If you think 800 HPs is worth the loss of mana from BotS, you're not casting enough.
Fire TB will be able to hold a lane much better than a BotS TB. With BotS you have to accept the fact that a lot of demigods will push you out. Now, you can flip that around pretty easily since BotS will let you push anyone else out given enough time (infinite mana).
But if I have a fire BotF TB and I'm standing on the HP flag and, say, Erebus comes to kick my ass I'm going to be able to hold it better with the extra 1000 hp (plus 100 larger monk heals) than I would if I were BotS. I understand once you get a helm the hp advantage drops to more like 500.
If you're on the mana side of Cataract, doing a BotF Fire TB is just stupid. I will completely agree. If you're fighting for the HP flag while your Oak is level'ing up on the mana side, doing BotF will help you hold it better.
I tried an AA build a long long while back. BotS and Gaunt of Brute for the +125 weapon dmg at level one. It starts out strong, but pitters out REAL quick.
This has been my experience as well. It's fun, it's really nice if you're laned against a general. But after first shop, you basically need to sell it to get your 400 gold back because that 400 gold is better put into a different item.
Agree, except that Fire Aura isn't more useful then Frost Nova and Deep Freeze together.
Frost Nova isn't effective 1v1. You just about lose more time than you gain until you get three points (level 2 you have a .4 second advantage for what that is worth). Many demigods have the means to dispel debuffs (Erebus, Sedna, Oak, Occulus) which hurts your DF combo (assuming you DF them as they are Frozen then they can't dispel the Frost Nova debuff but they can certainly dispel Biting Chill and the Rain of Ice debuff which comes out to -1000 damage or so with level 15 DF). Remember that for all of those but Erebus, they can do that to an ally and all demigods have access to at least 2 debuff removing items that they can incorporate into their builds.
At level 15 with just BotS (no helm) you have 3600 Mana. Your combo (including DF) costs 3615 (with regen you're fine, I think). This means that if someone comes up to you after just using one Rain of Ice to farm and BotS is on cooldown... you won't be able to execute your combination. If you /do/ get a helm, then you fall behind on the HP curve. (see argument above).
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Burst damage has advantages and disadvantages. It's great when you can see an enemy reach a magical number and finish them off in with your combination. But both Occulus and TB (without CoF and to a much lesser extent because of Fire->Ice AA buff) have a problem where if you just don't panic when they burst you you can do your skill cycles twice which can be enough to chase them off.
Remember that your "burst" also takes about 5 seconds to instrument and has two obvious abilities that can be interupted. Not a huge deal, sure, but it's enough for a monk heal which will be ~500 at that point in the game (half your fireball will be healed on impact as they approach and after you blow your load it'll be healing again). Also you blow both of your interrupts, which means if someone were doing crazy stuff they could pot in your face (unlikely, but for the purposes of theory crafting...).
Sustained DPS and tanking is more effective end-game when everyone is running around with 6k+ hp and quite possibly Orb of Defiance and Giants are smashing everything (more likely just your Giants 'cause you are TB. But don't dimiss Surged giants or Occulus ruining yours in turn).
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Again, I will stand on the opinion that DF is a fantastic ability when used against weaker players who don't notice the debuff pop-up. It's also great in 3v3 cluster-fucks because you effectively remove one enemy for 5 seconds which is enough to win the engagement.
However, until you invest 5 skill points into it (4.5 if you want to call Fire & Ice half a Fireball ability), it's an ineffective ability damage-wise.