A double dribble violation is basically: dribble-possesion-another dribble. A muff doesn't constitue possesion, but possesion can be with one hand or two. If A1 dribbles, loses control, picks it up with both hands (possesion), then starts to dribble - it's a violation. If A1 dribbles, muffs, then starts dribbling again without actually picking it up, there's nothing. If you felt the battting of either hand was under control rather than trying and failing to get the ball, you could have the violation.
One of my pet peeves, however, is calling a violation on something that just looks bad. If a player muffs the ball, is un-coordinated enough to not be able to pick it up right away, and three or four steps are taken in the process, many officials still call the violation (travel, double dribble, whatever). Everyone in the gym will nod their head in agreement with the call, but it would be a wrong call. The same pet peeve holds for the "high dribble" violation.
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