You hear coaches teach students, turn your hand when you punch. Rotate your hand so your thumb faces down at the end of the punch. Why? It rotates your shoulder so it covers your chin. It forces you to turn your waist, so if your feet are set it creates a stretch. You can verify this easily, find the hand rail on a stair case, or the stick of a broom, or any long pole. To get that last little bit of reach, you'll see that you have to turn your hand in order to stretch. If you turn your hand thumb up you see that you're fighting yourself, and you cannot stretch. If you instead turn the hand thumb down you see you can stretch just a little bit further. That stretch originates at the waist, that little stretch is like a scissor jack because it is using the linkage of your waist shoulder and elbow to multiply force. Furthermore, the effect goes both ways, if turning hand down is extending, then turning hand up is compressing. Again you can easily verify this yourself, if you rotate your hand as if it were in a tube, if you turn the thumb up, the leg under your hand becomes loaded, and the opposite leg unloaded. If you turn thumb down, the opposite leg becomes loaded. The load is a result of the waist, shoulder, and elbow, linkage pushing against a fixed point. Now you may be thinking, uppercuts and hooks are thrown with the thumb up, doesn't this invalidate everything you've been saying? Especially if you are using the opposite leg to generate power for those shots. To that I say, we have 2 hands and 2 legs, just because you're not focusing on your guard/power hand doesn't mean it suddenly doesn't exist. If you have a relationship on one side of your body, then it stands to reason that the relationship also exists on the other side as well. Therefore the rotation of your guard hand plays a role in throwing hooks and uppercuts, just as much as the punching hand. If turning your tumb up/outward causes compression, and down/inward causes extension, then to throw good hooks and uppercuts, we still have to follow the rules of body mechanics. The guard hand has to compensate for the thumb position in the other hand. If you're throwing a hook with the thumb up, the guard hand needs a bigger compression twist to compensate, otherwise its a weak hook. Likewise with an uppercut, it's all about where your guard thumb is in relation to the hand throwing the punch. You are balancing loading on the leg by rotating your hand. Again you can easily verify this, if you have a scale, put one foot on the scale, the other off it, and rotate your hand around a fixed axis. You'll notice the weight on the scale changes as you turn your thumb, increasing as it turns up/out, decreasing as it turns down/in.