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Keep in mind that career length affects this too I think. For example, Pete Rose played for 24 years. This means that he was in MLB for almost 1/4 of the 20th century. So if you have a random debut league that covers the 20th century, Rose would be in it when you started 24% of the time. At least that is how I assume it would work...otherwise it would be really wonky.
So you would expect to see those long career guys - Molitor, Rose, Ryan, etc. - show up frequently in the initial league. In fact, if you have four guys with 25-year careers (Rose, Yaz, Rickey, Ryan) then odds are that one of them is in your 100-year league. And by chance you will probably have a guy or two that shows up more often than expected - I know I saw old Rose quite a bit. Short career guys, who played only a year or two, they would be less likely. But there are many more of them, so the league still has plenty to go around.
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