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AS question

Creator: Trojan995 January 10, 2011 7:03pm
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Trojan995
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I've always been a little confused about how Attack Speed works. Take Ashe, for example. Her base attack speed is .658, and items that give attack speed ( Sword of the Divine, for example, gives 55% AS) are usually in terms of % bonus. Is this additive, like (.658 + .55)? Or is is multiplicative, like (.658)x(.55)?
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I'm not so sure how to works except for this; AS affects you more the higher your champion level. If you have 30% extra AS from runes and masteries you might get your AS to say, 0.813 but at level 2 it would raise to 0.93. So the percentage must be taken off an increasing amount.

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It's not additive, it's 55% of your total or base AS, then added onto your base AS.
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Ok AS is additive stat. So when you have items that give 50% 40% and 25% you will get total 115% AS.
When you trigger an ability that boosts AS by a % it also adds for example Yi ultimate will give you that 115% from items + 60% from ulti with total 175%.

On the AS on champs.
Each champ has a base AS stat and a % based increase.

Example Ashe
Her base AS should be 0.658.
Her bonus per lvl as should be +3.34%/lvl


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Attack Speed = (Base Attack Speed) × (1 + Bonus%) + (Attack Speed per Level) * (Level)

You can figure out the values for base attack speed and attack speed per level by rolling your mouse over the attack speed field ingame.

Here are the raw values from a quick custom game:

Character used: Ashe

Level 1: 0.625 + 0.033 = 0.658
Level 2: 0.625 + 0.055 = 0.680
Level 3: 0.625 + 0.077 = 0.702
Level 4: 0.625 + 0.099 = 0.724
Level 5: 0.625 + 0.121 = 0.746
Level 6: 0.625 + 0.143 = 0.768

Level 6 with dagger: 0.625 + 0.241 = 0.866

It should be noted that these values seem to be slightly inaccurate. For some reason, the game adds 0.011 bonus attack speed at level 1 seemingly out of nowhere as well.

I'm still trying to figure out exactly what is going on here. Some theories I've been testing:

0.625 * (1 + 0.15) + (0.022 * 6 + 0.011) = 0.86175 <- Close but off by 0.005
(0.625 + 0.143) * (1 + 0.15) = 0.8832 <- Completely off, disproving this formula
0.658 * (1 + 0.15) + 0.143 = 0.8997 <- Completely off, this is the base attack speed given by the lol wiki
(0.658 + 0.011) * (1 + 0.15) + 0.022 * 6 = 0.8634 <- Closer, but still off.

I'll try it using a level 18 char and different heroes shortly. I want to get to the bottom of this, as every single source seems to state something else.
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Caitlyn:

Level 1: 0.625 + 0.043 = 0.668
Level 2: 0.061
Level 3: 0.078
Level 4: 0.096
Level 5: 0.113
Level 6: 0.130
Level 6 + recurve: 0.398
Level 7 + recurve: 0.415
Level 8 + recurve: 0.432
Level 9 + recurve: 0.450
Level 10 + recurve: 0.467
Level 10 alone: 0.200
Level 10 + 2x recurve: 0.735
Level 10 + 2x recurve + dagger = 0.835

Attack speed per level = (0.200 - 0.043) / 9 ≈ 0.01744
Base attack speed: 0.625
Amount gained by adding a Recurve Bow at level 10: 0.267
0.267 is 40% of 0.6675. 0.6675 ≈ 0.668

Amount gained by adding 2x Recurve Bow + Dagger at level 10: 0.635.
0.635 is 95% of 0.668.

Revised Theory: (Attack Speed) = (Attack Speed at level 1) * (1 + Bonus%) + (Attack Speed per level) * (Level - 1)

It fits for the Ashe examples above as well:

(0.658 * 1.15) + 0.022 * 5 = 0.8667

Seems like the Wiki was correct after all, I was just misinterpreting the "Base" attack speed value as being the base value before level 1, not the value *at* level 1.

Update: On the other hand, the wiki appears to give incorrect values sometimes, at least for Caitlyn. The wiki's reported 0.651 attack speed at 1.75% bonus equates to 1.372 attack speed at level 10 with 95% increase, however the true value is 1.46 which can be obtained using the correct 0.668 attack speed at level 1. I'd appreciate it if somebody could update the wiki. (In %, the amount gained per level is 2.61% but I do not recommend using percentual values)
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I just fixed that. They probably took the stats from the official site. They rarely update them there.

I thought the formula was: base AS*(1+bonus AS+AS per lvl*level)
Do check it out if you can.
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Searz wrote:

I just fixed that. They probably took the stats from the official site. They rarely update them there.

I thought the formula was: base AS*(1+bonus AS+AS per lvl*level)
Do check it out if you can.


It's mathematically the same, leaguecraft gives you both forms.

AS*(1+bonus) + ASLVL*LVL
= AS*(1+bonus + ASLVL*LVL/AS)
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The first one is wrong when using the AS per lvl %. The second one is just wierd.. I use % AS per lvl in my calculations, not flat numbers. I'm pretty darn sure that the formula below is the correct one.

base AS*(1+bonus AS+AS per lvl*level)
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Searz wrote:

The first one is wrong when using the AS per lvl %. The second one is just wierd.. I use % AS per lvl in my calculations, not flat numbers. I'm pretty darn sure that the formula below is the correct one.

base AS*(1+bonus AS+AS per lvl*level)

By ASLVL I meant the flat values. The percentage form is equal to ASLVL/AS, for example Caitlyn: 0.01744/0.688 = 0.0261, or 2.61%.

The formulas given are both correct, since they're mathematically equivalent. For the percentage values, which I will call ASLVL%, the correct formulas are:

AS * (1 + Bonus + ASLVL% * (LVL-1))
or
AS * (1 + Bonus) + ASLVL%*AS * (LVL-1)

Since ASLVL% = ASLVL/AS; ASLVL = ASLVL%*AS

Ps. The wiki page is still incorrect, it's 0.01744 *flat* per level, and 2.61% *percent* per level. You wrote 1.75%.
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