Babe Ruth Best Baseball Player of all time?

Something that's always bugged me about baseball: Why was Babe Ruth so great? Sure, he put up nice numbers, but... that swing looks absolutely awful in what little footage I've seen of it. I'm not convinced at all that he was the best player ever. Best player of his time, yeah, but if you put the Babe against... say, Dontrelle Willis, I'd bet quite a lot of money that the outcome of the battle would not favour antiquity. Oh, and this wouldn't change even if Babe Ruth was alive and capable of swinging the bat. People are just better athletes in this day and age, baseball has a far greater talent pool to draw from, etc.

Mathematically: You're far more likely to have the greatest player of all time play in a time when there are more people playing baseball. Here's why... say there's a player... let's call him 1. Stick him in a list containing all past, present, and future baseball players (quite a long list, but bear with me). Shuffle said list, then break them up in order by time period. The likelihood of player 1 ending up in a time where not that many people were playing is... slim. Possible, but slim. Now let's say that there are all manner of numbers corresponding to a player's type. 1 for the greatest talent ever, and 10000 for well... people who can't even throw fastballs (me). There are only a set number of spots for baseball players in the major leagues (in this simplification, let's say there are 10). So... let's make a random pool of... 30 players and pick the top 10 for 1930... then follow that up with a random pool of 100 players, and pick the top 10 for 2000.

Note that I couldn't be bothered making any sort of talent randomization curve that follows reality, and thus decided it was linear to cut down on work.

1930

Pool: 9207, 8359, 2554, 7257, 2466, 1099, 7310, 2219, 5940, 8197, 9343, 4919, 948, 4020, 6456, 3516, 8147, 7294, 203, 3886, 3673, 2331, 1869, 2353, 7842, 4515, 3312, 7177, 9421, 7293.

Top 10: 203, 948, 1099, 1869, 2219, 2331, 2353, 2466, 2554, 3312

Average (top 10): 1935.4

Difference of best (203) from average: 1732.4

2000

Note: Not listing entire pool... because it's big. I did run one :P.

Top 10: 57, 152, 160, 500, 711, 739, 892, 1019, 1081, 1107

Average (top 10): 641.8

Difference of best (57) from average: 584.8

Ok. So, the second pool has an average player three times as good as the first. However, the measure of how good a player is would be something like the difference of best from average, which is far higher in the 1930 pool than the 2000 one. The player rated 203 would be remembered as some pitcher destroying beast, while 57 would just be a pretty good player, due to the talent pool which he inhabits.

This has the possibility of being utter garbage, of course. But it was fun to think about.