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Catch,
3Fingered gave you a good start. According to DIII baseball, there are about 20 or so DIII players drafted each year. Can vary up and down, but not very much.
So, 20 out of about 1,500 come from the DIII ranks.
I don't think there is any information about those that are signed but not drafted. One major reason is that number does not just include free agents from the 50 states, the number includes players from the rest of the world. The latter is becoming substantial, more than most realize...until you go to a Milb camp for Spring Training.
I don't know if I would count FA into the general scheme of things. FA are signed for many different reasons and many signed are those that are coming from other organizations (once drafted but released) as well as those (many seniors) that slipped through the draft and FA signings can occur at any time including during spring training.

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