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@Rik_Van_Looy
I don't think it's an arbitrary choice.... In the old days when you purchased cranks in person at a decent LBS they'd tell you what size you need by looking at your legs.
Presumably long-legged and big-footed types need longer cranks than their dinkier counterparts - I don't know if there's an algorithm or even a rule of thumb.
With a proper track frame you should be able to run the same cranks as your road bike without grounding a pedal - if your running a road conversion you probably want the shortest cranks you can get for road-rash related reasons described above...