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How are all diminishing returns calculated in League of Legends?

I was wondering how attack speed stacked. For instance, if I get two Phantom Dancers (each giving 55% attack speed), what would be the total buff to my attack speed?

Is there a point of diminishing returns, where stacking more attack speed doesn't matter?

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marked as duplicate by Raven Dreamer Apr 4 '12 at 14:13

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2 Answers 2

Your champion has a base attack speed it gets at level 1. Each level, it gains a percentage, and items can add percentages. The percentages stack with no diminishing returns.

Example: You have 10% from leveling, and 50% from items and a flat amount of 1.000 at level 1, you now have 1.600 attacks per second. the Maximum attack speed is 2.5 and can never, under any circumstance, be greater than 2.5 attacks per second.

Source: http://leagueoflegends.wikia.com/wiki/Attack_speed

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Is 2.5/sec just the 'unbuffed' cap; if you pop some attack-speed boosting skill or activate an item can you temporarily break it? –  Nick T Apr 4 '12 at 1:50
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Nope. For example, if you run a Graves with Beserkers Greaves, and 3 Phantom Dancers, and get your attack speed up at ~2.1, then even with the 80% AS boost from QuickDraw your AS won't exceed 2.5 –  Jordaan Mylonas Apr 4 '12 at 2:34
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First, as stated by the Aceofgods, attack speed adds up between your base attack speed of your champ, runes and items that add attack speed, and abilities that add attack speed. Any debuffs the enemy has will subtract from this attack speed. Attack speed cannot ever exceed 2.5 attacks per second. So if you want, you can try to build more than 2.5 attack per second so you can still have 2.5 attacks per second if the enemy have Lee Sin, Malphite, Frozen Heart, or Randuins, which can lower your attack speed.

However I ask what is the point of this question. Usually players want to have more attack speed because they wish to maximize their Damage Per Second or DPS. If you want to maximize attack speed because you have an on-hit dps build, like TF with his E, Volibear's W, and/or ionic spark then you can ignore the next part as the first paragraph already answers the question.

However if you are looking to maximize your effective DPS purely from auto-attacking and not counting an on-hit build (madred's bloodrazor, wits end, malady, ionic spark for instance), then you will see diminishing returns in terms of stacking attack speed.

DPS for auto-attacks to a target can be estimated by (Total AD) * (Attacks per second) * (100-Critical Chance percentage)% * Armor Reduction formula + (Critical Damage AD) * (Attacks per second) * (Critical chance percentage)% * Armor Reduction formula.

In other words, the Attacks per second, Critical Strike chance, and the Armor Reduction amounts multiplicatively affects damage, while the AD on a champ is additive. So if you want to see how much a certain item will impact your DPS, you can consider all of this. If you had 1.00 Attack Speed and you bought a Recurve bow that adds 40%, your DPS would increase by 40% because your attack speed with recurve bow would be 1.40 attacks per second. However if you bought another recurve bow, your attack speed would go from 1.40 to 1.80. This means your DPS with the extra recurve bow is only 0.4/1.4 = 28.6% higher.

TL;DR: Everything has diminishing returns as it is relative to what is your stat before the change and after.

Side note on DPS and its usefulness: To improve early game DPS in terms of runes, for instance junglers, getting attack speed is best since champions base attack speed at level 1 is around 0.6-0.7 attacks per second. Marks and Quints can give you 25% attack speed, which is almost a 50% increase to DPS. It should however be noted that in teamfights, players typically do not stand still attacking each other and using abilities. Rather they always try to reposition themselves by moving around the battlefield with abilities, summoners, or simply trying to kite or dodge enemies and skillshots. In this scenario, attack speed's effect in your dps is minimalized since you are always resetting your champion by moving them around. Rather than trying to attack as fast as you possibly can and being a sitting target for your enemy, you are poking them with a few shots at a time, trying to make the best use of your range advantage.

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