Because if you gain AP from beating just one other character, you advance relative to everone else. What this means is that I can seem to get ahead of one character by doing well against another character. It gives a lot of incentive to just attack the weakest character. With no transfers, then no matter how well you beat the slowest guy you still have to compete directly with the fastest guy without any advantage from the other contest (except not having lost).
It would work with transfers too. But I've never really seen the advantage to transfers. They only serve to make contest go for a potentially infinite length. Which is sorta interesting, but not really worth it, IMO. In any case, in this particular case I think that not using them makes the results somewhat more intuitive.
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