Anyway that game didn't last.... The main reason I use stats is for the hp, as you can see from the items I tend to hp stack. It addes a little more hp that makes me last just a bit longer in battle, take another shot from a tower, cast one more fireball, etc.... I am not saying stat increases are a better choice than aura but that its simply viable.
I personally use Aura over stats almost every game. I will use stats periodically when I play TB for a while and post the results if the game last longer than this one since you cannot clearly see the benifit.
I just feel that the benefit of HP is so much easier to quantify than run speed that it's deceptively appealing. Say you do eat a fireball, spit, or whatever and escape with 5 HP because you got 400 HP from stats, that's easy to attribute to your skill choice, but getting out of melee range two seconds sooner or getting back into range in time to fireball someone escaping into towers because of the run speed is sometimes difficult to attribute directly to the run speed but still immensely beneficial.
On a personal level I can see the appeal. I wouldn't do it myself, but I can see how someone else might. However fire TB lacks attack the speed debuffs, interrupts, snares, and stuns which other DGs (namely frost TB) bring to the table and he's only got one ability to make up for it: Fire Aura.

When you've got giants on the field running and swinging 15% faster it's a really big deal, and it's an even bigger deal when your team converges in a 3v3 and up and your rook can actually outrun someone or your UB becomes totally inescapable because of that run speed.

I dunno, I just think that without Fire Aura a fire build is extremely one-dimensional and less of a benefit to a team than pretty much any other spec or even DG. I don't mean to say fire TB isn't good, because if he could autoattack correctly I'd play him constantly, I just mean that fire TB without fire aura is like UB without foul grasp.

 

 

I guess what really got me going is that you ended up picking up Boots of Speed in that replay you linked. Those boots cost 1k gold and eat up an item slot. If you had two points of fire aura you could have just gotten footman's sabatons for nearly identical health, saved 400 gold, and given your team 10% run and attack speed... and that's assuming you're on a budget which won't allow you to get an even more powerful item than those boots.

I realize that's not a completely fair comparison because you got them later in the game than you did stats and the early HP matter more than late HP, but I still feel the team and reinforcement benefit outweigh it.

 

Lastly lemme highlight that the aura affects reinfocements and reinforcements really do more damage than most people seem to think. For example priests do 200'ish damage every single hit to towers and 20'ish to DGs. One nice thing about TB is his capacity to clear out a creep wave instantly, allowing reinforcements to focus fire DGs, and that can end up being hundreds of damage that an enemy DG might not expect to take.