, a case can be made that the Serb is the best of the three, although I wouldn't go so far myself. However, I'm not here to argue who is the GOAT (or BOAT for that matter), rather my point is that the all-surface list is not based on very relevant statistics.
So, what is the problem with the all-surface list? Well, I don't have all day, so I'll just point out some of the more obvious problems:
1) The title-count only focuses on "big titles" for the all-surface list. When doing the surface ranking, the OP realizes not all big titles are equal. In the surface rankings, the slams give 330, the WTF 160, and the masters 65 points. These exact point values can be debated, of course, but in any case, slam titles should be weighted well above masters and WTF.
2) The huge weight that is given to "Peak ELO", where Nole crushes his big three fellows. Okay, but what is wrong with this? Why shouldn't Nole be given due credit for soundly beating his rivals? Well, to some extent he should, of course, since he did earn the Nole slam fair and square (I think it is safe to assume that it was during this period Nole got his "peak ELO"). However, we are trying to evaluate whole careers against each other. Giving huge weight to something like "peak ELO" is strange, for at least two reasons. Firstly, it measures the relative strength between players during a short period of time, when it is the whole careers we are trying to measure. Secondly, you get a high ELO rating as much due to your own strength as due to the weaknesses of your main opponents. To me, Nole was more impressive in 2011, when he defeated really strong versions of Nadal and Federer, than he was during 2015-2016 when his "peak ELO" was generated.
3) The only column where slams are given extra weight (compared to masters and WTF) is the "slam win percentage". This is a really strange way to measure things. To see this, let's look at an example: Let's say that Federer struggles for much of 2020; lose in the second round in AO, the first round in RG, and the third round in Wimbledon. Some say age has finally caught up with him, others think he struggles with injury. It does not really matter, because Federer gets to triumph Sampras-style by winning USO in his last ever tournament. That would be somewhat of a fairy-tale-end for Federer. I think everyone would be hugely impressed by him winning USO at such an old age. Even some of Federer's detractors would grudgingly agree that he has improved his case as a GOAT-contender this way. Now let us see how such an imaginary turn of events would affect the all-surface list: Well, to start with, Federer would get one more big title (the same as if he had won Miami instead) and improve slightly in the first column. However, looking at the whole of 2020, the slam statistics would be worse than at the start of the year. With three losses and ten wins, the win percentage would be 77 % for 2020, lowering the previous value of 86 % somewhat. One of Federer's most triumphant years would be viewed as more of a setback when this list is compiled, and the old man would have been better off had he retired at the end of 2019. This argument has nothing to do with Federer specifically, and similar examples could have been made for Nole, Rafa or anyone else.
Conclusion: Well, as Mark Twain famously said: There is lies, damned lies, and statistics.
Hi @Henrik, thanks very much for the detailed feedback. I just saw your post, and wanted to clarify some things.
First, note that there are two, not just one, all-surface lists. The very first list (GOAT) as well as the second one you focused on (BOAT). I think the GOAT list already addresses most of your concerns, so I'm just pointing it out in case you haven't noticed it. That said, I'll comment on your points:
1) The title-count only focuses on "big titles" for the all-surface list. When doing the surface ranking, the OP realizes not all big titles are equal. In the surface rankings, the slams give 330, the WTF 160, and the masters 65 points. These exact point values can be debated, of course, but in any case, slam titles should be weighted well above masters and WTF.
Sorry to repeat myself a bit here, but keep in mind the first list does put far more weight on slams, and it is also an all-surface list. In that list, slams are given 50, WTF 25, Masters 10, etc...
But to focus on the BOAT list now, the thinking behind it was that winning Masters 1000 tournaments is extremely difficult. As mandatory tournaments, all top players usually participate. And although winning them is not as prestigious as a Slam, I thought it would be fair game to count them when measuring how good a player is. Winning a Masters won't make you as "great" as a winning a Slam does, but it's a useful measure to include when evaluating skill. Besides, the point of the BOAT list was to get a different take on what you'd see in the GOAT list. If they had the same weights, they would give the same result, and there wouldn't be a point to having two of them.
2) The huge weight that is given to "Peak ELO", where Nole crushes his big three fellows. Okay, but what is wrong with this? Why shouldn't Nole be given due credit for soundly beating his rivals? Well, to some extent he should, of course, since he did earn the Nole slam fair and square (I think it is safe to assume that it was during this period Nole got his "peak ELO"). However, we are trying to evaluate whole careers against each other. Giving huge weight to something like "peak ELO" is strange, for at least two reasons. Firstly, it measures the relative strength between players during a short period of time, when it is the whole careers we are trying to measure. Secondly, you get a high ELO rating as much due to your own strength as due to the weaknesses of your main opponents. To me, Nole was more impressive in 2011, when he defeated really strong versions of Nadal and Federer, than he was during 2015-2016 when his "peak ELO" was generated.
You're right that Peak Elo does not measure success over the entire career. However, that was also kind of the point: while the Big titles and other measures are there to measure success over the entire career, the Peak Elo rating's intended purpose is to measure how dominant a player was at his peak. I wouldn't call it a measure over "a short period of time" - it takes a long time to build a high Elo rating - especially once you reach 2,300 or so, it becomes incredibly difficult to build it up, so it does take time. This is partly why Djokovic reached his peak Elo I 2015-16, rather than 2011 - he was starting off from a more modest base, and it took him time to get to the peak.
I agree the measure has its shortcomings like any other, and perhaps it could be given less weight, but I think it's still very useful, especially as a BOAT criterion.
3) The only column where slams are given extra weight (compared to masters and WTF) is the "slam win percentage". This is a really strange way to measure things. To see this, let's look at an example: Let's say that Federer struggles for much of 2020; lose in the second round in AO, the first round in RG, and the third round in Wimbledon. Some say age has finally caught up with him, others think he struggles with injury. It does not really matter, because Federer gets to triumph Sampras-style by winning USO in his last ever tournament. That would be somewhat of a fairy-tale-end for Federer. I think everyone would be hugely impressed by him winning USO at such an old age. Even some of Federer's detractors would grudgingly agree that he has improved his case as a GOAT-contender this way. Now let us see how such an imaginary turn of events would affect the all-surface list: Well, to start with, Federer would get one more big title (the same as if he had won Miami instead) and improve slightly in the first column. However, looking at the whole of 2020, the slam statistics would be worse than at the start of the year. With three losses and ten wins, the win percentage would be 77 % for 2020, lowering the previous value of 86 % somewhat. One of Federer's most triumphant years would be viewed as more of a setback when this list is compiled, and the old man would have been better off had he retired at the end of 2019. This argument has nothing to do with Federer specifically, and similar examples could have been made for Nole, Rafa or anyone else.
You have a good point, and I did think of that issue when I was compiling the list and the criteria. But here are my counterarguments:
1. Federer has been playing for an incredibly long time. He has an enormous number of matches under his belt. Even losing in the first round for the next 8 slams (an unrealistic, extreme scenario) won't drop his winning percentage much.
2. Federer has in fact been boosting his Slam winning percentage well into his thirties! That's mainly because his percentage was quite low when he was young. I haven't verified this, but I believe it's the same for Djokovic and Nadal.
Conclusion: Well, as Mark Twain famously said: There is lies, damned lies, and statistics.
Your points are very good. I'm not saying they aren't - it's just that the endeavor of measuring GOATness objectively is never going to be perfect. So, we can either decide not to even bother, or we can try to make them as "least imperfect" as humanly possible, which is what I have tried to do in a way that I promise is sincere and not biased towards any player (at least not consciously).
By the way, if you can convince me of certain improvements, I would be more than happy to implement them.
For example, in my original thread, one poster successfully convinced me to change the weights I had on Olympic Gold.
Hi @Henrik, thanks very much for the detailed feedback. I just saw your post, and wanted to clarify some things.
First, note that there are two, not just one, all-surface lists. The very first list (GOAT) as well as the second one you focused on (BOAT). I think the GOAT list already addresses most of your concerns, so I'm just pointing it out in case you haven't noticed it. That said, I'll comment on your points:
Yeah, I actually discovered that there were two lists not too long after I wrote the post. I felt a bit embarrassed to write such a long reply without noting this fundamental fact, but I did not have the energy to correct my earlier post. To avoid being too wordy this time, I'll just say, keep up the good work.
i.e. Federer has made 4 RG finals more, 6 RG semis more, 9 RG quarters more and 9 masters finals more, & counting.
While Federer was making slam & masters finals on clay, grass & hard courts (6 RG losses to Nadal, 4 finals + 2 semis), Muster was skipping them or losing in 1R/2R to earn points at depleted clay 250 events.
We're into the quarterfinals at the Australian Open so it's time for classic MTF prediction threads. You can list your top three dream finals and then list the three finals that you think are the most likely to happen.
Dream finals
1) (1) Nadal def. (2) Djokovic 3-6, 7-6, 2-6, 6-2, 7-6(10-8)...
I cant believe what Im witnessing here. Lets first start of with cheating or unsportmanship, whatever you want to call it. Tennys hits an insane return just barely on the outer line.
Federer wasnt in position or remotely close to make that return, instead of applausing that amazing return, he...
The one we've all been waiting for.
Federer's road went from:
Hurkacz-Shapovalov-Berrettini
to
Millman-Fucsovics-Sandgren
but any problem cannot be found
Didn't see the first set but in the 2nd, Rafa let go and made some errors to let Kyrg back in the match. He seized his momentum and served fantastic in the 3rd. Rafa was a bit tight, though he was efficient on serve, save for one game which went to deuce. Then a nervy TB, Kyrgios was doing what...
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