Achromalia wrote:
[p/60] = points per hour
Well, you're sort of right.
Taking the first-degree Taylor Series of the equation for score posted on the first page with a = 3600 seconds (1 hour):
This can be simplified further:
.
This estimation (A.K.A. linearization) shows us that for 3600 seconds, 60 points are earned. 3600 seconds = 1 hour, so for 1 hour, 60 seconds are earned, so the estimation is 60 points per hour, or 60 p/h.
Keep in mind that this estimation is good only for times around 1 hour. From 0 hours to 1 hour, the estimation holds pretty good, as there is only about a 7-point difference max. It holds good for two hours as well, ad there is only an 8-point difference between the actual function and the estimation. However, for three hours, the difference between the two jumps up to about 20 points (too much for an estimation, IMO), so in that case, either a more accurate estimation is used (a 2nd degree Taylor polynomial), or you can just use the original formula. Of course, almost no one ever gets to three hours, so the estimation of seconds/60 or 60*hours works pretty well most of the time.
Damn, I absolutely love calculus.