Talk:Kassadin/@comment-31543294-20180716065407/@comment-28977071-20181103115849

Yes, the term "weak" is relative as such. It requires the comparison to refer to. Isolating any single resource entirely from the rest of the system (almost) always yields trivial linear self-dependency. is the most natural common denominator of most LoL resources, making the analysis very straightforward. Using different models, one can analogically optimize pene relatively to other resources, but sounded like the most obvious choice for demonstration.

As for, I indeed had it included in more complex models, but with as simplistic example on mind as possible I decided to focus just on the essentials. I also like to think of as a separate (albeit just bivalent) dimension of dmg scaling, leading to base. However, it can simply be degenerated into the discussed 2-dimensional case, one just can do a substitution "S→S" (multiplying the scaling has the same effect as multiplying the itself) and the result is once again applicable for situations with  included.

Models for DPS s include CDR as well, but this dimension can also quickly degenerate to the demonstrated case once CDR hits its cap of 40% (or 45%). And there is even more complex model that makes scaling a variable/another dimension (cuz there are few items that allow to add  scaling too), leading to a final base (,  scaling, , CDR, ) for s (there are still other meta-options to include such as player's skill, but at this point I always tend to stop).

But even with its entire complexity, it's still sorta simplified continuous model of in-game environment. It utilizes the fluent average values of stats, while the actual items slightly deviate from such benchmarking. Hence an entire really accurate model'd have to be discrete and at that point doing a simulation, maybe with some AI, requires less effort.

So much for the original issue on the topic. If we had to discuss your example and opinion of usefulness of pene in the late game, I'd say it's a bit different story. In such case I agree that you're maybe more right than you think:

Flat is a highly optimal purchase even late game. This is in full accordance with the formula I provided above. One does not need or even bonkers. Those variables are utterly irrelevant for the breakpoint estimation. What matters much more is how much of the combo is in base dmg and how much of it scales. The thing is that even though falls off with high resists, this point is usually set way too high to apply.

So, disregarding other factors and knowing that our combo dealing 1000 is gonna target something with, we get the breakpoint estimate of:

9/280 G +783/1120 × 1000/3 -100 ≈ 133 + G > 110 []Even without considering the investment, which is quite high in late game, target resists are safely under the critical point. And if we include the value of  (we did not include the value of initial  as the example offers little info about it, except for  which is evaluated separately) with prizes of  and / (subtracting the estimated  value of nonoffensive  in the first case), we get to a whopping breakpoint of cca. . There's no way a tank could reach such a limit in a real game, ever.

Ergo pene all the way. Your results are not only some special case, they're fully in accordance with the approximate formula I offered above. Pene is optimal even for the late game, dealing most dmg. The base dmg of your combo is just way too good to pass, and even if it wasn't, the formula states that once one invests into dmg in late game, the breakpoint hits  at the very least, no matter how low the base combo dmg is. It does not matter that pene eventually falls off with high resists if such point isn't even reached. The only limitation is its in-game amount available.