Master Cylinder Bore?

So the 15-16" gives you more pressure?

Yes, gives you more leverage by not having to push so much fluid at one time.
Gives just a little bit longer of a stroke on the pedal.

Like the Lever and The Fulcrum

LeverFulcrum.jpeg

The closer you put the Fulcrum (small rock) to the Big Rock, the less effort it takes on your part to do the work.

The Lever stroke increases more as you move the fulcrum closer to the big rock.

Same theory with your manual brake system.