Regarding gain ratio, I have two bikes with two different length cranks; one 170mm and the other 175mm.
The 175mm crank goes on a fixed gear mountain bike that I ride on ice and in deep snow.
The Ice Bike has big fat knobby studded tires and ultra-low gearing...48 gear inches.
I find with the 175mm cranks that I can't spin very fast, and if I try to spin fast enough to make up for the low gear inches I quickly get tired.
Comparatively, my good weather bike has skinny high pressure no tread tires and, with the 170mm crank, I can spin very fast and I don't get as tired as quickly.
Some folks who want to spin super fast go to 165mm cranks, and just that 5mm difference makes it so much easier to spin.
However, with each step down in length, one gives up leverage, or torque, and, subjectively, it feels harder to spin against resistance.
If one has a road bike frame converted for fixed gear, then, because of the lower bottom bracket of road bikes, it makes more sense to go with the 165mm cranks in order to avoid pedal strikes in turns.
I think, though, for most people of normal stature riding on a dedicated high bottom bracket fixed gear frame, the 170mm cranks represent the best compromise, all things considered.
I would avoid the 175mm cranks on a street fixed gear bike, not only because of the increased probability of pedal strike, but because of the increased difficulty in spinning fast.
So, in response to a question about gain ratio, I have discussed crank length because crank length changes gain ratio, with shorter cranks increasing gain ratio (and perceived effort) and longer cranks decreasing gain ratio (and perceived effort).
Remember, gain ratio refers to the number of inches the bike travels over the ground for every inch the pedal moves, so that a gain ratio of 4.5 means the bike moves 4.5 inches for every inch the pedal travels.
Notice that gain ratio will increase from 4.5 to 4.6, 4.7 or 4.8 with an increase in crank length from 165mm to 170mm.
So, go with 165mm or 170mm cranks on a street fixed gear bike; 175mm cranks on a fixed gear mountain bike; and, 165mm cranks on a dedicated track bike.
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The above said, many formulas exist for determining crank length from the rider's body proportions.
Ignore these formulas when thinking about a fixed gear bike.