Math help with gear sizing (not what you think)

[one piece crank]

Goal: I ride coaster brake on my BMX bikes and want to play with the backpedal (brake) engagement for ramps.

When you backpedal a coaster brake, the reverse cog direction drives a clutch that expands the internal brake shoes. The hub has a fixed amount of rearward cog rotation. The amount of chain travel however, is directly determined by the chainring and cog sizes.

So, the basic question - what is the effect on backpedal chain travel from the following,

1. Increasing the size of the front ring.
2. Reducing the size of the front ring.
3. Increasing the size of the tear cog.
4. Reducing the size of the tear cog.

There is a subtle correlation between the amount of rear pedal travel and resulting brake output. And honestly I’m not sure if I want to increase or reduce it.

I’m currently riding 25Tx14T.

 

[knobbyhead]

I'm sure it's like going forward. Bigger gears turn the rear wheel further and visa versa.

So 1, 3 decrease and 2, 4 increase rear pedal travel

 

[sandman]

At first I thought it wouldn’t change anything because the brakes are internal and rely on the cog moving the worm gear. No matter how many teeth on the cog it’s still a 1:1.
But after thinking of all your configuration's, I think it may change how it feels to your cadence. And that was or is your question.
Just to be clear, the 1:1 is from the cog to the worm. The length of the thread is where the delay comes from.
So no help from me.