The specific definition of a crow hop depends on what rules you are using. "XRay" on eteamz has done an indepth study of this and can expound at great length on the differences.
One difference is that ASA (unlike some others) requres that the pitcher push off from the replant in order for it to be illegal (they call it establishing a second point of impetus). So, strictly speaking, a replant without a push off is legal in ASA.
This makes calling a crow hop in ASA a bit tricky, since without stop action replay, it can be difficult to see the impetus with a highly skilled crow-hopper. And, with runners on base, the penalty for an illegal pitch can be severe and game-deciding, so umpires will not call the crow hop unless they are sure.
And, the trickiness tends to intimidate the less experienced umpires, who then don't call it at all.
Fortunately, most less skilled crow hoppers also leap (a different "illegality"), and that is easy to see with a two man crew. The only real issue with leaping is the hole in front of the plate, as WMB pointed out.
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Tom
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