Here is shimano saying exactly what the free stroke does, and more importantly how to set it – it’s not as simple as just turning the screw!
Shimano: Free stroke is defined as stroke of the lever before the pads start touching the rotor. The free stroke screw simply changes the starting point of the master cylinder piston. If the screw is all the way in, the master cylinder piston will be all the way in, and the free stroke will be the shortest. Turn the screw out a bit and the master cylinder will start further out. Because it has to travel further before it closes off the reservoir port, the free stroke is longer. In the picture of the clear brake posted above, the free stroke screw is turned all the way in.
I’ll admit that it is confusing because it seems to have the opposite effect when you turn the screw. The stock position is all the way in and that’s where most people like them. If you do nothing but turn the screw out, the pad contact point moves out. So it feels like you’ve made the free stroke shorter. The problem is that turning the free stroke screw also effects your initial reach adjustment. The pad contact point came out, but the starting position came out more. So it’s always at least a three-step process. First set the reach adjustment so that the lever starts where you want it, then adjust the free stroke screw to get the amount of free stroke you want, then turn the reach adjust knob to put the lever back where you wanted it.
I would personally like to see a lever that allows for an even shorter free stroke adjustment but as it is, when the free stroke screw is all the way in, the master cylinder is right up against the reservoir port. So really the only way to give people less free stroke would be to sacrifice clearance between the pad and rotor.