Theory Breaker: Building a Bigger, Better Basher

I've been wanting to write about Spirit Breaker lately. I don't know why. Something about the hero's caught my attentions and I can't get it out of my mind.

Oy. This isn't the kind of site for you to work out your weird cow fetishes.

... I'm not even going to dignify that with a defense.

Cause you don't have one.

Annnyways, my original plan for this article was to see how fast you'd have to get Spirit Breaker attacking in order for you to guarantee that, once Greater Bash came off cooldown, the Pseudo-Random Distribution would be primed in your favor to get you another one immediately. So I loaded up a Bristleback with 6 hearts, gave Spirit Breaker five Moon Shards and a 6th eaten one, and had at it.

The result was that the Pseudo-Random Distribution isn't calculated at all while Greater Bash is off cooldown. I was disappointed at first, but ultimately I find this result kind of satisfying. It means that attack speed items can only help Spirit Breaker up to a certain point, and validates some of the more theory-crafty ideas I've been having about the hero as of late.

Oh god. Don't tell me this is part 1 of a 2 parter.

Haven't decided. Maybe it will be, maybe I'll write a proper guide. Most likely, though, I'll end up shrugging it off as a stupid notion and canning it. But keep an eye peeled, dear reader!

Don't ever use 'dear reader' again. That's weird.

Shush. Anyways, in the wake of my quote unquote failure I was left with a horrendously abbreviated blog entry and a hankering for some sweet, succulent space cow theorizing, and was trying to figure out how to salvage my perma-bash idea. Then it dawned on me: the only way Spirit Breaker could ever truly 'perma-bash' someone in the first place is if his attack speed and the cooldown of Greater Bash synced up perfectly, ensuring that an attack would land exactly as another bash was available. With THAT in mind, we can do some interesting maths, and perhaps even fine-tune an optimal Spirit Breaker item build to boot! Maybe.

First off, the most important thing we'll need for this calculation is the tried and true attack time formula, given here:

Attack time = BAT / [(100 + IAS) × 0.01]

BAT is the hero's Base Attack Time, for those of you who are less familiar with the mechanical aspects of the game. For most heroes this is 1.7 but Spirit Breaker is a special child, having the second lowest in the game at 1.9. Doom beats him out, if you're curious, at a BAT of 2.0, though his attack range is 150 where litereally every other melee hero's is 128 so... I guess that makes up for it? Maybe?

His reach is lo... no, that's Shadow Friend. Why the heck?

I don't even, bruh. Anyways, knowing SB's BAT, and knowing that our desired result for his attack time is 1.5, gives us the following equation:

1.5 = 1.9 / [(100 + IAS) × 0.01]

With a bit of mathing and flipping and flopping, we get this:

1.5 = 1.9/1+.01*IAS ; 1.5 + .015*IAS = 1.9 ; .015*IAS = .4 ; IAS = 26.66

That's it?

Well, that's the first interval, yes. Keep in mind that getting MORE IAS then that will cause a desynchronization, which we'll get to in a bit. For now, let's say you've maxed Greater Bash by level seven, and now have the ability to get bash off cooldown before the stun from the first one is up.

Spirit Breaker's starting agility is 17, and his agility gain is 1.7. This means that without items, his agility at level seven is 28.9 meaning that, oh snap, even if we haven't bought a single item on Spirit Breaker we're already desynchronized. Well that was quick, wasn't it?

Dang. So what's the next interval?

Simple enough to find out. The next time synchronization happens is at two attacks every 1.5 seconds, meaning that the formula becomes:

.75 = 1.9/1+.01*IAS ; .75 + .0075*IAS = 1.9 ; .0075*IAS = 1.15 ; IAS = 153.33

That escalated quickly.

Yeah buddy. This all of a sudden becomes a non-trivial goal: can we reasonably reach 153.33 IAS by level seven?

Well, let's see, we stated earlier that his natural agility would be 28.9 at this point, meaning we only have to make up an additional 124.43 IAS, which still seems like a lot. Gloves of Haste by themselves will add an additional 20 to that, and building a Magic Wand will gives Spirit Breaker 4... which means we'd need a cheap item that gives +100 attack speed, but that's.. oh... oh god...

MASK OF FREAKING MADNESS. MASK OF MADNESS SPIRIT BREAKER IS MATHEMATICALLY LEGIT.

I... I did not expect this coming into this blog post. It seems so wrong, but the math doesn't lie. If your goal is to bash someone again and again and again as early as possible, you pick up... Mask of Madness. Without finishing Power Treads. But getting a Magic Wand, because sustain is important.

This, of course, becomes immediately de-synchronized once you finish said Treads or level up from killing someone, but for only 2765 gold you can keep someone truly and fully locked down if RNGesus smiles fondly on you.

But enough about that: lets talk end-game, yeah? Level 25, both bases on their last legs, and one solid pick-off on the enemy carry will net you the victory. What then? Well, Spirit Breaker will have gotten 10 levels of stats giving an additional 20 agility on top of his 1.7 per level, meaning that his base agility will be 62.5. This means that if we wanted to shoot for our original IAS goal of 153.33, we'd only need another 90.8 attack speed.

There are number of ways we can try and approach this: assuming we get Power Treads on Spirit Breaker and leave them on strength, that gives us 30 towards the total right there, leaving ~ 61 to go. We can actually hit this pretty easily using almost entirely items from Valve's recommended items list: an Assault Cuirass will give us 55, and turning that Stout Shield we got to survive the offlane into Poor Man's Shield gives us our final 6. Boom. Headshot. Charge that Spectre, and in God may you bash.

That is one poooor Spirit Breaker, though.

Yeah, that's the thing: we're level 25, and it's likely almost an hour into the game, and Spirit Breaker has just ONE major item? That's no good at all. His net worth looks a little better if you replace Treads with Boots of Travel and give him a Silver Edge but... still. Ain't no-one killing a six-slotted Anti-Mage before he can blink out like that. We need to go yet another threshold up, and attack THREE times every 1.5 seconds.

.50 = 1.9/1+.01*IAS ; .50 + .005*IAS = 1.9 ; .005*IAS = 1.4 ; IAS = 280

With the 62.5 natural agility we mentioned earlier, this means we need a total of 217.5 additional attack speed from items.

Moon Shard?

Yeah buddy. With Assault Cuirass + Silver Edge giving 85 attack speed and Moon Shard giving 120, we get 205 IAS right off the bat. This leaves us with a gap of 12.5 which is fillable by... some combination of two items. Aghanim's Scepter and Scythe of Vyse will both give 10, and Vladmir's Offering and Crimson Guard will both give two, so pick one from each category and you're set! A super-useful utility Spirit Breaker that can also perma-bash if they get lucky enough, it doesn't get much better than that!

You know... that actually doesn't sound too bad... and is like, really in line with how people already play Spirit Breaker.

I know, right? Even without running the numbers, players gravitated towards building the hero this way. It just felt right, like they were getting the best results out of it. And now we know why! The underlying mathematics behind it are kinda beautiful, actually.

This isn't the place for your weird math fetish either.

... shush.

Safecyn, signing out.