Fascinating. I've never heard of a gear ratio measurement for a pedal.

You can't have a gear ratio with only one gear. You need at least 2 for a gear ratio, i.e. 2:1. To calculate a gear ratio, you count the teeth of the gears and divide the driven gear by the drive gear. So if the driven gear has 45 teeth and the drive gear has 10, you have a gear ratio of 4.5:1.

You can measure cam rotation vs pedal depression, but this is the downward travel of a lever against the rotation of a pulley. It's a measure of distances. I see what Skilas is getting at, I just wish he would stop referring to it as a gear ratio as it is not. It's called mechanical advantage. For example, the footboard travels downward 1". A round cam with a diameter of 1.5" has a circumference of approximately 4.75" (for simplicity). If that cam rotates 120 degrees for that 1" of footboard travel, you have a mechanical advantage of 1.25:1. Another way to think about it is the cam travels 1" for every 0.8" of footboard travel. This is the simplest form.

If you really wanna complicate things, for an accelerator cam you have to calculate distance of footboard travel for each profile of the cam to get the true number. Sure you can do like the round cam, but that won't be correct since diameter vs travel changes as the cam profile changes.

To make things even worse, since the footboard is fixed in it's rearward location, the chain/strap/linkage doesn't pull consistently straight down. As the footboard travels downward, the front of it gets closer to the head. This creates an arc that the chain/strap/linkage follows, and this is the distance of travel you would actually measure for footboard depression. So now you must measure footboard length, double it and multiply by pi to get this circumference. Next figure the degree of travel of the footboard. This number divided by 360 will give you what you divide total circumference by to get the distance. So, again keeping it simple, if the total circumference of the footboard when allowed to rotate 360 degrees is 30", and your footboard travels 12 degrees, that's 1/30th, or 1" of travel.

So between a cam with one or more profiles, and footboard travel in an arc in relation to cam profile(s), you can calculate mechanical advantage. If you really want to. Or you can let your foot figure it out, as most people won't want to do or even understand the math and physics, even if it is presented to them on the box.

And yet a number still tells us nothing. You can still get the same result for two completely different pedals. Just like 3x4=12, so does 2x6, and 1x12, and 0.5x24.