Efficiency of void staff

[quote=europeanorigin]Hello everyone ! I have made some calculations about void staff and found some interesting results. Before sharing them, I'd like to make a quick poll to see if people already know this, or if it would actually be useful to people. Hint : it's not between 0 and 40 ^^.[/quote]

[quote=Pheyniex]silli vote of mine... :P[/quote]

[quote=europeanorigin]Thank you all for voting ! I'll wait until 20 votes are reached and I'll release my discovery ^^ (currently 13) Thanks again for the attention you've provided to this post.[/quote]

[quote=europeanorigin]Alright! I'm posting my findings. First of all, I'll do a small refresher on magic penetration and on how it works. Check the spoiler for it [spoiler="Damage calculation"] Each spell deals a certain amount of damage, let's say it does the amount "dmg". This amount is not what is dealt in reality, as you have to account for magic resistance/armor. Suppose the spell deals magic damage, then the formula for the "true/real" damage will be : [center][color=#333333]________________________[/color]100[/center] [center]"true/real damage" = "dmg" . _____________[/center] [center][color=#333333]________________________[/color]100 + True MR[/center] Pretty simple, isn't it ? At one exception, what do I call True MR ? True MR is the resulting magic resist after taking into account [color=#ff8000]flat magic reduction[/color], [color=#800080]percent magic reduction[/color], [color=#008000]flat magic penetration[/color] and [color=#ffff00]percent magic penetration[/color]. Wait ? Isn't [color=#ff8000]flat magic reduction[/color] and [color=#008000]flat magic penetration[/color] the same ? and what about [color=#800080]percent magic reduction[/color] and [color=#ffff00]percent magic penetration[/color] ? NO. Each of these are different things and the order of application is : [list=1] [*] Flat Magic reduction [color=#ff8000](FMR)[/color] [*] Percent Magic reduction [color=#800080](PMR)[/color] [*] Flat Magic penetration [color=#008000](FMP)[/color] [*] Percent Magic penetration [color=#ffff00](PMP)[/color] [/list] Therefore the "true MR" formula would be : [center]"true MR" = ((MR-[color=#ff8000]FMR[/color]) * (1 - "true [color=#800080]PMR[/color]") - [color=#008000]FMP[/color]) * (1 - "true [color=#ffff00]PMP[/color]") [/center] Now what are "true PMR" and "true PMP" ? Well, PMR & PMP stacking is a bit more complicated than the one of FMR and FMP which stack additively. (meaning that if you have 20 magic penetration - understand FMP - on one item and 20 on another you'll have 40 flat magic penetration ) PMR & PMP stack multiplicatively. Basically, it means that you have to multiply the percent of magic diminution (which would be 1 - PMP, for instance) of each item/mastery/spell. Example : if you take [[arcane knowledge]] (10 percent magic penetration) and [[void staff]] (40 percent magic penetration), you'll have 46% magic penetration, because : percent of magic diminution of arcane knowledge = 100% - 10% = 90% percent of magic diminution of void staff = 100% - 40% = 60% total percent magic diminution = 90% * 60% = 54% and thus total percent magic penetration = 100% - 54% = 46% Therefore if you have [[sorcerer's shoes]] and [[arcane knowledge]] and [[void staff]], and you're fighting an enemy with 205 MR (for example), he will have a "true MR" of : "true MR" = ((205 - 0) * (1 - 0%) - 20) * (1 - 46%) = (205 - 20) * 0.54 = 185 * 0.54 = 100 ! This means 100 true MR. If you come back to the first formula you'll have this : "true damage" = "dmg" . 100 / (100 + 100) = "dmg" / 2. So basically, you would deal half the damage of what is written on the tooltip of the spell. You must understand the way damage are calculated in order to fully understand when the void staff is most efficient. [/spoiler] Ok, so from now, I suppose you know everything about the way damage is calculated in League of Legends. In terms of damage, what is important is the amount of damage you actually deal to the enemy, what I called "true damage" in the spoiler before. Now what about void staff, when does it increase your "true damage" the most ? A quick reflexion tells you its not at low level of magic resist (0 magic resist * 0.6 = 0 magic resist). On the other hand, at high level of magic resist, the amount of magic resist that is taken away increase more and more: [list] [*] 0 MR -> 0 MR taken [*] 100 MR -> 40 MR taken [*] 200 MR -> 80 MR taken [*] 300 MR -> 120 MR taken [*] etc. [/list] So it is tempting to say that void staff is stronger and stronger against high MR target... WRONG ! The more enemy has magic resist, the more you take away, but an opponent with "very high magic resist" will only fall to the status of "high magic resist" hero, which means that he will take less damage from your spell anyway. For instance, if when he had 300 MR, your spell dealt him 20% of his life (which meant your spell would have dealt 80% of his life if he had no MR) then when he is brought down to 180 MR, your spell will now deal him 28%, so 10% increase in "true damage". So NO, void staff is not most efficient at high level of MR, nor at low level of MR. There is a sweet spot inbetween! And here is a graph that clearly shows it (for both void staff and void staff + arcane knowledge) [IMG]http://i.imgur.com/5G7Sh.jpg[/IMG] Now here is the formula calculating the ENEMY MAGIC RESIST PROVIDING MAXIMUM EFFICIENCY FOR A GIVEN PERCENT MAGIC PENETRATION : [center][color=#111111]_______________[/color]100[/center] [center]"magic resist" = _____________[/center] [center][color=#111111]_______________[/color]SQR(1-PMP)[/center] where PMP is the amount of magic penetration. So basically that means that the amount of magic resist for which [[void staff]] + [[arcane knowledge]] magic penetration is maximized is 136,08 MR. But that's without taking into account flat magic penetration. So if you take the [[sorcerer's shoes]] and [[greater mark of insight]] into account the true sweet spot is : [center][b][color=#ff8000]164.6 MR[/color][/b][/center] That's all folks ![/quote]

[quote=Xeronn]Cool.. This is applied to [[Last Whisper]] as well I'm guessing. My only question is how will it help us? I mean, doing the math is fun n' all, but I'm just wondering.[/quote]

[quote=europeanorigin]Of course it can be applied to LW. It can help you in determining if you need armor/magic penetration items. What is the AR/MR of your main target ? what is the mean AR/MR of the enemy team ? In general, what are AR/MR values of my enemies throughout the games ? If you can answer these questions, then by combining it with these results, you will be able to determine the correct amount of AR/MR penetration that you require from runes/masteries/items. This implies a better item setup, more efficient rune picks, etc. in order to get the best out of EVERYTHING you can. So yeah doin' math is fun n' all, but I also believe that you can outperform your opponent with it, even if you are slightly less talented than him.[/quote]

[quote=lifebaka]I'm afraid that I'm going to have to remain skeptical here. While it's certainly true that larger amounts of MR reduce the effectiveness of %MPen, in terms of the amount of true damage provided, you're not modeling the AP provided by a Void Staff. Or the rest of the items that the champion has built. These things really matter. To take an example, let's suppose you're targetting an enemy with 400 MR and currently have 100 AP (this hypothetical does not represent a realistic scenario). It's very likely that building a Deathcap will be a larger damage increase than building a Void Staff, because the champion doesn't do enough damage yet for the % increase from Void Staff to be very useful. Change those numbers to 400 MR and around 600 AP (difficult to achieve without already having a Deathcap), and the Void Staff is probably a better pick in order use its multiplicative effect on an already-larger damage pool.[/quote]

[quote=Darcurse]... Nice and fun but.... [list] [*]Void Staff becomes better than flat MR penetration the moment the %-reduction on the enemy's MR is higher than the flat one. Simple as that, no greater math required. [*]Everyone who can think logically realizes that the nullified dmg reduce becomes less if the enemy stacks more and more resistance, because the more Arm/MR you stack the less dmg is reduced with every point of resistance. [*]The info that Void/LW falls off at some point is totally irrelevant, simply because at this point flat reduction isn't even worth trying anymore and %-reduction is still more efficient than plainly stacking AD/AP. [/list][/quote]

[quote=Xeronn][quote=lifebaka] I'm afraid that I'm going to have to remain skeptical here.[/quote] I was skeptical at first, but now I'm [color=#ffffff][b]Platinum[/b][/color] ranked ;D[/quote]

[quote=europeanorigin]@lifebaka : I apologize for not making it clear in the post: I worked only on the maximum efficiency of magic penetration. If I did that it is not because I disregard AP vs magic penetration! No, it is because the other items will bring in AP, which will result in some damage that you can calculate by reading the spell description (like 250 + (350) magic damage or something for instance). Now the thing is this does not matter in order to see for which quantity of magic resist the void staff increases most the damage output. However, I agree that if you want to measure the efficiency of the item OVERALL (increase of the item with regards to the build), there are plenty of things that are missing (like the build :p). But this is far too complicated, to be done in a generalized way. You can only simulate data for some specific spell, with a specific rune build and a specific item build. And then you'd have to find the combination of all these that would max the damage output of the void staff... Not easily feasible. @Darcurse : [quote]Void Staff becomes better than flat MR penetration the moment the %-reduction on the enemy's MR is higher than the flat one. Simple as that, no greater math required. [/quote] I totally agree with you on this : simple math. But that means finding what is best between void staff and SOMETHING ELSE. Here, the idea was to find the MR that made void staff the most efficient by itself! This way you can consider building a set of runes so that when your opponent reaches late-game, your opponents MR falls inbetween close bounds of it, which would increase the overall damage/gold ratio of the item. This implies considering different sets of runes and finding which one suits it best. I believe the possibility to adapt your build to your enemy to be particularly suited for ranked games, but I may be wrong. It also means that [[abyssal scepter]] can work very well with [[void staff]] in some very particular cases, like against a mid galio (if your work is to actually clean the galio) Same for the AD carry. If you plan to take LW, is brutalizer still viable ? Depends on the target. I believe it is abit more complicated that what most people think, and gaining even 2% true damage is extremely strong. [quote]Everyone who can think logically realizes that the nullified dmg reduce becomes less if the enemy stacks more and more resistance, because the more Arm/MR you stack the less dmg is reduced with every point of resistance.[/quote] Once again, I can only agree about that, a quick explanation "with the hands" and you are convinced of it. But my objective was to see where this optimum was exactly. [quote]The info that Void/LW falls off at some point is totally irrelevant, simply because at this point flat reduction isn't even worth trying anymore and %-reduction is still more efficient than plainly stacking AD/AP.[/quote] Interestingly, my results seems to suggest the opposite. You only have one % PENETRATION item (LW), which does not stack. So now imagine you took your LW because they were starting to stack some Armor. And then they do it again. Should you go for flat armor penetration ? YES, and no, it's bit more complicated actually. But the idea is that stacking flat armor penetration after percent armor penetration is something that can be considered in some cases. (to move the true damage percentage back to its peak) So to sum up : This won't change your life in general, but if you try building accordingly, it could end up in a stronger damage output. Then again, nothing revolutionary, yet interesting. The thing you guys do not consider is the fact that IT IS NOT efficiency of void staff WITH REGARDS TO SOME ITEM. It is about void staff solely.[/quote]