Multipliers and Scaling

[quote=MungoGeri]Hello, everyone. This post is a reaction to two threads of thought permeating the comments to my Jungle Lulu guide. One of those threads of thought has to do with questions regarding the item builds, especially the AD Lulu build. A couple of times people have suggested builds that focus exclusively on a few key elements (e.g. AD and attack speed) and dismiss other elements (e.g. crit% and armor penetration). The other thread of thought was asking why I felt that an AP [[lulu]] doesn't not scale well into the late game. The answers to both threads of thought are the same: understanding multipliers. I hope to respond to both threads of thought here. [color=yellow][h1]The Importance of Multipliers[/h1][/color] [rule] To understand the power of multipliers, let's take a simplistic game where the amount of damage that one can dish out depends on four factors. At level 1, each of these factors is at 1, so: damage = 1 x 1 x 1 x 1 = 1 Then, each level you can choose to place a point in any of the factors. At level 9, you'd have 8 points to distribute. How should you distribute them? Let's say that you like the first factor more than the others, so you dump all your points into it. Then, you'd get: damage = 9 x 1 x 1 x 1 = 9 What if you split the points between the first and second factors? damage = 5 x 5 x 1 x 1 = 25 How about splitting them between the first three factors? damage = 4 x 4 x 3 x 1 = 48 How about splitting them evenly? damage = 3 x 3 x 3 x 3 = 81 This exercise illustrates the power of multipliers. Each of the examples uses the same number of points and yet the final configuration does nine times more damage than the first configuration. [color=yellow][h1]League of Legends ADC Item Damage[/h1][/color] [rule] Let's now do a similar exercise using LoL ADC items. Here, we are ignoring player skills and just looking purely at physical basic attack damage. In my examples, I'm going to pretend that we're equiping a level 18 [[lulu]] as an ADC (because [[lulu]] is undeniably the most awesome champion in the game) and ignoring her [[pix]] damage or any damage from her abilities. Also, for now, we are concerning ourselves only with the damage that the item combination dishes out and not any other factors (e.g. health, life steal, cooldown reduction, movement speed, etc.). Also, for this exercise, we are using the patch 4.9 values -- e.g. [[the bloodthirster]] has 100 AD, [[infinity edge]] has 70 AD, etc. This is because the 4.10 patch shifts things around quite a lot and I think the 4.9 patch item list illustrates multiplier effects better. The four factors that determine the damage that an ADC item combination delivers are AD, attack speed, crit% (including a possible [[infinity edge]] multiplier), and armor mitigation. However, let's say that you're a person who just loves to chunk people down. You love AD and only AD, so you get six [[the bloodthirster]]s. The damage you would deal over 4 seconds would be: [table bgcolor=green width=400] [tr bgcolor=black] [td][b][color=yellow]Items[/color][/b][/td] [td][b][color=yellow]Enemy Armor[/color][/b][/td] [td][b][color=yellow]Damage over 4 seconds[/color][/b][/td] [/tr] [tr bgcolor=black] [td][icon=the bloodthirster width=15][icon=the bloodthirster width=15][icon=the bloodthirster width=15][icon=the bloodthirster width=15][icon=the bloodthirster width=15][icon=the bloodthirster width=15][/td] [td]100[/td] [td]1230[/td] [/tr] [tr bgcolor=black] [td][/td] [td]200[/td] [td]829[/td] [/tr] [tr bgcolor=black] [td][/td] [td]300[/td] [td]625[/td] [/tr] [/table] You think about it some more and say, "Well, I'll give up a little AD and add some crit." So, you substitute in an [[infinity edge]]. [table bgcolor=green width=400] [tr bgcolor=black] [td][b][color=yellow]Items[/color][/b][/td] [td][b][color=yellow]Enemy Armor[/color][/b][/td] [td][b][color=yellow]Damage over 4 seconds[/color][/b][/td] [/tr] [tr bgcolor=black] [td][icon=infinity edge width=15][icon=the bloodthirster width=15][icon=the bloodthirster width=15][icon=the bloodthirster width=15][icon=the bloodthirster width=15][icon=the bloodthirster width=15][/td] [td]100[/td] [td]1619[/td] [/tr] [tr bgcolor=black] [td][/td] [td]200[/td] [td]1090[/td] [/tr] [tr bgcolor=black] [td][/td] [td]300[/td] [td]822[/td] [/tr] [/table] That seemed to work. What about removing some AD but adding some fast attack speed and some more crit% with a couple of [[phantom dancer]]s? [table bgcolor=green width=400] [tr bgcolor=black] [td][b][color=yellow]Items[/color][/b][/td] [td][b][color=yellow]Enemy Armor[/color][/b][/td] [td][b][color=yellow]Damage over 4 seconds[/color][/b][/td] [/tr] [tr bgcolor=black] [td][icon=infinity edge width=15][icon=phantom dancer width=15][icon=phantom dancer width=15][icon=the bloodthirster width=15][icon=the bloodthirster width=15][icon=the bloodthirster width=15][/td] [td]100[/td] [td]3218[/td] [/tr] [tr bgcolor=black] [td][/td] [td]200[/td] [td]2168[/td] [/tr] [tr bgcolor=black] [td][/td] [td]300[/td] [td]1634[/td] [/tr] [/table] That was a dramatic change. What if we added in some armor penetration with a [[last whisper]]? [table bgcolor=green width=400] [tr bgcolor=black] [td][b][color=yellow]Items[/color][/b][/td] [td][b][color=yellow]Enemy Armor[/color][/b][/td] [td][b][color=yellow]Damage over 4 seconds[/color][/b][/td] [/tr] [tr bgcolor=black] [td][icon=infinity edge width=15][icon=phantom dancer width=15][icon=phantom dancer width=15][icon=last whisper width=15][icon=the bloodthirster width=15][icon=the bloodthirster width=15][/td] [td]100[/td] [td]3416[/td] [/tr] [tr bgcolor=black] [td][/td] [td]200[/td] [td]2491[/td] [/tr] [tr bgcolor=black] [td][/td] [td]300[/td] [td]1961[/td] [/tr] [/table] Armor penetration seemed to help. What if we added some armor reduction and penetration with [[the black cleaver]]? [table bgcolor=green width=400] [tr bgcolor=black] [td][b][color=yellow]Items[/color][/b][/td] [td][b][color=yellow]Enemy Armor[/color][/b][/td] [td][b][color=yellow]Damage over 4 seconds[/color][/b][/td] [/tr] [tr bgcolor=black] [td][icon=infinity edge width=15][icon=phantom dancer width=15][icon=phantom dancer width=15][icon=last whisper width=15][icon=the black cleaver width=15][icon=the bloodthirster width=15][/td] [td]100[/td] [td]3541[/td] [/tr] [tr bgcolor=black] [td][/td] [td]200[/td] [td]2663[/td] [/tr] [tr bgcolor=black] [td][/td] [td]300[/td] [td]2134[/td] [/tr] [/table] Now you can see the power of multipliers at work in the League of Legends. By increasing each of AD, attack speed, crit%, and armor penetration rather than focusing on one at the expense of the others, we've arrived at a build that does three times as much damage. Please understand that this does [color=yellow][b]not[/b][/color] mean that this is the perfect build in all cases. For one thing, I avoided using a [[blade of the ruined king]], because I didn't want to get into calculating the varying damage from its passive and actives. Second, the specific build that you choose to use will also depend on the skills of the character you are playing (more on this below). [color=yellow][h1]Example of a Bad Build[/h1][/color] [rule] At the risk of seeming to pick on a fellow member, I want to use the example of a build that was suggested by a commenter for my Jungle Lulu guide. This build was suggested for an AD Jungle [[lulu]]: [[muramana]] [[feral flare]] [[ionian boots of lucidity]] [[iceborn gauntlet]] [[youmuu's ghostblade]] [[blade of the ruined king]] The commenter tried to come up with a [[lulu]] build that was similar to a blue [[ezreal]] build. Let's ignore the fact that [[lulu]] doesn't have access to the [[mystic shot]] or [[arcane shift]] abilities that makes a blue [[ezreal]] work. Let's instead focus on the damage, because we can immediately tell that these items don't synergize well. The build does have some added AD and attack speed. However, it has very little crit% and armor penetration (just the amounts on the [[youmuu's ghostblade]]). In addition, the damage from the [[iceborn gauntlet]] doesn't benefit from the added AD or attack speed and the [[ionian boots of lucidity]] don't act as a multiplier on the basic attack damage at all, which is supposed to be the idea behind an AD or on-hit [[lulu]]. Please understand that I appreciate the commenter's contributions. I just want to use the suggested build as an example of the traps players can fall into. Make sure that you take into account all of the multipliers at your disposal when you are choosing the items that you want your champions to use. [color=yellow][h1]Other Multipliers -- Skills, Area-of-Effect, and Defense[/h1][/color] [rule] [color=#0080ff][h2]Skills[/h2][/color] [rule] Besides the way items multiply with one another, character skills are obviously another important multiplier. For example, [[twitch]] has an ability that gives him a 70% attack speed burst when he comes out of stealth. With that in mind, he will probably benefit from a high AD, high crit%, high armor penetration, lower attack speed item build, because he will already have the benefit of the attack speed that [[ambush]] provides. This does not mean that [[twitch]] should not build any increased attack speed items (he does need to build up his stacks of [[deadly venom]] on the enemy after all). However, it probably means that he can afford to replace one item that gives attack speed for one that focuses on AD, crit%, or armor penetration. Also, [[lucian]] has several abilities whose damage is based on his attack damage, so again, a higher AD build is probably best for him. One has to look at the AD and AP ratios and the cooldowns on various skills to get an idea of how your skills multiply the power of your items. Obviously, items with cooldown reduction on them are also a way for items to multiply the power of skills as well. [color=#0080ff][h2]Area of Effect[/h2][/color] [rule] If a skill or an item has an area-of-effect ability, its power will be multiplied by the number of people likely to be affected by the ability. [color=#0080ff][h2]Defense[/h2][/color] [rule] You can't damage people if you're dead -- or protect teammates either. The longer you can stay alive, the longer you will be able to assist your team, which acts as another multiplier. [color=yellow][h1]Why Are Some Champions "Late Game" Characters and Others Not?[/h1][/color] [rule] Put simply, whether a champion is a late game character or not depends on how their items and skills are able to multiply off one another. Let's take the example of two AP characters that I play a lot: [[lulu]] and [[zyra]]. My contention is that [[zyra]] is a late game champion while an AP [[lulu]] does not get as comparatively strong in the late game. Let's say that both characters have the standard caster offensive masteries and have built their first five items similarly: [[sorcerer's shoes]], [[athene's unholy grail]], [[rabadon's deathcap]], [[void staff]], [[liandry's torment]] or [[lich bane]]. Both now want to add a [[zhonya's hourglass]]. Which character will benefit from it more? [color=#0080ff][h2]Zyra[/h2][/color] [rule] [[Zyra]] will benefit tremendously from the addition of the [[zhonya's hourglass]] in the late game: [list] [*]All four of her abilities benefit from the additional AP. [*]All four of her extra powered abilities will multiply off of the magic penetration from the [[void staff]], [[sorcerer's shoes]], and [[liandry's torment]]. [*]All of her abilities are AOE abilities in some way. How many players will be hit by each skill will vary by the situation. However, in late game team fights, it's very common for each of the skills to hit more than one person. [*]While [[Zyra]] is in the [[zhonya's hourglass]] stasis, her plants will continue to damage the enemy. In addition, often her abilities will come off cooldown in that time, so she can do another burst of damage before she dies. [/list] [color=#0080ff][h2]Lulu[/h2][/color] [rule] [[Lulu]] won't benefit quite as much from the [[zhonya's hourglass]]: [list] [*][[Glitterlance]] and the [[lich bane]] proc will benefit from the extra AP and [[lulu]]'s magic penetration. However the [[lich bane]] proc is a strictly single-target spell, and while [[glitterlance]] can sometimes hit more than one enemy champion, in most game situations its short range means that it rarely does. [*][[whimsy]] benefits very little from the added AP. If cast on an enemy, the added AP makes no difference. If cast on an ally, it will increase the target's run speed a bit more -- but really, what's the difference between an increased run speed of 80% versus 90%? Either way, you'll either catch your enemy or successfully run away. [*][[help, pix!]] is a purely single target spell. If cast on an ally, it does not benefit from magic penetration. [*][[rampant growth]] benefits from the extra AP but does not benefit from magic penetration. It's crowd control abilities remains unaffected and the heal only affects one target. [*][[pix]] benefits from the added AP. If Pix is on [[lulu]], then [[pix]] will benefit from magic penetration but will shoot at a very slow rate. If [[pix]] is cast on an ally, it will benefit from their added attack speed but will not benefit from [[lulu]]'s magic penetration. Either way, [[pix]] remains a single target spell. [*]While [[lulu]] is in the [[zhonya's hourglass]] stasis, she can't do anything to help her team. She might get a couple of spells off cooldown during that time, however. [/list] [color=#0080ff][h2]Conclusion[/h2][/color] [rule] As you have seen, the reason that [[zyra]] scales well into the late game is because she can more easily take advantage of the magic penetration and area-of-effect multipliers with late game items. However, an AP [[lulu]]'s abilities often can't. Now, I don't want to dismiss an AP [[lulu]]'s contributions to the late game entirely. After all, as the *enemy* gets stronger, [[lulu]] is able to prevent more damage using [[whimsy]] and the knockup on [[rampant growth]]. However, in general [[lulu]]'s overall power does not scale as well into the late game. I hope this discussion provided some background on how multipliers affect item builds and how well different champions scale into the late game.[/quote]

[quote=Firehusary]1 word. WOW.[/quote]

[quote=FalseoGod]You're confusing things: AP Lulu's utility improves with ap, 90% or 80% speed is indeed relevant as is how much AP she has for Glitterlance, passive, ult, shield, etc. Also, using [[zyra]] for the comparison was terrible, ap [[zyra]] is mediocre at best due to skill interaction and scalings. That comparison actually works more against the point you're trying to prove, although I get what you're trying to say.[/quote]

[quote=utopus]Take your +rep, already! It's clear you've done a lot of work for this thread already. I agree with falseogod though. You didn't make the most sound of comparisons, since AP lulu is chosen for her lane safety and utility, whereas AP zyra... isn't picked for her lack of mobility. There's no question that AP zyra would outdamage an AP lulu. One comparison that may have worked better would have been something like, kayle vs ziggs or something. That'd be pretty interesting[/quote]

[quote=FantasySniper]I need to use this for people that think more than 1 [[Bloodthirster]] or [[Infinity Edge]] is somehow a good build. This is going to be filed in the Forum-Weapons folder, thank you, have some Rep.[/quote]