Movement speed

Movement speed is a champion statistic that represents the rate at which a champion travels across a map. One movement speed point translates to one game distance unit traveled per second (as a frame of reference, diameter is 100 units). For example, a champion with 300 movement speed will be able to walk three in one second.

Each champion begins the game with a base amount of movement speed that ranges from 315 to 355 (e.g ). The base amount of movement speed a champion can have ranges from 285 ( while unmounted) to 400 ( at level 18). For a list of all champions' base movement speed, see base champion statistics.

This base movement speed can be increased by flat bonuses and percentage bonuses and reduced by slows. These effects can come from items, champion abilities, summoner spells, runes and environmental buffs.

Calculations
A champion's movement speed is given by the following formula:
 * (Base MS + Flat MS bonuses)(1 + Sum of all Additive Percent MS bonuses)(1 - Highest Slow ratio)Product of (1 + any Multiplicative MS bonus)
 * "MS" is an abbreviation for Movement Speed

Add any flat bonuses to the champion's base movement speed; the total flat movement speed will be the baseline for the percentage bonuses. Add all additive percentage bonuses together, add 100% to the result, and multiply it with the total flat movement speed. Then, if applicable, apply the slow reduction and any special multiplicative bonuses (Heal, Mercurial Scimitar, and certain champion abilities) one at a time. If the result is over 415 or under 220 movement speed, apply soft caps as described below.

Movement speed caps
When the raw movement speed is greater than 415, there are two soft caps applied: The two ranges have their reductions applied at the same time before being added back together.
 * The raw speed between 415 and 490 gets multiplied by 80%.
 * The raw speed over 490 gets multiplied by 50%.
 * As an example, if the calculated raw speed is 600 before soft caps kick in, it is reduced to (600490)(490415)415530, which means an  reduction of the original movement speed.

These are the simplified formulas:
 * If the raw speed is 415 or lower, no cap is applied.
 * If the raw speed is between 415 and 490, final speed is soft capped to RawMS83.
 * If the raw speed is above 490, final speed is soft capped to RawMS230.

When the raw movement speed is less than 220 another soft cap is used:
 * If the raw speed is below 220, final speed is changed to RawMS110.
 * Example 1: If the calculated raw speed is 180 before soft caps kick in, it is increased to 180110200.
 * Example 2: If the calculated raw speed is 0 before soft caps kick in, it is increased to 0110110.

Only slow with the highest value affecting particular champion is taken into calculations. All additional slows are ignored until higher-valued slows wear off. When highest valued slow decays, another affecting slow is calculated into.

Slow Resist
Slow Resist is a statistic that reduces the effectiveness of slows by a percentage.

Movement speed as scaling
These use the champion's personal movement speed to increase the magnitude of the ability. By building movement speed items or casting spells you can receive more benefit and power from these abilities in most situations.
 * (dash distance increases with boots tier and dash speed with movement speed)
 * (movement speed increases with boots)
 * (dash distance increases with boots tier and dash speed with movement speed)
 * (movement speed increases with boots)
 * (movement speed increases with boots)
 * (movement speed increases with boots)

Increasing flat movement speed
The bonus given by these items or champion abilities are flat increases to the champion's base movement speed. These flat bonuses will increase the effectiveness of percentage bonuses.

Purchasing boots from the store grants a champion a flat increase in movement speed. Movement speed boosts from boots are unique passives, hence the bonuses from multiple pairs of boots do not stack. The bonus from boots is quite big compared to their cost and is essential for all champions.

Champion abilities

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Increasing percentage movement speed
The bonus movement speed given by these items or champion abilities are based on a percentage of the bonus compared to your total flat movement speed (before all sources of percentage movement speed bonuses are factored in). Percentage movement speed will stack additively with other sources of percentage movement speed, unless the bonus movement speed is one of the few exceptions that stack multiplicatively.

All percentage bonuses from the items listed below stack additively with one another.

Champion abilities

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Neutral Buffs

 * Visiting the shop on Summoner's Rift starting at 20 minutes in game grants 75% bonus movement speed that decays over 7 seconds, scaling up to 150% at 40 minutes.
 * With, the bonus becomes 125% and 200% respectively.
 * The Speed Shrine buff on Dominion grants 30% bonus movement speed.
 * The Speed Shrine buff on Dominion grants 30% bonus movement speed.

Multiplicative speed boosts
Most speed boosts stack additively, but a select few stack multiplicatively with other speed boosts. These do not stack additionally with other percentage movement speed bonus, but rather are multiplied after all other percentage movement speed have been calculated. Movement speed obtained thanks to the formula is still affected by movement speed caps (see above).

Champions

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Decreasing movement speed
There are many ways to decrease a champion's movement speed, with the most usual one being through champion abilities. For a full list of slows, see here.

Old slow stacking
'''Since patch V5.13 only slow with the highest value is affecting. All additional slows are ignored.'''

Prior to patch V5.13 slow stacked:

Slowing effects followed particular rules when stacking:


 * If a champion was affected by multiple slows, the strongest one would be fully applied, while the others were applied sequentially with 65% reduced effectiveness down to 35% of its original strength.


 * Slow effects derived from items with the same name or named item effect did NOT stack, even when coming from different champions. Only the strongest item slow was applied at any moment. The exception to this was the active effect of, , and , which stacked with other slowing items normally, because they were considered champion abilities for slow stacking purposes.


 * Attacking a champion with the buff when the target was already affected by that slow would reapply the debuff, resetting its duration. It would NOT increase the slow amount. The same holded true for the  summoner spell.

Example
A champion with a raw movement speed of 400 was affected by a 2 second long 40% slow and a 5 second long 20% slow at the same time.


 * For the first two seconds, they would have (1)(1) of his original movement speed (a effective slow). So he would have 400 raw movement speed.


 * For the following three seconds, the effective slow would be 20% and so he would have 400320 movement speed.


 * After that, he would return to his normal speed of 400.

Trivia
Last updated: November 21, 2017, patch V7.23


 * Without using, what may be the highest movement speed attainable is about , being a level 18.


 * +335 movement speed
 * 1 activated
 * 1 activated
 * 1 activated
 * 1
 * 1
 * 1 at 100 stacks of Momentum
 * Buffs:
 *  will need to have, , and  alongside him.
 * to proc
 * active and passive
 * Has to has impaired movement to proc.
 * empowered by
 * Three empowered with the
 * Relevant mathematics:
 * to proc
 * active and passive
 * Has to has impaired movement to proc.
 * empowered by
 * Three empowered with the
 * Relevant mathematics:
 * Has to has impaired movement to proc.
 * empowered by
 * Three empowered with the
 * Relevant mathematics:
 * Three empowered with the
 * Relevant mathematics:
 * Three empowered with the
 * Relevant mathematics:


 * AP:
 * Items = +  +  =
 * AP = 80 + ( + + ) =
 * Runes = +  +  +  =
 * Buffs = +  =
 * AP Multiplier = 1 + +  =
 * AP = ( + + ) = 
 * bonus = 120 + =  flat movement speed


 * AP:
 * Items = +  +  =
 * AP = 80 + ( + + ) =
 * Runes = +  +  +  =
 * Buffs = +  =
 * AP Multiplier = 1 + +  =
 * AP = ( + + ) = 
 * bonus = 30% + (7 / 100)% = +% movement speed


 * AP:
 * Items = +  +  =
 * AP = 80 + ( + + ) =
 * Runes = +  +  +  =
 * Buffs = +  =
 * AP Multiplier = 1 + +  =
 * AP = ( + + ) = 
 * bonus = 30% + (5 / 100)% = +% movement speed


 * movement speed:
 * Base = 335
 * Items = +  +  +  +  = 215 flat movement speed + 107% movement speed
 * Runes = +  +  +  = 58 flat movement speed + 55% movement speed.
 * Buffs = +  +  +  +  +  +  +  +  =  flat movement speed +  movement speed
 * Total Movement Speed Multiplier = =
 * Movement Speed = ( + +  + )(1 +  +  + ) movement speed before soft caps


 * Movement Speed + 230 =  movement speed
 * Movement Speed + 230 =  movement speed

Infinite MS-Theory
There is a theory that allow 2 players, one from each team, to reach infinite amount of movement speed. It require the same set-up as seen just before, twice, each per team, but with a replacing the. The theory is simple: speeds up Malphite 1, and as soon as he reaches his highest amount Malphite 2 steals Malphite 1 movement speed with, and get speeds up by. Then as soon as he reaches his highest amount Malphite 1 steals Malphite 2 movement speed with and get speeds up by. Repeat the operation an infinite amount of time and in the end Malphite 1 or Malphite 2 will have an infinite amount of movement speed. As seen in this video.