1/ Crediting Sir Issac Newton here, this thread will hopefully clarify the role and importance of the lower half in the throwing motion

First Law: Inertia --- an object will continue in a constant state of motion (or rest) unless an external force is applied to it

2/ Enter the lead leg block. The lower half is projecting the pitcher's center of mass down the mound and in order to stop the center of mass continuing to travel, there must be an external force applied to stop said constant motion. The faster the motion, the more force required

3/ Leading us to the Second Law: Acceleration

Simply put, F=m*a

The amount of force imparted on the ground is directly proportional to velocity in which the athlete is moving down the mound, and the mass of the athlete.

*disclaimer: mass and weight are not equal. don't be fat

4/ Third Law: Reacting Forces

Every action has an equal and opposite reaction. As each segment decelerates in a well sequenced throw, the subsequent segment will accelerate until finally, that last segment is not attached to the body (aka the ball)

5/ This is seen as optimally or efficiently producing ball velocity given the athletes size and mass

Enter the Impulse, Force x Time

The one constraint of all field sports is time. If you can manipulate one or the other, that effectively captures the lead leg block

6/ By either increasing raw force applied (strength) or lengthening time which force is applied (power or positional) that is the most effective way to capture energy from the ground to transfer up the throw