Reviewing this guide again, I feel that this guide is too weak. Average mages do a ton more damage and can become more tanky than you and STILL do more damage.

What is the point of getting crit chance in masteries when you don't even HIT much?

Sunfire still sucks. Its weaker than usual, does help with weak amounts of tankyness, overall not worth it.

You still didn't change much aspects of the build.

Your jungle build of elixer of fortitude and 6 pots is still ****. Its like telling Fiddlesticks to go get that to jungle. Both of them uses their spells > Actually hitting.

Bandage toss at level 7 jungler? This means that you jungle all the way to level 7, or use flash unnecessarily to try and score a unlikely kill.

Note : You can save instead of publish, so it won't be shown yet. Then you can slowly work it out and tune it to perfection in your way.

Rylai is good, its like a perma slow with despair.

I always like to play Amumu aggressive in lane. Which means I try to start fights. Even if I can't, I make sure I have it ready ASAP to help my teammate.

By mid game, you'll notice you need to use your ulti alot. Many times because of CD problems my team got picked off on teamfights or we stall, usually badly, seeing they know we have problems.

Hope it helps.

I don't think you read the guide did you? I messed up a few things because I don't know how to make the guide properly. I'll redo the builds later, but Rylai's is not good on Amumu. There are no cooldown problems early game because you don't get into a fight every 18 sec before the bandage toss cooldown goes away. Please read the entire thing before voting down/commenting.

Your end game items include :
No boots (You said speed was impt)
2 extra items that aren't used (Boots/Sunfire)
An early game item as a replacement for Sunfire Cape(Sunfire still sucks, it gives poor tankyness and barely any damage) (Fyi, Aegis is useless that late. If you want to get it, get it early. Its better then and you/your team's damage increase suck late game)
Big cooldown problems early-mid game (18 sec for bandage toss. You need to up this since you don't get ionian boots)
2 Rabbadon's Deathcap (Its passive doesn't stack since its unique, and the fact that Amumu barely does any damage until full items, might as well get a rylai scepter/RoA early.

Hope it helps :)