Why are lower gears the opposite of what they’re supposed to be numerically? Asking for a friend.
It seems counterintuitive, and it is confusing to beginners, but lower gears are numerically higher than tall gears. In other words, a 4.56 gear is lower than a 3.07. Why? The numbers represent the number of rotations the pinion (attached to the driveshaft) has to make for every revolution of the ring gear (attached to the axles). So with a 3.73 gear, the pinion (and therefore the driveshaft) has to rotate 3.73 times for every rotation of the ring (and therefore the tires).
Why is this important? It has to do with torque multiplication. The more rotations the pinion has to make, the less effort it takes to rotate it. So, it has to spin more but it takes less force to do it.
You could also look at it from the opposite direction. When we increase the diameter of the tires on a vehicle from stock, we increase the tires’ leverage on the axle (and ring gear) because the contact patch with the ground is farther from the axle than it used to be. By swapping to a lower gear ratio, we compensate for that longer lever by increasing the number of times we have to rotate the driveshaft. It also means that the tire doesn’t travel as far with every driveshaft rotation, but it takes less effort (force) to do it.
The ratio of a gearset is dictated by the number of teeth on the ring-and-pinion gears. In the case of most stock gear and some aftermarket ones, tooth counts will be stamped on the side of the ring gear. You simply divide the numbers to get the ratio; e.g., 42 divided by 11 is 3.73.