As I noted in my initial comment on this aspect of the string - baseball is in position due to the new found diversity of the last 25 years, Hispanics and Asians on the field but also the increasing numbers of Blacks and Hispanics on coaching staffs and managing. Now with Jeter and Johsnon in ownership the game is more vertically integrated than ever before giving it a chance to dispel that it is a white game to American blacks.
The backdrop of CTE and injury in general in football adds to the opportunity to attract these players. As for the numbers and delta's among the players/sports and countries - I will l admit I do not have science - just my lying eyes. 
I do agree with PG that basketball has another breed of cat in it. Those guys have real hand eye coordination - you have to think that Curry, Thompson, Leonard and George to name a few would have been prodigious prospects in baseball.