I consider offhand the worst of all possible alternatives. Probably have shot about a third of my big game animals that way, mostly because I didn't know any better for a long time. I normally carry shooting sticks when walking open grassy areas, and if I don't have them find a fence post, tree or rock, and if I can't find one of them I sit, and If its too wet to sit I kneel.
If I feel I have to take a running shot I do it offhand. And I have killed a bunch of stuff when it was running. But I seldom choose to shoot running game any more.