In Modern boxing the power is definitely related to the hips but it was not always the case...the falling step was used in the past for incredibly powerful straight punches from the lead and rear hand.
Let's see what Jack Dempsey had to say concerning the jab and whether you should throw it as a powerpunch or not:
“I use the expression “left jolt” instead of “left jab” because I don’t want you to confuse the type of straight left you will throw, with the futile straight left or “jab” used by most current amateur and professional boxers. Most of them couldn’t knock you hat off with their left jabs. With their lefts, the tap, they slap, they flick, they paw, and they “paint”. Their jabs are used more to confuse than to stun. Their jabs are used as shuttering defensive flags to prevent their poorly instructed opponents from “getting set to punch”. A good fighter doesn’t have to “get set” He’s always ready to punch. Some of them use their jabs merely to make an opening for their rights. And that’s dangerously silly, for the proper brand of feinting would accomplish the same purpose. With but a few exceptions, they “do not use the left jab as a smashing jolt that can be an explosive weapon by itself” - that can knock you down or knock you out”
“There are two reasons why the left jolt is a rarity in fighting today. First, nearly all current boxers launch their jabs with the non-step shoulder whirl. Secondly, nearly all have been fed the defensive hokum that it’s less dangerous to try to tap an opponent with the left than to try to knock him down with the left.
“Concerning that defensive hokum, let me say this: Any time you extend your left fist either for a tap or for an all-out punch, you’re taking a gamble on being nailed with a counter punch. And the sap who uses “light stuff” - tapping, flicking, etc, - has his left hand extended much more often than the explosive left-jolter, who doesn’t waste punches - doesn’t shoot until he has feinted or forced his opponent into an opening. It’s true that you can “recover” your balance more quickly after missing a tap than after missing a hard punch. But it’s also true that an opponent who is defending only against taps and slaps will be much more alert to counter than an opponent who is being “bombed”
“My advice to all beginners is this: Use a light jab only in one instance - in the so-called one two punch - when your left fist strikes the opponent’s forehead to tip his head back, so that your immediately following straight right can nail him one the chin."
