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Owing to the recent rash of tantrum amumus recently, I have decided to run an analysis to figure out which one is really better.
Assumptions: Amumu goes wolves blue 9/21/0. magic pen, armor yellows and quints, boots + 3 pots, no help.
Assuming these specs, amumu gets 21.3 armor and -6 dmg from jungle creeps.
Wolves don't have magic resist, so amumu will be doing true damage to them, except the giant wolf, which he will be attacking for a -15 MR reduction, resulting in a 13% damage increase.
The total base damage of the wolves 14+14+24-6 = 46*1.25 crit modifier = 57.5 damage *0.679 atk speed for 39.0425 dps.
If you start tantrum, you get an extra -1 damage modifier on the base damage, resulting in 38.19375.
A tantrum mumu does 77.8 dmg per tantrum to small wolves, and 87.914 dmg to big wolves with a base cd of 9.6. With the passive cdr on tantrm, he 2.037 second reduction every second, meaing the real cd is somewhat lower, as it decreases at a rate of 3.037 second every second rather than one. 9.6/3.037 means the real cd is around 3.16. Assuming mumu attacks the giant wolf with his base dmg of 50.8, he deals 87.914/ 3.16 + 50.8= 78.62 the big wolf, and 77.8/3.16 ~25 dps to the small wolf, so it will take roughly 550/78.62~7 seconds to kill the big wolf, and then he still had to bludgeon the small wolves to death
Meanwhile, the wolves are have dealt 38.19275 dps * 7 seconds = 267 dmg to mumu.
If Mumu takes despair first, he deals a flat 8 magic damage to nearby enemies, + 1.5% max hp, meaning he deals a pitiful 12 dps to wolves and 16.25*1.13+50.8 = 69.1625 dps to the big wolf.
And so, I must conclude tantrum is better for the wolves.
But is it better for the blue?
Well, the greater hp from the blue means that despair actually does (1372*0.015 +8)*1.13+50.8 = 83 dps to the blue, which is a mere 5 extra dps above tantrum mumu.
tl;dr, start tantrum on mumu.