Monday, October 28, 2013

Leauge of Legends Item Maximization

Even though I am only gold in league, I have seen one too many players that can't think on their own and blindly follow static build paths or guides, this post is something I wanted to write about for a while.
Most of the players will at least have a feeling for everything I post below, but I still hope I can help make some things clearer about their choices, and shed some light on possible facts many ignore.
Let me know if you see something I missed, errors, or just generally badly typed sentences (sorry bad englando).
_________________________________Maximizing your effective health________________________
  • HP, Amor and Magic resistance
Resistances multiply your effective Hp, so for every point of armor or mres you get, you will be able to sustain 1% more damage (at 200 armor, you have an effective 300% hp). It is a myth that stacking armor gives lesser returns, health becomes better with good resistances but armor doesn't become worse, even against % penetrations
So: damage you can sustain = Hp x (1 + armor/100)
The trick here is maximizing the function minimizing the cost, approximately health is 10 times cheaper than armor.
To maximize the amount of burst damage you can live through, you need 1k health and then 100 armor for every 1k on top of it (if you have 1200 health and 0 armor, adding 1 armor will add 12 health, 12 > 10, and vice versa).
So, effective builds would be: 1.5k health with 50 armor, or 3k health with 200 armor.
Things get a little more complicated when you think about % and flat resistance penetrations and the fact that health works for all magic, normal, and true damage.
For a burst of mixed damage, get 50 of each resistance every 1k health and not 100.
1.5k health with 25 armor/mres, 3k health with 100 armor/mres
With flat armor penetrations the optimal builds just go up that exact amount of resistance penetrated. With % pens however, you need to reduce the amount of armor per point of health by that amount.
You can see health stacking is very strong, however we have not taken into account % health damages, introduced by riot to counter precisely this mechanic and, most importantly:
  • Sustain
Armor has a hidden passive, it makes every point of regenerated health harder for the enemy to tear through, since every point of armor multiplies to give you a 1% boost in your max hp, it also provides you with a 1% bonus from healing from all sources.
Imagine an enemy with a million health and 10 hp/s, you can kill him, eventually
Now imagine an enemy with 1k health but 100k armor and 10 hp/s, can you kill him? No way.
Going from 0 to 20 armor is like buying a spirit visage in terms of the effective healing, resistances are great on champions with some form of sustain, or against general sustained and slow poke, if you can keep chugging potions armor will help you a great deal.
Effective healing % = [100 + (armor value)] x 1.2(if you have a spirit visage)
  • Other Methods of adding effective health
Armor pretty much synergises very well with anything that artificially increases your health, Shen, for example, which has a spammable shield,he can double its effectiveness by buying armor, other examples would be ultimates such as Lulu's or Renekton's.
_______________________________Maximizing your auto attack damage_______________________
  • Attack damage, Attack Speed and Critical Chance
We need to maximize your dps minimizing cost, and so damage per second = Damage per hit x AS
[Ad x (1+crit chance)] x AS
If we look at the brawlers glove, longsword and dagger we see the prices of the stats are a little different but we will assume they are equal to not make things complicated, and this post half the internet long.
If your attack damage is greater than 100, you should get a point in crit chance for every point of AD over 100, at 101 AD 1 point in crit gives you an additional 1.01 dps, at 100 AD and 100% crit chance, 1 point in AD gives you 2 dps. 155 AD, 55% crit chance is an efficient point to maximize your sustained damage, for example.
Something similar applies to attack speed, except it isn't the raw AD what should be taken into consideration, instead the mean damage per hit should be used. If your damage per hit is 150, you should have 50% bonus attack speed. Your champion gains AS naturally, you need to take that into account.
Have in mind this is for sustained damage
For trading damage, when you auto an enemy once or twice and then walk away, the attack speed component is not going to be nearly as important, damage per hit is a lot more useful, you don't care about attack speed if you can only land one hit.
  • On hit effects
You need to factor them into the damage per hit, if botrk does 50 average on hit damage, and your "natural" damage per AA is 150, you should have 100% bonus AS to maximize your dps.
  • Armor Penetration Care! I might have this wrong! Need to do some math to confirm
This one took me a while to get my head around, but let's start with the armor mechanics.
If a target has 50 armor, they have 150% effective hp, meaning you need 150% the damage you needed before to 0 his health. If you reduce that armor to 0 thanks to armor pen (be it flat or %), you are back at needing 100, every point in armor penetration has increased your damage output by 1%.
It is also false that flat armor penetration gives decreasing returns, it is just as effective against high armor targets as it is against squishies
To prove the point above:, if you reduce a target from 50 to 0 armor you get a 50% damage increase, reducing an enemy from 25 armor to 0, give you a 25% boost. If reducing an enemy from 50 to 25 gave you less than a 25% damage increase, then reducing that same enemy again from his 25 to 0 should give you more than 25%, which is not true, no point in flat armor pen has gone to waste.
When at 100AD, all AD, AS, critchance and 1 point in armor penetration increase your damage by 1%, armor penetration is costly early on and decreases in price (thanks to last whisper % pen, and enemies gaining armor) as the game goes on.
_______________________________Maximizing your ability damage___________________________
  • Ratios
In my opinion one of the most important things not covered or mentioned anywhere in league of legends (you need to go to external websites to find them out ._.).
A good ratio would usually be anything above 0.6-0.7 on an ability or above 0.9 on an ultimate, champions with good ratios and poor base damages benefit a lot from buying ability power.
Another interesting concept is the ratio/cooldown, even though alistar has good ratios on his abilities, their rather big cooldowns make it so his damage per second does not increase by a lot when he gets ability power, lissandra on the other hand, has a spammable Q with a bad ap ratio, but ability power benefits its damage greatly, since she can use it around 20 times a minute (compared to alistar's 3 knockups)
  • Cooldown Reduction
At 40% CDR you can cast your abilties 66.6% more often, resulting in a massive increase of nearly 70% of your abilities damage, and most importantly, utility
The more CDR you have, the more effective another point in CDR is
If you ever reached 100% CDR you could have infinity DPS with your abilities.
CDR artificially puts up your ratio/cooldown numbers, making ability power more useful than before.
Even though CDR is great for increasing your sustained damage, it suffers from a similar problem as attack speed, it does not matter how fast you can cast your abilities if you only have space to cast 1 combo, if you can't get off your ultimate 2 times in a teamfight, your increase in dps suffers greatly.
This is why CDR is great on champions with naturally low cooldowns, that can get off more than one cast of every ability easier.
CDR is aso greatly countered by silences and Cc, since you rely on steady dps and many spell casts, a silence increases its effective duration, instead of preventing 3 spells, it prevented 7.
  • Armor and Magic penetrations Again, might be wrong, look into the comments for second opinions!
Great on bursty champions or champions with high base damages and low ratios, they also become more powerful the more stats you put into your ratios, 1 point in flat penetration will give you a 1% increase in damage.
_____________________________Items deserving a special mention__________________________
Sheen procs: Champions with low cooldowns that auto attack inbetween spells (Ezreal, Corki, Lucian, Udyr), or champs that apply on hit effects with their spells (Ezreal, Fizz).
Tear: Champions that can fill it fast, without using too much mana, and benefit from the massive mana pool it's upgrades give (Ryze, karthus)
Liandrys: Mages with a lot of damage over time spells or built in Cc (Teemo, Swain).
Rylais: Mages in need of Cc with spammable single target spells, or that seek to double Liandry's passive on dot (Mordekaiser, Brand)
Botrk: Auto attackers with low ratios on their abilities that benefit from the additional peel / chase potential (Vayne, Nocturne), the main drawback of botrk is that it does not scale with crit chance like BT does.
Runaan's Hurricane: Auto attackers with on hit effects that benefit from having 3 targets (Kennen for constant stuns, Kog maw, Twitch or TeemoakaSatan )
Sunfire Cape: Can you stay in the middle of the enemy team for half an hour?

Remember this is all an estimate! in practice you cannot choose to build stats on their own (they are usually tied to other stats and passives), and I have many assumptions and cost aproximations in order to not write a 20 page essay

originally posted here