I understand the point that you're trying to make, esp. in your penultimate above, but the question, "Who is the better player?" is still too open to interpretation, is it not? It seems like the ELO rating is trying to tell us who had the more "consistent" career over time. I get why Ferrer has such a high number, and, as you know, I'm a fan, as well as having been a huge fan of Safin. And even you pick Safin. I don't think anyone would say that Ferrer was more "gifted" or "had more weapons" than Safin. But, as you rightly pointed out, Safin was WILDLY inconsistent, for various reasons, and only most of them were above the neck. This is where I remind everyone that, after Safin won the 2005 AO, he never won another tournament. And, unlike Sampras, it's not because he retired.
Nice reply. I think a lot of your points of divergence go along with what I was saying in my previous post - that complaints about stats tend to be somewhat orthogonal to what fancy stats are actually for, or what they seek to answer. But I do think you are correct, that Elo doesn't tell us how good a player can be in a given match--as I said in my last post re: Safin--but it does tell us the
relative level of dominance, over time. And yes, consistency has something to do with it. Thus Ferrer reached a higher Elo than Safin, even though we all know Safin was capable of greater heights (I'm not disputing that), or Sampras's Elo are closer to Becker than they are even Lendl and McEnroe, because his weakness on clay brought it down every year, probably by about 100 points (meaning, take clay out of Sampras' seasons and you can add 100 or more Elo to his year-end numbers).
Elo pretty much gives us a number that represents how good a player is playing s at any given moment, based upon their recent history. It doesn't tell us how good they'll play in a specific match, or even necessarily what direction they're trending (except through comparing it to their past Elo...and therein lies one of its uses). A player could have a very high Elo but completely tank - like Andy Murray did starting in mid-2017.
In fact, let's look at Andy in 2017 and beyond. He started that year with a 2500 Elo - the peak of his career, and at a level equalled by only eight other players in ATP history (Laver, Connors, Borg, McEnroe, Lendl, and the Big Three...not even Pete got to 2500, due to his weakness on clay). He performed well at first, going 12-2 in his first 14 matches, though losing to Novak in the Doha final and Mischa Zverev in the 4R of the AO, but also winning Dubai (over Verdasco). But come March, the cracks started to show. He entered Indian Wells with his Elo dipped a bit to 2476, but after going 4-5 in his next nine matches, by Roland Garros his Elo was down to 2391...still really high, but a rather steep drop.
That 2391 in a vacuum doesn't adequately represent how Andy was playing as RG started...that's higher than Wilander's and Edberg's peak, and Andy obviously wasn't playing like those two at their best. So one thing Elo doesn't give us, at least taken as a static number, is trending direction...but we can see that his Elo dropped over 100 points in a few months.
Andy reached the SF of Roland Garros, which boosted him back over 2400. And he also reached the QF of Wimbledon, but then got hurt and finished the year at 2353, which was the fifth highest of his career and almost exactly the average Elo for the year-end #2 in the Elo rankings. He had gone 25-10 for the year, a 71 W% that is below his current career rate of 76%, and only won a single ATP 500. Meaning, it wasn't his fifth best season - so in that regard, Elo doesn't tell us how well a player performed over a distinct span of time like a year. What it
does tell us is how well he matches up against the rest of the tour, at least based upon recent history.
Andy's Elo continued to drop rather steadily from that point on. He ended 2018 at 2255, 2019 at 2186, 2020 at 2141, 2020 at 2054, and 2061 at 2005. As I and others have mentioned, his last five years or so are somewhat reminiscent of the later years of players like Hewitt and Wilander...and stand out because most all-time greats (and near greats) retire much before they fall that far, let alone hang out in journeyman status for years on end.
Similarly, Roger ended 2021 at 2257 after going 9-4 that year and 5-1 the year before. 2257 is the typical Elo for a top 3-5 player...and he wasn't even that by 2020-21, or at least didn't play enough to earn that claim.
I used Andy as an example of how you're actually right, that Elo doesn't tell us everything, and really emphasizes the past more than the present - or at least certainly not the future. Andy wasn't a 2353 Elo player at the end of 2017, nor was Roger really a 2257 player by the end of his career - at least based on his performance over the last two seasons (14-5, no titles). But what Elo
does tell us is where a player is at in any given moment, based upon recent history. And where he is at vs. where he was a year ago, and where other players are at. It is also supposed to cross eras, so we can say that Novak in 2015 was roughly the equal to Borg in 1980, and no one else has reached that level of consistent dominance.
Your example of Gaudio/Nalbandian/Davydenko is interesting, and flawed, I think. I do get your point, which is that fans tend to prize Majors, but I don't think anyone would rank them differently than their ELO ratings, which is, in same order: 2137/2196/2291. Everyone knows that Gaudio was a bit "right place, right time" in winning that RG 2004. Nalbandian was an excellent player, but a bit like Safin, without the Majors, and Davydenko did have his talents, even though he also tended to beef up his resume with small tournaments.
But that's my point: Elo gives us a more accurate picture of their talent level than their Slam counts, and in that case, people do realize it and consensus opinion is more aligned with Elo. Again, in this particular instance. I chose those players because consensus opinion matches up with Elo more than it does Slam counts.
Ferrer and, say, Wawrinka are a bit different. Stan is in a similar category as Safin: some amazing tournaments and years as a good player, but his lack of consistency led to a rather pedestrian peak Elo of 2291 - the same as Davydenko, and very similar to Hewitt and Nishikori, and below players like Zverev, Medvedev, Del Potro and Ferrer (OK, 2291 isn't pedestrian..but certainly lower than one might expect based on the "Legend of Stanimal").
This comes back to your point: consistency is a factor. While we tend to like to look at Stan as a guy who, at his best, was able to beat the arguable GOAT during his peak years at Slams, we can switch that slightly and say that Stan truly only had three great tournaments: the three Slams he won. He won only one other big title, and just 16 titles overall. So a pretty good career, but rather weak compared to those three tournaments. Take those three Slams away, and he is a run of the mill top 20 guy. Those 16 titles is the same number as far lesser players like Vijay Armitraj and John Isner, and less than guys like Zverev and Tsonga, and far less than Ferrer's 27.
People will say that Ferrer padded his title total with weak titles, and certainly all but one of his 27 were ATP 250s and 500s. But again, he was consistent, week after week, and Elo recognizes a player's "floor" just as much as their "ceiling." In that regard, it does a good job of taking both into account: it recognizes when a player beats a better (higher Elo) player, but also when they lose to a worse (lower Elo) player. What you're left with is a number that places you relative to other players. A moving scale, if you will.
So for me the missing link, or what Elo doesn't satisfy for me, is telling us how good a player was
capable of playing at their very best...which probably is best represented by looking at the so-called "big titles" (I almost wrote
titties...haha).
I don't see how, in sports, ignoring the pure results of trophies is necessarily a good thing. Winning the hardware IS the goal, and it says something about the player. And I'm still not clear how ELO tells us 'who is the better player at their peak, A or B?" Because Safin is the better player, at his peak, over Ferrer, to use the current example. I suppose we could argue Davydenko v. Nalbandian, but I bet Nalbandian would win, around here.
I can see why it's useful across eras. I can also see why you like it, as a stats guy, but I still think it's an "averaging" tool, and sports is about actually winning. I may not have been paying the best attention, but I have been trying to ride along with this. Sorry, just jumping back in after the holidays.
I'm not saying that we should ignore trophies, which is also why I like but don't love Sackmann's methodology. I think a good GOAT ranking has to include actual trophies (which is why I'm playing with something that essentially averages Elo and what I call "Title Shares"). I'm merely pointing out that Elo gives us a different line of data, that is divorced from the trophies and titties, I mean
titles - that gives us a sense of a player's level of play over a period of time.
As for your statement about Safin being the better player than Ferrer at his peak, I think you are using "peak" in a specific way that is different than what Elo characterizes, or from how I use the term. You are, I think, equating "peak" with how good a player can play at their very best in a specific match, but not "peak" as in the apex period of a player's career, meaning a solid span of time (more than just a tournament here and there). Meaning, "absolute peak" vs. "career peak."
Or maybe this is a good way to differentiate "peak" and "prime" - or what you mean by prime is what I mean by peak, at least as far as Elo is concerned: or career peak. But if we use your usage, a player's "peak" is the absolute best they're capable of playing - so in that sense, we can say that a lot of players have similar
absolute peaks, that sublime tennis is sublime tennis. Remember Marin Cilic at the 2014 US Open? He looked--and was--unbeatable. He was Stanimal for a tournament, and Stanimal, at his best, was equal to the Big Four. Was Cilic's absolute peak less than Roger's or Rafa's? He was as unbeatable at the 2014 US Open as they were in their Slam wins, and beat some very good players to earn the trophy, including a straight-set SF win over Roger, and a straight-set win over Nishikori in the Final, who had just beaten prime Novak and was also playing at his absolute best. Meaning, Cilic could have beaten anyone in that tournament; the only player(s) who might have beaten him in the final are guys like the Big Four playing at their very best (absolute peak level), and then it likely would have been a crapshoot. But even so, we're left with Cilic as the winner: he played at the highest level during that tournament.
In a way, such a usage of the term becomes meaningless, because
many tennis players have reached sublime heights - have similar "absolute peaks." We've all seen random guys play lights-out tennis and beat the best of the best, and it isn't simply or only a matter of the match being on the better player's racket, and they blew it. Remember Dustin Brown? Or what about the various guys who have upset Federer, or Novak? Nalbandian in late 2007? I mean, even Novak said that once you get to the top players--I can't remember if he said top 10 or 20 or even 100--the talent level is similar. It becomes mostly mental (I think he meant 10 or 20, but even so...).
Elo is better at characterizing a player's
prime, or their "career peak" - not their absolute peak. But I don't think we need a metric for that, except to ask, "Have they been unbeatable at the biggest tournament level?" Or in other words, "Have they won a Slam, and in so doing, beaten the best of the best to get there?" If you've won a Slam, and not a window-of-opportunity Slam like Gaudio's, then you have reached that same "absolute peak." I'm not sure there's any way to differentiate degrees of "absolute peakness."
Elo is good for comparing
career peaks, or how good players were over a significant period of time at the best phase of their career. In that sense, I think it isn't wrong to say that Ferrer's prime (or career peak) was higher than Safin's, even if we all know and agree that Safin was capable of a higher
absolute peak. Otherwise Ferrer would have found a way to burst through the wall that was the Big Four and win a Slam. But he didn't. Alas! Safin did, or at least he did in 2005 against Roger - and that was Roger at his best.
So in short, career peak and absolute peak are not the same thing. Elo is good at measuring career peak, but not absolute peak - but nor does it need to, or is there really any way to do so except by looking at whether a player has been the best player at a big tournament, against the top players. If they have--as all of the ATGs have, and a bunch of other players besides--then they're capable of reaching a similar "absolute peak."
(Sorry for the novel, or at least short story!)