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### [Mechanics] How Move Speed and Armor/Magic Penetration Work in LoL

TiberiusAudley

After scouring old posts and patch notes to confirm my data, and seeing several people ask "how does ___ work?" I've decided to make a thread explaining two of the most commonly asked about mechanics in League of Legends: Move Speed calculations and Armor/Magic Penetration calculation order.

Disclaimer: If any of this information is wrong, blame Zileas or Guinsoo, as the information comes from posts they've made in the past, or blame ByronicHero/Pendragon for posting faulty patch notes. If it is wrong, hopefully they will come correct it.

First, Movespeed.

The way Movespeed is calculated:

Step 1: Base Movespeed.

Step 2: Enhanced Movement Speed directly modifies your base movespeed. This is why Boots do not say +% speed. Enhanced Movement Speed x = 30 + 20x. Thus, Enhanced Movespeed 1 = 50, 2 = 70, 3 = 90, and 5 = 130. Again, these are directly added to your base movespeed.

Step 3: Additive modifiers are calculated. These are all added together before affecting your movespeed at all. *MOST* Hastes are Additive (Highlander is not) and *ALL* slows are Multiplicative. This means that the majority of the time, Hastes will take effect before Slows. Additive modifiers modify the result of Step 2.

Step 4: Multiplicative modifiers are calculated.

Step 5: Diminishing returns are calculated. If your movespeed is above 490, harsh diminishing returns (50% effectiveness) are inflicted. If it is above 415, soft diminishing returns (80% effectiveness) are calculated. If it is below 220, the effects of all slows are halved.

To explain this with a few examples:
First, let's go with a Gangplank with Mercury Treads under the effect of Raise Morale Level 5.

Base Movespeed: 315.
Raise Morale Level 5 = +10% Move Speed.
Movespeed After Hastes = 385 * (1+0.1) = 423.5
Diminishing Returns: Movespeed = 415 + [(423.5 - 415) * 0.8]
Final Movespeed = 415 + 6.8 = 421.8 (422 Movespeed*)

* = League of Legends keeps track of all floating decimals, so your actual movespeed will be 421.8, not the displayed value of 421 or 422.

Example #2: NOTE: THIS EXAMPLE IS NOW OUTDATED MECHANICALLY. TIME WARP IS A +55% MULTIPLICATIVE MOVESPEED HASTE. I am leaving it as it is to display the mechanic of additive hastes and diminishing returns, but note that this is not an applicable in-game example anymore.
Twitch with Boots of Mobility, out of Combat, under the effects of Blood Boil Level 4 and Time Warp with Movespeed Quints and Masteries.

Base Movespeed: 310
Equipped BoM, Out of Combat: 440 (EM5)
Time Warp = +65% Move Speed, Blood Boil Level 4 = 17.5%
Movespeed Quints = +4.5%, Masteries = +3%
Movespeed after Hastes = 440 * (1 + 0.65 + 0.175 + 0.045 + 0.03) = 440 * 1.9 = 836.
Diminishing Returns:**
**Note: I'm not sure if Boots can actually be affected by diminishing returns, so I'm calculating this twice. The first calculation is if Boots ARE affected, the second is if they are NOT.

415 + (75 * 0.8) + [(836-490) * 0.5]
415 + 60 + 173
Final Movespeed (Calculation 1): 648

430 + (60 * 0.8) + [(836-490) * 0.5]
430 + 48 + 173
Final Movespeed (Calculation 2): 636

Now, taking the same Twitch from the step above, let's say he steps into combat, and is hit by Ashe's Level 3 Frost Arrow and Kayle's Reckoning.

Base Movespeed: 310
Equipped BoM, In Combat: 390 (EM2)
Movespeed after hastes: 390 * 1.9 = 741
Ashe's L3 Frost Arrow: 24%
Kayle's Reckoning: 25%

741 * 0.75 = 555.75 * 0.76 = 422.37

Final Movespeed = 415 + (7.37 * 0.8) = 420.896.

If Zilean's Time Warp wears off shortly after, this movespeed drops to 277.875.

One last example, an Anivia with Boots of Speed is hit by Nunu's Ice Blast and Ashe's Level 5 Frost Arrow

Anivia Base Movespeed: 290
Boots: 340 (EM1)
340 * 0.5 = 170
170 * (0.62) = 105.4

Final Movespeed: [(220-105.4) * 0.5] + 105.4 = 162.7

Diminishing returns on slows pull you out of a little bit, but you can see they won't save you! Better keep Cleanse handy

Next, the easy thing to calculate.
ARMOR PENETRATION

The order in which Armor Penetration is calculated:

Base Armor+Items.
Armor After Reductions from status effects/skills/items.
% Armor Penetration.
Flat Armor Penetration.

Say a champion has 140 Armor after items.

They have five stacks of Black Cleaver on them, and are hit by someone using Last Whisper and 20 Armor Penetration from Runes.

They will have 80 Armor at the start of penetration calculation (-60 Armor, Black Cleaver)

80 * 0.4 = 32 armor ignored from Last Whisper.

80 - 32 = 48. 48-20 = 28 Total Effective Armor during damage calculation.

If a Champion starts with 50 armor, and is hit by 5 stacks of Black Cleaver, their armor will be -10. When ARMOR or MAGIC RESISTANCE is reduced to or below ZERO, penetration is not calculated.

Reduction is generally the better choice since it benefits the damage your allies will deal as well. However, penetration is usually the cheaper choice. %-based penetration is at its greatest effect against extremely high armor/resist opponents.

NOTE: Only *FLAT PENETRATION* works on Towers in regards to armor. September 17th Patch Notes mention "Last Whisper - No longer works on turrets" and Towers are not affected by any debuff. I do NOT know if Void Staff can penetrate tower's Magic Resistance.

Now example two:
A champion has 85 Magic Resist.

Soraka, with Level 3 Starcall, Void Staff, and Sorcerer's Shoes hits four times. Soraka also has the Archaic Knowledge mastery.

The first attack, prior to damage calculation, the target's magic resist is reduced by 8, it is now 78.
For the first attack, the target is calculated as having 78 * 0.45 = 35.1 - 20 = 15.1 Magic Resist. (Note, the 0.45 is for the 55% penetration from Void Staff and Archaic Knowledge)

For the second attack, prior to damage calculation, the target's magic resist is reduced by 8. It is now 70.
70 * 0.45 = 31.5 - 20 = 11.5. Despite the target's magic resist being reduced by 8, they only have 3.6 less magic resistance during damage calculation.

For the third attack, the target's magic resist is now 62.
62 * 0.45 = 27.9 - 20 = 7.9.

For the fourth and final attack, the target's magic resist is now 54.
54 * 0.45 = 24.3 = 4.3.

Each step reduces the target's effective magic resist by 3.6 for Soraka, despite reducing it by 8 for everyone else. Of course, the closer it gets to 0, the greater the returns for each point removed due to the method by which magic resist and armor are calculated. (Damage reduced = x / 100+x )

And, finally: YES. ARMOR AND MAGIC RESIST CAN GO INTO NEGATIVE VALUES.

Thanks for reading, I hope you learned something. (And I hope none of this data has changed recently, making me wrong >.&gt

Kelty13

Recruiter

I hope this gets stickyed. This would be a great help to many players, new and old.

CuteFluffyBunny

Senior Member

Quality post, should add thornmail Mechanics on to it as well.

IMSavior

Senior Member

Quote:
TiberiusAudley:
Now, taking the same Twitch from the step above, let's say he steps into combat, and is hit by Ashe's Level 3 Frost Arrow and Kayle's Reckoning.

i thought slows didnt stack?

if you're slowed 50% for 3 seconds and 20% for 7 seconds you would be slowed for 50% for 3 seconds then 20% for the 4 seconds after was how i was told/under the impression it worked

MegaZero

Senior Member

Quote:
sAviOrZelda:
i thought slows didnt stack?

if you're slowed 50% for 3 seconds and 20% for 7 seconds you would be slowed for 50% for 3 seconds then 20% for the 4 seconds after was how i was told/under the impression it worked

Nope, Tiberius has it right.

IMSavior

Senior Member

Quote:
MegaZero:
Nope, Tiberius has it right.

!!! someone lied to me

TiberiusAudley

Quote:
sAviOrZelda:
i thought slows didnt stack?

if you're slowed 50% for 3 seconds and 20% for 7 seconds you would be slowed for 50% for 3 seconds then 20% for the 4 seconds after was how i was told/under the impression it worked

The only slows that do not stack are item slows.

If you are hit by Rylai's and Frozen Mallet, whichever is the stronger slow will take effect.

So the person who told you that was half-right.

Holepuncher

Senior Member

Quote:
TiberiusAudley:

Step 5: Diminishing returns are calculated. If your movespeed is above 490, harsh diminishing returns (50% effectiveness) are inflicted. If it is above 425, soft diminishing returns (80% effectiveness) are calculated. If it is below 220, the effects of all slows are halved.

Base Movespeed: 315.
Raise Morale Level 5 = +10% Move Speed.
Movespeed After Hastes = 385 * (1+0.1) = 423.5
Diminishing Returns: Movespeed = 415 + [(423.5 - 415) * 0.8]
Final Movespeed = 415 + 6.8 = 421.8 (422 Movespeed*)

I'm confused.....

If diminishing returns are applied to speeds above 425, and the speed is 423.5, why are they applied here?

TiberiusAudley

Quote:
Holepuncher:
I'm confused.....

If diminishing returns are applied to speeds above 425, and the speed is 423.5, why are they applied here?

Bah, thanks for catching that. It's 415 and 490, not 425... Was a typo. Fixing.