In the footage of the young Mike that's around, he does a lot of leg strengthening during his shadow boxing, it was integral to his style that he'd dip or rotate low to avoid a punch on the way in and springing up with a hrad counter.
I used to do weighted squats in the gym when I used to play rugby, but I belive my legs are much stronger and more coordinated now since moving to a more running based training with intense shadowboxing. IMO doing reps of 10 (or whatever) heavy squats will get you conditioned for just that, 10 heavy shoves at a time. If your movement around a ring and slipping and punching involves a lot of knee bends, then the repetitions you require are in the 100's!!
When I started boxing, I skipped predominatly using the calves to bounce over the rope, and my footwork would be the same. Eventually I figured out that there was no coordination between my footwork and punching. I remedied this by initiating the bounce from my thighs (bending the knees) and eventually felt in more control of my body through the hips and torso. While actually boxing I don't dip my knees much obviously, but I find exxaggerating the motion during a few rounds of shadowboxing and skipping have increased the strength in my legs.
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