Read Scrap's post (again) then think about WHERE you are hitting....

If you hit with a left hook to the head you are likely going to have to come over his shoulder (or arm) AND want to get a straight (not glancing) blow into his head -- having the elbow up, and forearm perpendicular to the target surface is usually going to be more efficient, but....

Sometimes you can't get it all the way up to a level forearm or the target may not be a vertical surface (like the side of the head) so you do the best you can (in the first instance) aiming to get it up, and you adjust it appropriately (in the second case) and hit directly into (perpendicular) the target shuch as hitting up under the ribs for a body shot hook to the liver.

Shovel hooks (are not uppercuts and) hit almost vertically upward with the elbow down on or near the hip so they represent the extreme of the elbow being low.

See Dempsey's book for a good explanation of (various kinds) of hooks.

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HerbM