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El Dude

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But, again, is he "putting" them, or is he living with the results of his own formula? You keep saying he's going to "place" them, and his thesis statement says that he's, within a few points, relying on his numbers.
Without re-reading the intro, I don't know. I do remember him saying that there's a subjective element, but not sure if that's just on picking criteria and a formula.

Anyhow, I'm not saying that Serena doesn't deserve to be #1 among women...for me her, Graf, and Navratilova all have an argument, with Evert and Court just a hair behind.
 

Moxie

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As someone who has dabbled with trying to create a ranking system, one of the biggest problems is how to balance peak vs. career. Almost every system ends up making players who are good to very good for a very long time look better than players who had a higher peak but shorter prime. So in Sackmann's system we have Ferrer and Roddick ranked higher than Courier and Wawrinka, even though the latter had much higher peak levels.

I don't know Sackmann's formula, so don't know why his rankings are the way they are. But it seems clear that he balances more towards career than peak. So presumably he has some method of "accumulative Elo."
Please explain "accumulative ELO."

I know that you have worked hard at some rankings formulas, and they have been appreciated. I actually like a lot that you work with groupings, such as via era, as it's less one-to-one than a sense of like-to-like.

He's got Stan (127), with 3 Majors, below Ash Barty (101) with 3 Majors, and both below Elena Dimentieva, with no Majors (96.) 16 total titles. Why not Myskina, who at least won a Major, and is of that era. (Both now basically forgotten.) I can't even think how you could justify this based on competition. Surely, he has some formula, but every time I look at this list, it gets more opaque.
 

Moxie

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Without re-reading the intro, I don't know. I do remember him saying that there's a subjective element, but not sure if that's just on picking criteria and a formula.

Anyhow, I'm not saying that Serena doesn't deserve to be #1 among women...for me her, Graf, and Navratilova all have an argument, with Evert and Court just a hair behind.
I agree with you that Navratilova, Graf and Serena all have an argument for #1. I went in order of age. Call them a 3-headed GOAT. Which I think you have campaigned for amongst the men, and I'm down with that, certainly for this era, and for most. In order of age: Federer, Nadal and Djokovic. Now tell me, taking those 6 names, mix them up and place them in order. It's not possible. IMHO. Going back to your point earlier, he would have been better served to split the men and women, in the first place. I'll be curious where he lands, though.
 
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El Dude

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Please explain "accumulative ELO."
It isn't an official phrase, but what I mean is adding up ELO ratings for each year. So for instance, let's say one player has five years at 2000 ELO, and another four years at 2400. The former adds up to more (10,000 vs 9,600), but most would think the latter was a better player because 2400 is truly great, while 2000 is merely garden variety elite - roughly a top 10 player (e.g. Casper Ruud has a 2,012 ELO right now, 10th in the ATP).

So I'm guessing his formula adds up year end ELO then averages it with a player's best five or seven or ten seasons, or perhaps a more complex version of that.

BTW, UltimateTennisStatistics.com has ELO ratings - total weeks at #1, year-end ELO for every player, etc. Kind of fun to look at, as an alternate window into rankings.

Here's a chart with the year-end Elo Ratings of Nishikori, Wawrinka, and Ferrer. Screen Shot 2022-10-11 at 12.37.11 AM.png

Based on that, it is hard to see why Kei is ranked higher than Stan. Ferrer actually has the highest peak, but both he and Stan have significantly longer periods in the elite range, and Stan's peak is as high as Kei's. I'm actually a bit surprised Stan's isn't higher. I'm guessing that despite those three Slams, his overall performance in those years wasn't consistent enough for a higher rating. And when you add in Stan's three Slams (and one Masters), it is hard to see how he could be ranked lower - especially than Nishikori.

I know that you have worked hard at some rankings formulas, and they have been appreciated. I actually like a lot that you work with groupings, such as via era, as it's less one-to-one than a sense of like-to-like.

He's got Stan (127), with 3 Majors, below Ash Barty (101) with 3 Majors, and both below Elena Dimentieva, with no Majors (96.) 16 total titles. Why not Myskina, who at least won a Major, and is of that era. (Both now basically forgotten.) I can't even think how you could justify this based on competition. Surely, he has some formula, but every time I look at this list, it gets more opaque.
Yep. I wish he'd share his formula.
 
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El Dude

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I agree with you that Navratilova, Graf and Serena all have an argument for #1. I went in order of age. Call them a 3-headed GOAT. Which I think you have campaigned for amongst the men, and I'm down with that, certainly for this era, and for most. In order of age: Federer, Nadal and Djokovic. Now tell me, taking those 6 names, mix them up and place them in order. It's not possible. IMHO. Going back to your point earlier, he would have been better served to split the men and women, in the first place. I'll be curious where he lands, though.
As an aside, one thing that really differentiates the female 3-headed GOAT from the male is the era gap. Navratilova was born in 1956, Graf in 1969, Serena in 1981 - that's a span of 25 years, which each separated by 12 or 13 years. Now of course Martina had Evert just two years older, though Evert peaked earlier, and Steffi had Seles born four years later, but then her tragic attack shortened her peak. So they weren't just all on their lonesome without other inner circle greats - except for Serena. She played alongside a bunch of lesser greats, but no one in the same vicinity.

One thing that makes Navratilova so impressive is that despite playing most of her matches vs Graf in the latter half of her career (from 1985-94), she was still 9-9 in the H2H. Actually, Evert vs. Graf was also very close (6-7), though Evert won their first six matches and Graf their last seven. Martina and Steffi were more balanced, thought Martina won five of their first six and Steffi won 8 of their last 12.
 
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Moxie

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It isn't an official phrase, but what I mean is adding up ELO ratings for each year. So for instance, let's say one player has five years at 2000 ELO, and another four years at 2400. The former adds up to more (10,000 vs 9,600), but most would think the latter was a better player because 2400 is truly great, while 2000 is merely garden variety elite - roughly a top 10 player (e.g. Casper Ruud has a 2,012 ELO right now, 10th in the ATP).

So I'm guessing his formula adds up year end ELO then averages it with a player's best five or seven or ten seasons, or perhaps a more complex version of that.

BTW, UltimateTennisStatistics.com has ELO ratings - total weeks at #1, year-end ELO for every player, etc. Kind of fun to look at, as an alternate window into rankings.

Here's a chart with the year-end Elo Ratings of Nishikori, Wawrinka, and Ferrer. View attachment 7260

Based on that, it is hard to see why Kei is ranked higher than Stan. Ferrer actually has the highest peak, but both he and Stan have significantly longer periods in the elite range, and Stan's peak is as high as Kei's. I'm actually a bit surprised Stan's isn't higher. I'm guessing that despite those three Slams, his overall performance in those years wasn't consistent enough for a higher rating. And when you add in Stan's three Slams (and one Masters), it is hard to see how he could be ranked lower - especially than Nishikori.
That was helpful. Though I see it even confuses YOU how ol' Jeff's numbers eventually got him where they did. I'm also surprised that Ferrer has the highest peak. What does that really tell us? I'll offer this about Stan, based on memory only. He beat Rafa in the 2014 AO final. Then, at RG, on arguably his best surface, he lost in the first round. We all remember that Stan was wildly inconsistent. I always thought that Magnus Norman helped him a lot, and should get real credit for his 3 Majors. Sort of like Peter Lundgren helped tame Marat Safin long enough to get HIM one more Major. Anyway, maybe the inconsistencies account for the weird ELO rating. Ferrer was nothing if not consistent. And Kei, well, with injuries, not consistent. Still doesn't explain his ranking on this man's system. And, even if you say that there is some bell-curve involved, wouldn't you, if you were Jeff, rethink your system, if you had Stan that low, Kei so high, and Dementieva up there above Wawrinka and Barty? I would have thought: "Back to the drawing board." But no, he plowed forward. At a certain point, IMO, he's falling in love with his own formula, common sense be damned. And, yeah, whatever the formula is.
 

Moxie

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As an aside, one thing that really differentiates the female 3-headed GOAT from the male is the era gap. Navratilova was born in 1956, Graf in 1969, Serena in 1981 - that's a span of 25 years, which each separated by 12 or 13 years. Now of course Martina had Evert just two years older, though Evert peaked earlier, and Steffi had Seles born four years later, but then her tragic attack shortened her peak. So they weren't just all on their lonesome without other inner circle greats - except for Serena. She played alongside a bunch of lesser greats, but no one in the same vicinity.

One thing that makes Navratilova so impressive is that despite playing most of her matches vs Graf in the latter half of her career (from 1985-94), she was still 9-9 in the H2H. Actually, Evert vs. Graf was also very close (6-7), though Evert won their first six matches and Graf their last seven. Martina and Steffi were more balanced, thought Martina won five of their first six and Steffi won 8 of their last 12.
I don't think that does matter, if we're going to try to identify Greatest(s) of All Time. Because when we say GOAT, we are not saying "of their era," which is a distinction some would make. (Which is where I incline.) It's handy that Fedalovic happened to play in basically the same era AND eclipse most other records, but it doesn't mean that the GOAT conversation doesn't include all eras on the men's side, too. You do get credit for trying to shoehorn Laver in there, sometimes. But if there IS to be a GOAT debate, it doesn't matter that Martina, Steffi and Serena are much more from different eras. Right? Certainly this guy Jeff's accounting for greatness has no respect for era or even Open Era.

Actually, your H2H info of Steffi v. both Martina and Chrissy is very interesting. I wouldn't have guessed it. Also, I don't agree that Serena only played "lesser greats." She did play Venus a lot. Not sure where Sharapova will land, or if she gets an asterisk, but she has the career slam. And, is Serena not somewhat like Federer, to the Federer fans, when there are complaints about "weak era": in that, there was no one like Serena, so how could there be competition? Chicken or egg? What happened to Roger is that 2 ATG's followed right on his heels. For Serena, beyond her sister, there was basically no one. Justine Henin was very much in there, but she retired long ago. I'm going to say 2 things here: I still think that if women played best of 5 at Majors, there would be less changing of hands at the top of the game, and lead to better rivalries. Also, it is a fact of life that women quit sports to have babies, therefore, often, shortening their careers and eliminating time when they could create better rivalries. There is no solution to that part, other than what the WTA has done to freeze players' rankings for maternity leave, which is recent. We may see some effect of that down the road.
 

El Dude

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That was helpful. Though I see it even confuses YOU how ol' Jeff's numbers eventually got him where they did. I'm also surprised that Ferrer has the highest peak. What does that really tell us? I'll offer this about Stan, based on memory only. He beat Rafa in the 2014 AO final. Then, at RG, on arguably his best surface, he lost in the first round. We all remember that Stan was wildly inconsistent. I always thought that Magnus Norman helped him a lot, and should get real credit for his 3 Majors. Sort of like Peter Lundgren helped tame Marat Safin long enough to get HIM one more Major. Anyway, maybe the inconsistencies account for the weird ELO rating. Ferrer was nothing if not consistent. And Kei, well, with injuries, not consistent. Still doesn't explain his ranking on this man's system. And, even if you say that there is some bell-curve involved, wouldn't you, if you were Jeff, rethink your system, if you had Stan that low, Kei so high, and Dementieva up there above Wawrinka and Barty? I would have thought: "Back to the drawing board." But no, he plowed forward. At a certain point, IMO, he's falling in love with his own formula, common sense be damned. And, yeah, whatever the formula is.
Yeah, that last is why I ended up abandoning the ranking formula project...I always ended up with rather disconcerting things, like GOAT Points ranking Connors and Lendl above Sampras. I understand the logic - both were very consistent and played a ton of matches, winning a lot more titles than Sampras, but literally no one ranks them higher than Sampras.

I think this is where the word "accumulation" is relevant. Just about every ranking system inevitably weights towards career totals - the stuff that accumulates over time. But the problem is that you can't ignore this stuff, because part of greatness is longevity and consistency.

As for Ferrer's peak, I think it is crucial to point out that it was in 2012-13. I've called 2012 "The Year of the Big Four" - because it was the only year that they all won a Slam, and also the year that they were probably closest to each other. Ferrer was a distant #5, but given the four above him, that is nothing to be ashamed of. And of course in 2013, Rafa had arguably his best year and Novak was still in his prime. Ferrer finished #3, ahead of an ailing Roger.

Here's another stat - David Ferrer vs. the Big Four, in 2012-13:
vs. Rafa 1-8
vs. Novak 0-5
vs. Roger 0-2
vs. Andy 1-2
vs. Big Four 2-17 (11.8%)
vs. Everyone else 134-22 (85.9%)
Overall 136-39 (77.8%)


I think those last three tell a lot...Ferrer only won 2 of 19 matches vs the Big Four during 2012-13, but was pretty dominant against everyone else.
 
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El Dude

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I don't think that does matter, if we're going to try to identify Greatest(s) of All Time. Because when we say GOAT, we are not saying "of their era," which is a distinction some would make. (Which is where I incline.) It's handy that Fedalovic happened to play in basically the same era AND eclipse most other records, but it doesn't mean that the GOAT conversation doesn't include all eras on the men's side, too. You do get credit for trying to shoehorn Laver in there, sometimes. But if there IS to be a GOAT debate, it doesn't matter that Martina, Steffi and Serena are much more from different eras. Right? Certainly this guy Jeff's accounting for greatness has no respect for era or even Open Era.
I don't think it matters either - just pointing out that the context of their co-GOATness was different.
Actually, your H2H info of Steffi v. both Martina and Chrissy is very interesting. I wouldn't have guessed it. Also, I don't agree that Serena only played "lesser greats." She did play Venus a lot. Not sure where Sharapova will land, or if she gets an asterisk, but she has the career slam. And, is Serena not somewhat like Federer, to the Federer fans, when there are complaints about "weak era": in that, there was no one like Serena, so how could there be competition? Chicken or egg? What happened to Roger is that 2 ATG's followed right on his heels. For Serena, beyond her sister, there was basically no one. Justine Henin was very much in there, but she retired long ago. I'm going to say 2 things here: I still think that if women played best of 5 at Majors, there would be less changing of hands at the top of the game, and lead to better rivalries. Also, it is a fact of life that women quit sports to have babies, therefore, often, shortening their careers and eliminating time when they could create better rivalries. There is no solution to that part, other than what the WTA has done to freeze players' rankings for maternity leave, which is recent. We may see some effect of that down the road.
I paused when I wrote "only lesser greats," especially when I considered Venus, Clijsters, and Henin. But what I meant was that she didn't play alongside another GOAT-esque player, like Navratilova and Evert, and adding Graf in towards the end, or Graf with Seles. And fair point about comparing it to Roger's gen, as I think there is some similarity, even if their dominance followed a different pattern. It does seem like there have been several "almost next top dog" on the WTA that didn't quite pan out...Azarenka comes to mind, as well as Osaka.

And it looks like the WTA might have their next great in Iga Swiatek, perhaps to be joined soon by Coco Gauff. I thought it was going to be Naomi Osaka, but who knows if she'll ever be the same. And it did seem like the baton was being passed to Osaka, even if it was marred by one of Serena's worse diva moments (I'm talking the 2018 USO).
 

Moxie

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Yeah, that last is why I ended up abandoning the ranking formula project...I always ended up with rather disconcerting things, like GOAT Points ranking Connors and Lendl above Sampras. I understand the logic - both were very consistent and played a ton of matches, winning a lot more titles than Sampras, but literally no one ranks them higher than Sampras.
All greats, but exactly.
I think this is where the word "accumulation" is relevant. Just about every ranking system inevitably weights towards career totals - the stuff that accumulates over time. But the problem is that you can't ignore this stuff, because part of greatness is longevity and consistency.
But here is where the Borg Problem comes in. I agree that part of greatness is longevity and consistency. But the longer you stay, the more your numbers go down. That is natural attrition. Then you have Borg...die young and leave a gorgeous corpse. He messes with everyone's formula, because they also want to place him high. Rightly, IMO. But he had basically a 10 year career. Roger and Rafa have played twice as long. Novak nearly so.
ThAs for Ferrer's peak, I think it is crucial to point out that it was in 2012-13. I've called 2012 "The Year of the Big Four" - because it was the only year that they all won a Slam, and also the year that they were probably closest to each other. Ferrer was a distant #5, but given the four above him, that is nothing to be ashamed of. And of course in 2013, Rafa had arguably his best year and Novak was still in his prime. Ferrer finished #3, ahead of an ailing Roger.

Here's another stat - David Ferrer vs. the Big Four, in 2012-13:
vs. Rafa 1-8
vs. Novak 0-5
vs. Roger 0-2
vs. Andy 1-2
vs. Big Four 2-17 (11.8%)
vs. Everyone else 134-22 (85.9%)
Overall 136-39 (77.8%)


I think those last three tell a lot...Ferrer only won 2 of 19 matches vs the Big Four during 2012-13, but was pretty dominant against everyone else.
Those are amazing stats. And for everyone I've argued with over the years that Ferrer was more than just some pusher, you just rested my case. Thank you.
 
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Moxie

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I don't think it matters either - just pointing out that the context of their co-GOATness was different.

I paused when I wrote "only lesser greats," especially when I considered Venus, Clijsters, and Henin. But what I meant was that she didn't play alongside another GOAT-esque player, like Navratilova and Evert, and adding Graf in towards the end, or Graf with Seles.
Venus, but for Serena?
And fair point about comparing it to Roger's gen, as I think there is some similarity, even if their dominance followed a different pattern.
The "different pattern" was that Serena was more dominant.
It does seem like there have been several "almost next top dog" on the WTA that didn't quite pan out...Azarenka comes to mind, as well as Osaka.

And it looks like the WTA might have their next great in Iga Swiatek, perhaps to be joined soon by Coco Gauff. I thought it was going to be Naomi Osaka, but who knows if she'll ever be the same. And it did seem like the baton was being passed to Osaka, even if it was marred by one of Serena's worse diva moments (I'm talking the 2018 USO).
I was thinking of Osaka when I wrote this, and good to point about Azarenka, who was really threatening to be a rival to Serena. Remember that Visa lost time on the tour due to custody issues with her baby-daddy. I'm sorry that Osaka is not currently panning out, but she would have been very late competition, anyway. I didn't forget Clijsters, but left her out because she left tennis to have kids. Yes, she came back and won, I think, 2 Majors post-babies, but at least one. Point being, again, you do lose time to competition to have babies, even if you come back. Most don't, though.
 

El Dude

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Venus, but for Serena?

The "different pattern" was that Serena was more dominant.
That's debatable, but not what I was getting at. I agree that when Serena was on, the gap between her and everyone else was larger than peak Roger (or Rafa or Novak) and everyone else. But Serena never had a four-year period like Roger's 2004-07. In a way, her career is more similar to Rafa's - lots of high peaks, and a nice string here and there, but without the same consistent dominance as Roger, Novak, as well as Martina and Steffi.
I was thinking of Osaka when I wrote this, and good to point about Azarenka, who was really threatening to be a rival to Serena. Remember that Visa lost time on the tour due to custody issues with her baby-daddy. I'm sorry that Osaka is not currently panning out, but she would have been very late competition, anyway. I didn't forget Clijsters, but left her out because she left tennis to have kids. Yes, she came back and won, I think, 2 Majors post-babies, but at least one. Point being, again, you do lose time to competition to have babies, even if you come back. Most don't, though.
Well yes, exactly. That's simply part of the nature of the WTA.
 

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As an aside, one thing that really differentiates the female 3-headed GOAT from the male is the era gap. Navratilova was born in 1956, Graf in 1969, Serena in 1981 - that's a span of 25 years, which each separated by 12 or 13 years. Now of course Martina had Evert just two years older, though Evert peaked earlier, and Steffi had Seles born four years later, but then her tragic attack shortened her peak. So they weren't just all on their lonesome without other inner circle greats - except for Serena. She played alongside a bunch of lesser greats, but no one in the same vicinity.

One thing that makes Navratilova so impressive is that despite playing most of her matches vs Graf in the latter half of her career (from 1985-94), she was still 9-9 in the H2H. Actually, Evert vs. Graf was also very close (6-7), though Evert won their first six matches and Graf their last seven. Martina and Steffi were more balanced, thought Martina won five of their first six and Steffi won 8 of their last 12.
Navratilova winning into Graf's prime is what, in my opinion, puts her ahead on my GOAT list. Had Navratilova won 1994 Wimbledon, I feel there would be no debate. I rank Graf behind because her two main rivals, Seles and Capriati, missed years of what should have been their primes. Seles was never the same and Capriati became an elite player again only after Graf retired. Capriati beating a young Serena on a consistent basis in the early 2000s only proves how talented she was and that she probably would have won several slams in the years that she missed, potentially preventing Graf from winning those slams.
 

El Dude

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Andy Murray slides in at #29 - higher than Becker, Edberg, Agassi, and Wilander. Commence outrage.

While I wouldn't rank Murray higher than those guys, as I've said before, I do think he is historically underrated, mainly because people generally over-emphasize Slam titles and he was over-shadowed by You Know Who. But he reached 11 Slam finals (tied for 9th in the Open Era, with McEnroe, Wilander and Edberg, and one more than Becker); he won 20 big titles (12th in Open Era, and more than Wilander and Edberg), and was the 4th best player in the game for about a decade, finishing a year at #1 - during the Big Three era. Oh, and a bonus: the only player to win Olympic Gold twice. In a different era he would have won twice as many Slams.

Anyhow, that's 48 of the 100 so far as men, so it looks like he's going for roughly half. That means with 28 to go, we'll probably see 14-15 men. My guesses:

Bill Tilden, Don Budge, Jack Kramer, Pancho Gonzales, Ken Rosewall, Rod Laver, Jimmy Connors, Bjorn Borg, John McEnroe, Ivan Lendl, Pete Sampras, Roger Federer, Rafael Nadal, Novak Djokovic.

That's 14....If it was all of tennis history I'd guess Anthony WIlding, but given that it is only 1919 on, I can't think of anyone else. So while I disagree with some of his rankings, I do agree that those are the top 14 men's players of 1919-2022....I wouldn't supplant any of them for the guys already ranked.
 
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Moxie

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Andy Murray slides in at #29 - higher than Becker, Edberg, Agassi, and Wilander. Commence outrage.

While I wouldn't rank Murray higher than those guys, as I've said before, I do think he is historically underrated, mainly because people generally over-emphasize Slam titles and he was over-shadowed by You Know Who. But he reached 11 Slam finals (tied for 9th in the Open Era, with McEnroe, Wilander and Edberg, and one more than Becker); he won 20 big titles (12th in Open Era, and more than Wilander and Edberg), and was the 4th best player in the game for about a decade, finishing a year at #1 - during the Big Three era. Oh, and a bonus: the only player to win Olympic Gold twice. In a different era he would have won twice as many Slams.

Anyhow, that's 48 of the 100 so far as men, so it looks like he's going for roughly half. That means with 28 to go, we'll probably see 14-15 men. My guesses:

Bill Tilden, Don Budge, Jack Kramer, Pancho Gonzales, Ken Rosewall, Rod Laver, Jimmy Connors, Bjorn Borg, John McEnroe, Ivan Lendl, Pete Sampras, Roger Federer, Rafael Nadal, Novak Djokovic.

That's 14....If it was all of tennis history I'd guess Anthony WIlding, but given that it is only 1919 on, I can't think of anyone else. So while I disagree with some of his rankings, I do agree that those are the top 14 men's players of 1919-2022....I wouldn't supplant any of them for the guys already ranked.
Andy Murray is so complicated, and you lay out most of the reasons why very well. Since it's ELO-based, his competition puts him high, right? He was the 4th Beatle in the crazy-strong era of Big 3. He was the only other man in 13 (?) years to reach #1, besides Roger, Rafa and Novak? First British man to win Wimbledon in 77 years? I know these aren't part of the formula, but they are part of his resume.

With the really old ones, I really don't know who you have a feel for them? Is it pure stats? How much video is even available?
 
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El Dude

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Andy Murray is so complicated, and you lay out most of the reasons why very well. Since it's ELO-based, his competition puts him high, right? He was the 4th Beatle in the crazy-strong era of Big 3. He was the only other man in 13 (?) years to reach #1, besides Roger, Rafa and Novak? First British man to win Wimbledon in 77 years? I know these aren't part of the formula, but they are part of his resume.

With the really old ones, I really don't know who you have a feel for them? Is it pure stats? How much video is even available?
Stats and reputation, mostly--especially what other players and high profile historians (e.g. Bud Collins), and the odd video. And of course whatever Jack Kramer had to say is always a good read.

But I have no idea how Sackmann does ELO for the Pro/Amateur Era.

There's a website called Tennis Base that I used to check out, which has rankings all the way back to the 19th century, and uses a greatness formula similar to GOAT Points. But they started charging for a subscription a few years ago, so I can't check it anymore.
 

Moxie

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Stats and reputation, mostly--especially what other players and high profile historians (e.g. Bud Collins), and the odd video. And of course whatever Jack Kramer had to say is always a good read.

But I have no idea how Sackmann does ELO for the Pro/Amateur Era.

There's a website called Tennis Base that I used to check out, which has rankings all the way back to the 19th century, and uses a greatness formula similar to GOAT Points. But they started charging for a subscription a few years ago, so I can't check it anymore.
I did love Bud Collins, and he went back a long time. But the amateur era was SO different. It was basically a club game. Are the players from that era plausibly comparable? Did you ever read the book that we tout around here on occasion: A Handful of Summers? @Kieran will remember who wrote it. It is arguably the most poetic book ever written about tennis. It talks about what it was like in the amateur game. Aside from the geometry within the lines, it's not even the same game anymore.
 
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El Dude

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I did love Bud Collins, and he went back a long time. But the amateur era was SO different. It was basically a club game. Are the players from that era plausibly comparable? Did you ever read the book that we tout around here on occasion: A Handful of Summers? @Kieran will remember who wrote it. It is arguably the most poetic book ever written about tennis. It talks about what it was like in the amateur game. Aside from the geometry within the lines, it's not even the same game anymore.
Yeah, though that's true of most sports. But it relates to one of the common questions around ranking greats across different eras. How can you possibly compare Bill Tilden and Roger Federer? Or Babe Ruth and Aaron Judge? Imagine sending Judge back to the 1920s - he'd probably hit 100 HR in a season. Baseball a century ago was very different: Ruth only played seven different teams, only white players, and faced pitchers who not only threw 10+ mph slower, but usually pitched the whole game. Etc, etc. On the other hand, Ruth dominated his context in a way that Judge hasn't - except for one year - and should be considered the greater player because of it. Or we could imagine traveling back to the 1960s and kidnapping prime Rod Laver, then placing him in today's ATP tour. Would he be any better than David Ferrer? And maybe not even that? Yet in the 60s, he was the best player in the world, and relative to his peers he was as dominant as anyone ever has been - and that should be recognized and lauded.

In other words, players can only play within the context that they play in (not sure if that sounds ridiculous repetitive or poetic). Which is why I like to emphasize context - how good a player was relative to his or her peers. Meaning, two things can be true at the same time: In terms of skills and ability, players tend to get better over time but...in terms of greatness, should only be judged contextually - relative to their peers.
 
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tented

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Andy Murray is so complicated, and you lay out most of the reasons why very well. Since it's ELO-based, his competition puts him high, right?
Sackmann does rely heavily on the ELO system, yet he also more or less discards that system when saying of Murray: “Illuminating as they are, these numbers miss much of what makes Murray great. The tactical game begins before anyone steps on court, and that tilts the scale even further in Andy’s favor.” [Emphasis mine.] So it’s not 100% numbers driven, although numbers are a big factor.
 

Wander

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Sackmann does rely heavily on the ELO system, yet he also more or less discards that system when saying of Murray: “Illuminating as they are, these numbers miss much of what makes Murray great. The tactical game begins before anyone steps on court, and that tilts the scale even further in Andy’s favor.” [Emphasis mine.] So it’s not 100% numbers driven, although numbers are a big factor.
I think his placing on the list is in fact entirely driven by the Elo formula. There are a couple of names where he had to abandon the algorithm due to lack of data. Namely Karel Koželuh and Ora Washington, but I think at this point the order of the list is entirely down to what the algorithm spat out. The articles themselves of course contain a combination of statistical and subjective analysis of a player's greatness.

Andy Murray is simply one of those players who ends up higher than expected on a list like this because of playing essentially the entirety of his career in a very difficult era where big titles were hard to come by. The fact that he broke through to be comfortably the 4th best player of the 2010s gives him very good Elo numbers (both for peak and longevity). The Elo algorithm rates the 2010s so high that even Kei Nishikori and David Ferrer made the top 128, and at much higher placings than most would ever expect.