Talk:Kassadin/@comment-31543294-20180716065407/@comment-28977071-20181102172110

Sry for a late response, I really wanted to respond when having enough free time and think this through carefully. My former post was indeed quite facile as I believed that there's not much to talk about, but this time I'm going a bit more into depth (still trying to not go extremely deep, maybe next time if this won't prove to be sufficiently enough..). As there are far too many points, I'd like to react to and I did not, I'm going to recite and respond to each passage one by one:

SchookingSkelYT: .., building magic pen is useless because of passive ,..

'Useless' ≠ 'not strong'. When building MPene clearly does something, the stat is not useless. The sentence is either an exaggerating rant or (and either way) false. SchookingSkelYT clearly stated in other posts that (s)he's sorta ranting and I temperately took the post as such, nevertheless I cannot agree with it being right.

Weedlayer: ∀

My opinion's still unchanged, I find this to be a perfect response. I cannot find a single flaw in the argumentation. Maybe I just wasn't looking enough though..

Gmboy324: ∀

A bit fuzzy reasoning imo, but not really the point of my interest. I believe that Gmboy324 didn't really understand your post, Double Slap, as you were referring to base values instead of current ones (which is imo both misleading and wrong). Which relates to my next point.

AnataBakka: ''yes, currently that makes no sense. What do you mean by "18 magic resistance Makes the MR boost. 1.18x"?'' ..

Here we go, another person confused with the comparison to unusual base values. Basically the sentence (s)he cited was exactly the reason of my own first response. Even though I got which stats were mutually compared, I didn't see a valid reason why to evaluate efficiency of buying something by comparing the result with initial state that ceased to exist long ago, instead of an immediate state aforegoing the purchase.

Kk, from now on it's just your points, Double Slap, that I'd like to react to. Having a different opinion than yours was also one of my reasons why I delayed my response until I had enough time to think a bit about the entire issue (and also trying to look at it from your perspective). You know that I quite respect you and your ideas, so if anything from what I'm gonna say would sound even a bit like sarcasm or mockery, rest assured that it was just an unfortunate wording and no offense was meant at all.

First of all, I'd really like to appreciate your approach with EHP. In the past I indeed looked at many problems, including this one, via such EHP models. Basically my entire personal generic approach to problem solving revolves around the essence of this. The abstraction, reduction of the complex system to its simplest form, by substituting anything takeable apart with its equivalent replacement, so that one can imagine the entire system in its full complexity in one's own mind at once. That's exactly how I prefer to solve problems and what your EHP transformation does. Hence I really like your approach. Our conclusions differ, however.

Double Slap: It's because you are thinking of the damage reduction percentages, which is largely skewed to rounding error, instead of EHP. ..

Do not mistake my usage of rounding for my inability to work with perfectly accurate expressions. I'm a fairly strong mathematician with technical skills by far surpassing needs of this wiki. It's just that I want to talk in a way understandable to a common wiki reader when I fall back to such simple tricks as rounding. My only reasons for rounding were you and my easy-to-read post.

Double Slap: ..Have you ever thought to yourselves, what truly is the essence of penetration?..

Yup, actually I did. A very smart idea imho, thumbs up. And I basically agree with anything about EHP you wrote in that post.

Double Slap: .. ''then what is making the mere subtraction of this susceptible to a nonlinear rate? The answer: it isn't.'' ..

Except for this. My answer: the other variables. MPene & EHP isn't an isolated system but a part of the game environment as a whole. As this is my main concern, more on this later.

Double Slap: .. I implore everyone to stop using the percentage graphs that are bounded from 0 to 100%. ..

Np with that. The true truth is an invariant and shall demonstrate itself within any correct system transformation. EHP is such a transformation.

Double Slap: .. It's simply an issue with trying to set inflexible graph boundaries to represent reality.  ..

Cannot really agree on this, but nvm, I don't think that it really matters for the sake of this discussion. Just a remark, math's prefectly fine with'em and models the reality just ok by correctly using limits. If you don't like the %, we can do just fine without percents.

Ok, so much for direct reaction to different former passages. Now, onward to something new. With EHP, without percents:

So, as I said, I consider your EHP model to be fully legit. Why, you may ask, are its conclusions completely different from % interpretation then? The thing is, they are not. You correctly transformed flat MPene into the flat opponent's EHP decrease. Furthermore, this properly translates into flat and equal decrease in "takedown time" of such opponent. However the catch is that there is no point to compare these values to base takedown times of the opponent that are no longer valid. If they were squishy, then reducing their takedown time from 3s to 2s by a single second means a real lot. If they were tanky, then reducing the takedown time from 11s to 10s by the same single second probably won't matter that much. The reason of a non-linear rate lies in the fact that a squishy is squishy cuz it prolly invested its instead into stats that carry the game and can do a lot more (e.g. of damage) within the same time then a tank. The same EHP amount has a very different real value for the two. The reason why I involve the opponent's dmg into this, being simple. Cuz if you transform the model into EHP, you no longer evaluate the MPene's efficiency via the carrier, but opponent. One cannot simply just evaluate the stat of a subject via stat of a different subject (there's a need to ideally transfer the entire metrics system to a single subject).

Another approach, % are banned here, there are gonna be exact variables instead. Despite KDA, objectives, mastery, emotes, friends, opinions, bans, blahblahblah, etc., there's only one thing that really matters, mechanics-wise. The win. And dmg itself is clearly the only direct input to this. So how does MPene contribute to this? We can have a background story (just last two living opponents left after a teamfight, both nexi barely standing, one inevitable encounter decides it all), but this is the core of all such encounters in a nutshell:

The maximized dmg output is the only direct concern that translates into the win.

That's it. No need to think about percents or EHP, maximizing and optimizing own dmg is all that truly matters. Sooo..

Let one player be a burst mage (going with simplest possible cases, the other examples are possible but more complicated nonetheless). Let G be the total amount of that they managed to spend on dmg. Only and  matter for the sake of a burst mage (the simpliest case, just two stats to decide between). Let'em spend on the first and consequently the rest on the latter stat. Again, with simplicity in mind we assume average efficiency of both stats, 87/4 and 280/9, respectively. Let us denote base damage of our 's full combo as B, let's denote the combo's dmg scaling with as S. Now, what was the best  investment for this ? To further simplify things we can assume that no skillshot will be missed and no other elements except for dmg and health bars will come into play. Let R be the amount of opponent's. If this maximum possible burst dmg exacly matches opponent's left and enemy also has potential to kill the  before the next spell rotation, this is an either-or situation. The optimal dmg output being the deciding factor between win or loss. What was the winning move?

Omitting some calculations inbetween (that can provided on demand), here's the short summary. The total dmg done by the burst combo is:

100 ( B +4/87 Sx)/( 100 +R -9/280 ( G -x))    , for x ≤ 280/9 R -G ( B +4/87 Sx)                                             , otherwise

where 0 < B, G, R, S are all positive constants and a variable x ∈ [ 0; G] represents the investment distribution.

The other branch of the function is strictly monotonic and bounded from above (e.g. with boundary B +SG) with its domain being an open set, hence it does not contain the maximum we are looking for.

The first branch is, except for the degenerated case, also strictly monotonic (more specifically, part of a hyperbole, possibly degenerated), hence only the domain boundaries can reach the maximum we want. Which of the two is it, is therefore determined by the sign of its first derivative. All in all:

If R < 9/280 G +783/1120 B/S -100, then the biggest burst is achieved for x = min { 0, G - R} (..if that much pene was obtainable at all).

If R = 9/280 G +783/1120 B/S -100, then any combination of stats will do (the degenerated case).

If R > 9/280 G +783/1120 B/S -100, then the biggest burst is achieved for x = G (all spent on ).

Clearly the ratio between base and scaling dmg plays a big role in here. The bigger base values play in favor of pene obviously. But the important thing for the sake of this discussion is the existence of a breakpoint. It clearly shows that while against low resists it's optimal to buy as much pene as possible, at a certain treshold the scales flip around and buying pene is super-suboptimal. It has nothing to do with a "feeling" of something being weaker or stronger. It directly and objectively impacts the win/loss output.