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"Formula! Did you get the formula?!" (from a deodorant commercial)
Here is an excerpt from the "Physics of the Heroes World" reference guide (
http://homm3world.narod.ru):
CALCULATING THE NUMBER OF POINTS RECEIVED FOR A GAME IN HMM III:
POINTS = [200-(D+10)/(Z+5)+B+G]*R, where:
D - the number of days spent
Z - the number of castles captured
B - bonus for defeating all enemies (25 points) - however, if the map did not specify the condition "Defeat all enemies," this bonus will not be counted.
G - bonus for the Grail (25 points)
R - game difficulty coefficient (maximum - 2)
Moreover, in (D+10)/(Z+5), the fractional part is discarded, so the maximum is 500 points.
(I haven't been playing Heroes 3 as long as some, so I won't reveal my personal record. But there's something to strive for!)