Wednesday, 30 October 2013

Multiplier Theory: Stat Synergy explained with Polytopes

(Would like to start out apologizing for the somewhat awkward terminology used, I wanted to be clear, and the day-to-day terms for these things are very ambiguous in English)

The Concept
Imagine a quadrate. The length of one side is your AD, the length of another is your ASPD. The area of the quadrate is your DPS. The best ratio between circumference and area for a quadrate is found when all sides are equally long, i.e. when it's a square. So when you have a lot of AD, more ASPD gives the quadrate more area than AD does. Now, make sure you understand this metaphor, as I'll be using it a lot.

The two lengths of the sides of the quadrate is what I call a "multiplier" or an "axis" in mechanics lingo. And they're very important for understanding scaling and stat interacting. When there are two multipliers involved, it's a quadrate. Now, if I add Crit to it, what happens? It turns into a hexahedron, going from a 2-dimensional shape to a 3-dimensional shape. Now, the DPS is the volume. Once again, the longer the other sides, the better the shorter sides get.

The problem with this metaphor is that it gets fairly abstract once we add flat percentage damage increase like those from masteries or various abilities. Now it's the 4-dimensional equivalent to the 3D hexahedron and the 2D square. So it gets harder to visualize. I'll be sticking to 3D in the examples of this post though.

Concrete Examples
Lets look at the hexahedron with AD, ASPD and Crit as the length of its sides. How does stat extensions interact with this? Like Malphite's Shield scaling off a percentage of your health. I've been met with a lot of skepticism when I say it scales just as well off armor and magic resistance. It actually scales off EHP - effective health points. The defensive equivalent of DPS.

What about Infinity Edge? That multiplies Crit damage much like Malphite's shield multiplies HP. Well, the thing is, Malphite's shield always applies, it directly multiplies EHP. Crit damage is only applied to the Crit part of your DPS. So if you had 100% Crit, then yes, the Crit damage part of IE could be considered a full multiplier. Otherwise, it's worth 50% of your Crit Chance.

What about an item like Deathcap, that multiplies the main damage stat of AP which many considers the direct equivalent of AD. But it's not, because AD carries auto attack damage comes entirely off one polytope, where all the stats interact with eachother. AP only interacts with the scaling of abilities, not the base. So while a 10% increase in AD is a total auto attack DPS increase of 10%, an increase of 30% in AP is not 30% more ability damage dealt.

And that is the mechanical explanation of why the AD carry has the highest damage scaling. Almost all of the stats interact with each other in one polytope with many effective dimensions.

This is also why on hit effects, such as the one on BoRK, are less good than they seem. Especially when it first came out, BoRK's on hit damage was often compared directly to the AD of Bloodthirster. But that's not the case. BoRK does not scale with Crit or abilities, but AD does. It's the same with other on-hit effects and abilities.

There's a reason the timeless Zerker Greaves, IE, PD, LW build is so damn good on ADCs. It's two ASPD items, two AD items, two Crit items, an ARP item and a Crit Damage item.

No comments:

Post a Comment