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, basic attack has a range of 625 game distance units).

Each champion begins the game with a particular base movement speed, ranging from 300 (, and 11 others) to 330 ( and ) units per second. 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, spells, masteries, runes or neutral buffs.

Calculations
A champion's movement speed is given by the following formula:
 * (Base Movement SpeedFlat Movement Bonuses)(1Percentage Movement Bonuses)Slow Ratio

Diminishing returns are then applied to the result.

Movement speed bonuses
Flat bonuses are applied first, then percent bonuses and slows, then diminishing returns. Most bonuses and slows are given as percentages. The exceptions are:
 * Boots.
 * The passive aura on.
 * The passive aura on.
 * The passive aura on.
 * The passive aura on.
 * The passive aura on.
 * The passive aura on.
 * The passive aura on.
 * The passive aura on.
 * The passive aura on.

Remember that because bonuses and slows are applied to each other, a champion affected by a 20% bonus and a 20% slow still has a net reduced movement speed (e.g. 3001.20.8288).

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)0.5(490415)0.8415530, which means an 11.7% reduction of the original movement speed.

These are the simplified formulas:
 * If the raw speed is 415 or under, no cap is applied.
 * If the raw speed is between 415 and 490, final speed is soft capped to RawMS0.883.
 * If the raw speed is above 490, final speed is soft capped to RawMS0.5230.

When the raw movement speed is less than 220 another soft cap is used:
 * If the raw speed below 220, it gets multiplied by 50% and added to 110.
 * Example: if the calculated raw speed is 180 before soft caps kick in, it is increased to 1800.5110200.

Slow stacking
Slowing effects follow particular rules when stacking:
 * If a champion is affected by multiple slows, the strongest one will be fully applied, while the others are applied sequentially with 65% reduced effectiveness down to 35% of its original strength.
 * Slow effects derived from items' passives do NOT stack, even when coming from different champions. Only the strongest item slow is applied at any moment. The exception to this is the active effect of, and , which stacks with other slowing items normally because they are considered champion abilities for slow stacking purposes.
 * Attacking a champion with the buff when the target is already affected by that slow will reapply the debuff, resetting its duration. It will NOT increase the slow amount. The same holds true for the  summoner spell.

Example
A champion with a raw movement speed of 400 is affected by a 2 second long 40% slow and a 5 second long 20% slow at the same time.
 * For the first two seconds, he will have (10.4)(10.20.35)0.60.9355.8% of his original movement speed (a 44.2% effective slow). So he will have 4000.558223.2 raw movement speed.
 * For the following three seconds, the effective slow will be 20% and so he will have 4000.8320 movement speed.
 * After that, he will return to his normal speed of 400.

Increasing flat movement speed
Purchasing boots from the store grants a champion a flat increase in movement speed. The effect given by boots is called Enhanced Movement and is unique, which means that if a champion has multiple pairs of boots, they will only receive the highest Enhanced Movement bonus. The bonus from boots is quite big compared to their cost and is essential for all champions.


 * Enhanced Movement 1 increases the base movement speed of a champion by 50.
 * Enhanced Movement 2 increases the base movement speed of a champion by 70.
 * Enhanced Movement 3 increases the base movement speed of a champion by 90.
 * Enhanced Movement 5 increases the base movement speed of a champion by 130.

Enhanced Movement gives 20 movement speed per rank plus a flat 30 movement speed. As such, basic boots have a higher speed-to-cost ratio than upgraded boots.

In addition, some champions have abilities that increase their movement speed by a flat amount.

Boots
This is a complete list of boots, ordered by cost:

The bonus given by boots is a flat increase to the champion's base movement speed, meaning that it will increase the effectiveness of percentage bonuses.

Flat increase

 * passively grants her 10 flat movement speed while she is in spider form.
 * grants her flat movement speed for 3 seconds each time she hits an enemy champion with her abilities. This effect stacks up to 4 times.
 * grants him 40 movement speed for 1.25 seconds each time Transform is cast.
 * grants him 310 flat movement speed for 3 seconds.
 * passively grants her 25 flat movement speed after not taking any damage for 5 or more seconds, increasing by 9 each second up to 70 flat movement speed.
 * passively grants her 20 flat movement speed while she is in cougar form.
 * grants him flat movement speed for  seconds.
 * grants him flat movement speed for 25 seconds.
 * grants her 50 flat movement speed for 2 seconds after landing a basic attack on an enemy champion.
 * passively grants nearby allied champions flat movement speed.
 * passively grants her 30 flat movement speed when moving towards an enemy champion. The activation of grants her 90 flat movement speed for  seconds when moving towards an enemy champion instead.

Other items
These items increase the movement speed of a champion by a percentage of their base move speed (ordered alphabetically).

Champion abilities
Note: Only the movement speed bonus effect of these abilities is shown here. To read more about each of these abilities, follow their respective links.
 * grants him increased movement for 8 seconds.
 * grants her increased movement for three seconds if she hits a champion with the ability.
 * grants him extra movement speed for 12 seconds.
 * grants him 5% movement speed for each bleeding enemy champion.
 * grants him movement speed for 1.5 seconds. The movement speed bonus decreases rapidly over its duration.
 * grants her movement speed for 3 seconds.
 * increases her movement speeds by for 3 seconds for each basic attacks she lands, stacking up to 3 times.
 * creates a directional draft for 5 seconds which increases the movement speed of allies passing through it by.
 * grants him movement speed passively. He can also activate this ability to increase his movement speed by  instead, also increasing nearby allied champions' movement speed by half of that amount for the duration.
 * grants him 35% increased movement for seconds.
 * grants him 75% movement speed over the course of three seconds, ending one second afterward.
 * increases the movement speed of all allied champions by 3% while she's alive.
 * passively increases her movement speed by and enables her to pass through units. This bonus is lost while the ability is in cooldown.
 * deploys an Acceleration Gate for 4 seconds, increasing the movement speed of all allies who pass through it by for 3 seconds. This bonus fades over the duration.
 * creates a beam between her and an ally or enemy for up to 5 seconds. Allied anchors move faster and enemy anchors are slowed by . The beam also applies the same movement speed adjustment anchors receive to any champion it passes through for 3 seconds (depending on wether they are allies or enemies). The beam breaks if the bonded target is stealth or if they walk too far away from Karma. If a  charge is used on the ability, then all movement speed modifiers are doubled.
 * increases her movement speed by for 1 second if she hits an enemy with this ability.
 * increases an allied champion's movement speed by for 3 seconds.
 * grants him 40% movement speed for 1 second.
 * grants her or an allied champion 35% movement speed for 5 seconds.
 * steals movement speed from the target as a flat movement speed bonus for 4 seconds. The flat bonus is applied after any other movement speed bonuses.
 * increases his movement speed by 40% for seconds.
 * grants her 15% movement speed for 2 seconds when moving through brush.
 * increases his movement speed by while in the trail made by the ability or left by enemy champions hit by it.
 * grants him and the target allied unit increased movement speed for 15 seconds.
 * leaves an electric field on the area for 3 seconds. The field speeds up allies and slows enemies by that walk over it. This effect diminishes to normal over 2 seconds after leaving the area.
 * grants her increased movement speed for 5 seconds when activated.
 * grants him 30% initial bonus movement speed plus additional bonus movement speed while active (roughly 10% of his movement speed every second). It lasts up to 7 seconds.
 * grants him increased movement speed for up to 7 seconds, until he uses an ability.
 * grants him increased movement speed for 1 second. When in the "Danger Zone", this amount is increased by 25%.
 * grants her increased movement speed for 3 to 7 seconds, this bonus movement speed decreases over time.
 * grants him a flat bonus of increased movement speed for 25 seconds.
 * grants her and nearby allies 20% extra movement speed for 10 seconds.
 * grants him an absorption shield for up to 6 seconds and extra movement speed for as long as the shield remains.
 * increases the movement speed of nearby allies by for 1.5 seconds upon activation.
 * will stealth him for 2.5 seconds and give him 40% increased movement speed.
 * increases his movement speed by until he is struck by a champion or a turret. He can activate it to gain double the passive, for 3 seconds, which will not be lost even if he is hit.
 * infects a target location with his curse for 8 seconds, granting him movement speed while on it.
 * grants him 20% movement speed while stealthed, maximum duration of seconds.
 * grants him increased movement speed for  seconds upon activation.
 * grants him 30% movement speed bonus for 3 seconds if the Hex Core is.
 * grants him 15% bonus movement speed for 4 seconds. The bonus increase to 45% if he is moving towards a nearby visible enemy champion.
 * senses enemy champions under 50% life within distance of him; while he detects a low-health enemy, he gains  increased movement speed.
 * gains him an increasing 5% movement speed bonus every half second for the duration of the spell, with the bonus disappearing once he stops spinning.
 * : upon deactivation, Xerath gains 35% movement speed for 2 seconds.
 * summons a ghoul, which when alive (max duration is 5 seconds) grants Yorick increased movement speed.
 * increases an allied champion's movement speed by 55% for seconds.
 * increases an allied champion's movement speed by 55% for seconds.

Summoner spells

 * allows your champion to ignore unit collision and gain 27% movement speed for 10 seconds.

Masteries

 * mastery grants a massive movement speed boost (125%) for a short duration upon casting.
 * mastery increases the movement speed of your spell to 35%.
 * gives Movement speed when above 70% health.
 * gives Movement speed.

Runes

 * runes increase movement speed.
 * Quintessence of the Speedy Specter runes increase movement speed by 1.39% each. (Tier 2.5)

Neutral Buffs

 * The Speed Shrine buff on Dominion grants 30% increased movement speed.

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

General video guide regarding movement speed and slows
http://www.youtube.com/watch?v=XAfhaIsKouw

Trivia
Assuming calculations are correct, the maximum movement speed possible is 119,140. It is obtained by, reaching the maximum of while under the effects of , a fully-stacked , 3 x , , an  effect, enhanced  and , , and , passing through  and , with 3 Greater Quintessences of Swiftness, 4 points in , and 3 points in.