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How long does a UHC season take?
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Well, a comment by GenerikB in his S11E01 video inspired this quick bit of back-of-the-napkin mathematics. How does the running time of a UHC season scale with the number of participants?

Assuming a modified predator-prey model (in UHC there is no distinction), we have

dN/dt = -gN2

where g is an unknown constant depending on skill level, map size, team size, etc. This equation has solutions

N(t) = 1/(gt 1/N(0))

Sample graph here, with values chosen to fit season 10. Now let's set N(t)=1 and solve for the final time T:

T = (1-1/N(0))/g

This means that practically no matter how many players you choose, a UHC season will never run longer than a certain maximal length, which is 1/g.

Based on season 10 we can estimate g ~ 2.9ยท10-3 min-1 giving season 11 an upper running length of 330 minutes, which is about 17 episodes, only ~10% longer than season 10. Of course this is a very rough estimate, and the model is particularly poor once N gets small. The model also assumes no death to PvE, which is clearly false, but in the later seasons probably negligible (last season there was only one PvE death).

Still, those who claimed that a season running length does not depend very much on the number of players in the game were probably correct. Beyond about 7-8 players the running time is practically constant.

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