Brakes are all about the mechanical advantage of the entire system, brake and lever as one. For a rim brake, the mechanical advantage refers to the amount of force that the pad places on the rim as compared to the amount of force applied to the brake lever. This can also be thought of as the amount of movement at the brake lever as compared to that of the pads. For example, a very powerful brake will have pads that move a relatively small distance as compared to how far the brake lever moves, and will exert much more force on the rim than the hand squeezing the brake lever.
At the brake end of the system, road calipers and cantilevers have relatively low mechanical advantage (the brake pads move roughly the same amount the cable has been pulled) while V-brakes have a high mechanical advantage (the brake pads move much less than the amount of cable pulled). A low mechanical advantage brake caliper requires a brake lever with a high mechanical advantage to work properly, like a standard or short pull version that pulls a small amount of cable as compared to the movement of the lever. High mechanical advantage V-brakes require the extra cable pull and lower mechanical advantage of long-pull levers.
Mix and Match?
The wrong lever and brake combination isn’t always obvious, and can be counterintuitive at first. Pairing a long pull lever with a cantilever brake gives a very firm feeling brake in the workstand, but on the road it will be hard to pull the brakes hard enough to stop the wheel due to the low mechanical advantage of the entire system. On the opposite side of the spectrum, V-brakes and standard pull levers will give a very spongey brake lever feel but will in reality have too much mechanical advantage to work properly. Even though the mismatched system has a lot of mechanical advantage and power to spare, the brake pads will need to be so close to the rim that even when fully retracted they may still make contact. Otherwise you may find that you run out of lever pull before the pads fully contact the rim—in either case the brakes will not work as they should.
There is more to the eventual feel and stopping power of brakes than matching the proper lever and caliper, but this is a vital first step. Different levers and calipers have different braking attributes based on design and manufacture, and sometimes require some experimentation to find the combination that feels