It's well known that the legs generate most of the power in your punches.
What are the most important leg muscles for power, and what is a recommended routine to work them out using resistance or functional training.
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The proper power association in punches is not just a leg muscle, but the pivoting of the body behind the punch. This being the case depending on which side you are using most of the leg muscles are utilized, but the leg muscles themselves aren't the powerhouse, but the pivot torque power is what contributes to the force of the punch.
That being said if you want to strengthen your punching then practice weighted pivots to evenly strengthen all the muscles related to pivoting instead of focusing on a single leg muscle. You can do this in a number of ways:
I'm sure other people have exercises as well, but the goal is the pivot strengthening so that when you pivot your full weight of the lower body muscles gets put behind it. Anything that helps the body move in the motion you are pivoting and adds resistance without hurting yourself is a good choice.
I found the short answer is : "your back foot big toe"
This is because a properly thrown technique is helped at some point using your back foot toe to move your body forward while delivering a punch or kick.
So any explosiveness training to propel your body forward would work. Sprinter block starts, leaping mobility, tyre work ... I found forefoot striking running really improves ankle and calf strength and mobility as you're keeping on your toes all the time.
also try cutting the big toe out of your training and see how much difference it makes. this is really obvious during an injury on the back foot toe.