Yes but we don't need absolute perfection, right? The basic stats provided by ATP MatchFacts is better than some guy writing a clickbait article that says "this is true because I says so", and the stats I'm asking for would be better than that, right? We don't need to be able to convince god or he'll send us to hell.
Yes, that is true....but as you can see here...there are people demanding "evidence" and "stats'....as if the really puny stats we have can provide proof....of course, I like stats, and I'm interested in them, but there is little value in them (really none at all with the limited data we have) to questions like the one in the OP. Levels of idiocy here:
1.stating opinion as fact
2.stating #1 as a rebuttal ie."that's your OPINION!" - wow, good one
3.stating we need "facts"
4.pretending the puny stats you have in fact "prove" that...say...Federer is the greatest
I applaud your effort to fantasize about better stats.....no problem with that....but you'd never have the stats - they can't exist even in theory - to back this premise. Even with better data - which I'm all for - I don't think you would get a convincing argument at all.....I'm not calling for absolute proof, trying to differentiate between 3 unique, but first class returners like Connors, Agassi, Djoko, across totally different opponents, will be impossible with black box statistics....to be honest, and hey, I pride myself on an astute tennis eye (lots of stories there...but I have worked with world class players)...it is probably impossible even to make a good subjective judgment. I've seen Connors and Agassi return in person....I've seen them in hundreds of TV matches....I have an opinion....but it's only an opinion and a very arguable one since we are talking about subtleties of all time greatness in an extremely varied shot under varied conditions, with varied strategies, against varied opponents.
The serve is a much more controlled, repeatable shot, orders of magnitude so.....yet I could not honestly tell you who the "greatest" server was either. I can give a trite, TW style answer....but to honestly address the question, or to try to define it statistically - impossible. Absolutely impossible. Not even close to being possible.