What exactly is a 'crow hop'? Well it's the basic technique that everyone preaches, but the more you look at different fielders the more you realize that there are many ways to do the crow-hop. This page shows 3 versions - we've used wireframe illustrations so the animated versions can demonstrate the amount of field-grid travelled.
Same label, different throws.

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From a standing catch the simplest crow-hop is more of a
shuffling slide step. It is effective and has the advantage of being less likely to cross you up - keeping the movement and the throw in line.

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Cross-over crow-hops sustain the momentum and the hopping foot can cross-over in front or behind. Notice, too, that in one of these animations, the fielder slows to get his feet lined up for the hop, whereas in the other the forward motion is continuous.

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Side drift can cause some loss in momentum or accuracy. (Both the 2nd and 3rd examples show this happening, with the 2nd going the most off line.)
Crow-hops are just the beginning.
Power and accuracy are required, so once you've mastered the footwork of the crow-hop, make sure it translates into throws that go to the right side of the cut-off or relay player. Here's why...
Hitting the Relay
These two images, and supporting QuickTime animations (for WebBall Team Players) demonstrate the importance of training for accurate throws to the infield cut-off.

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Body shift... Login to see it In-Motion.
The quick glove-side relay on the left takes 1.2 seconds or less from catch to release. The relay that pulls the fielder into a forced spin-around throw (on the right) takes 1.9 seconds or more from catch to release. That can be the difference between an out and a run scoring. (Timings based on the actual real-time In-Motion sequences.)