Agassi's 20th on my list of greatest players post WWI. I don't rate guys prior to that, due to a lack of information - I use some results from McCauley's book for example.
Also, greatest to me is most accomplished. It's the same for any respectable list, including that of Bill James for baseball. Exceptions can be made for the very early years, but with good reasons.
However, I consider the list to be made for fun only. Guys are easily interchangeable in some places and therefore I give only serious consideration to 'tiers' - also based on accomplishment.
Studying history and giving opinions is a fact of life. Cyborg, you mentioned Bill James as a great example. Bill changed the course of baseball thinking with his study of baseball history and analysis. Baseball teams nowadays go by many of his studies.
And yes Bill did give opinions on the greatest players of all time as did Bill's great friend and sports statistician and analysis Pete Palmer. Of course Bill or Pete never saw Ty Cobb, Babe Ruth or Honus Wagner play but they studied them and analyzed their careers objectively and were able to give their opinions on their greatness or perhaps lack of greatness. Baseball, contrary to what some have said here has changed tremendously over the decades, with the strike zone changing, the height of the mounds, steroids and other performance enhancing drugs, the dead ball era, the lively ball era, different stadiums, minority involvement in baseball and a million other things I have not mentioned. I would venture to day you can argue baseball has changed as much as tennis, maybe more so. But these great baseball experts can give INFORMED objective opinions on players of the past which they have never seen.
And we all can do this in tennis. That is one of the great joys of sport, to give opinions whether they are right or wrong. We can debate and dispute each others points but we can also argue whether Henri Cochet can play well in today's game or not.
Why was Rod Laver, in his fifties able to give Ivan Lendl a battle in practice matches in the late 1980's if like some write, he couldn't compete against the modern players today if he was in his prime? Yet these same people may argue Lendl would do well now and Laver wouldn't.
It's all opinion. I think a Bill Tilden, with his physical talent, great analysis of the game and his great will to win would easily adapt to today's game and be a top player. Someone else may say Tilden would be tripled bageled by Serena Williams. I would think Tilden, if magically transported to today and given time to practice and adapt would easily crush Serena in tennis.
Let's put it this way, Serena and Venus Williams hit with tremendous power and spin with today's rackets and can serve over 120 miles per hour. Does anyone think Bill Tilden, a man over 6 feet tall (I think 6'2") wouldn't be able to hit the ball over 120 mph on serve and hit the ball on his groundies pretty well with today's rackets? Maybe, maybe not but I think he probably would. Just give Tilden some time to adjust to the new styles and rackets and I think he would do very well. It's a fun debate and we should be allowed to discuss and debate this despite the fact it was a long time ago.
I don't rank Andre in my top ten but if he didn't waste some years perhaps he could have been in the top ten.