Joe DiMaggio
I can't speak to things like racquetball and darts, but if we're considering the major "real" team sports you have to give strong consideration to Joe DiMaggio. I know this is a curious choice but it is only because he played so long ago, and very few people alive have actually seen him play. Also, he retired in 1951 when baseball was just starting to be televised, so there is very little record of his fielding capability.
For starters, DiMaggio was the most anticipated minor leaguer to come to the big leagues in history. The buzz was amped up even more because DiMaggio's start was delayed a month due to an injury (a stupid trainer scalded his leg in trying to treat a sore foot). So how does the young DiMaggio perform during this intense media blitz? He responds by getting the most hits in a rookie's first month, 48, a record that still stands. This included 4 triples and 4 home runs. Also, in the 7 years prior to DiMag's arrival, the struggling Yankees made 1 World Series appearance. After his arrival, and without any other significant changes to the team, the Yankees go to the World Series in 9 of the following 10 years. The impact he had on his teammates was incredible.
My 86 year old father used to live near the stadium and watched him play many times. Several years ago I got into a conversation with him and said, "C'mon now, how good was he really." His answer was this: "Take Derek Jeter and put him at shortstop at your local high school baseball game. Everybody will immediately notice that the guy at short is a helluva lot better than the rest of the players. The difference between Jeter and the high school players is not as great as the difference between DiMag and the rest of the professional players." I had trouble believing this, so in the ensuing years he ended up writing a book on DiMaggio, now in its second printing! Umpire Art Passarella (who had also umpired in the negro leagues) said, "He had the greatest instinct of any ball player I ever saw, he made the rest of them look like plumbers." I guess that is another way of saying it!
Amazingly, there are many books on DiMaggio, but none devoted to analyzing his game statistics and the intangibles. Throughout the course of the book, you learn all these amazing things he did that nobody ever heard about, but the kicker is that if you didn't actually see him play you can't appreciate how good he was. He was even better than the numbers show, and if you look at the numbers on an annual basis, he is unparalleled (not even close). Consider this one: in 1937 he hits for the cycle. OK, it's been done before, what's the big deal? For starters, he not only hits for the cycle, but he also hits an extra home run in the same game (9 innings), a feat that has never been matched. OK, let's call that a fluke. 11 years later in 1948 and after missing 3 prime years to WWII, DiMaggio hits for the cycle again AND hits an extra home run again (9 innings)!
Of course I'm not trying to convince anybody in a few short paragraphs and I'm not intending to sell books here. I'm just saying that by the time you finish reading this book you will conclude that he was the best player in baseball, recent history included, and that included Babe Ruth (Ruth single-handedly saved baseball after the black sox scandal and was freakish in his pitching/hitting capability, but he wasn't as valuable all around as DiMaggio).
Great thread!