Movement speed

The Movement Speed affects 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 move speed. That base move speed can be increased in several ways.

Base movement speed ranges from 300 to  330 units per second.

Boots
Purchasing boots from the store grants a champion an increase in movement speed. The effect given by boots is called Enhanced Movement and it is unique, meaning that if a champion has more than one boots item, they will only receive the highest Enhanced Movement bonus.
 * 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.

Every point in Enhanced Movement will thus increase a champion base movement speed by 20, plus a flat 30 speed bonus. As such, basic boots have a higher speed/cost ratio than the other types of boots.

A complete list of boots in the game is the following (ordered by cost):
 * Enhanced Movement 1. 350 Gold.
 * Enhanced Movement 2. +25 Armor, +12% Dodge. 850 Gold.
 * Enhanced Movement 2. +25% Attack Speed. 920 Gold.
 * Enhanced Movement 3. 1000 Gold.
 * Enhanced Movement 2. Passive: When out of combat for 5 seconds the effect of these boots is increased to Enhanced Movement 5. 1000 Gold.
 * Enhanced Movement 2. 15% Cooldown Reduction 1050 Gold.
 * Enhanced Movement 2. +20 Magic Penetration. 1100 Gold.
 * Enhanced Movement 2. +25 Magic Resistance, +35 Tenacity 1200 Gold

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

Calculation
A champion movement speed is given by the following formula:

There are however two soft caps applied to movement speed:
 * If calculated speed is over 490, every point above 490 gets reduced in half.
 * If calculated speed is over 415, only 80% of the excess is given.
 * As an example, if the calculated speed is 600 before soft caps kick in, it is first reduced from 600 to, which is further reduced to  , which means a 13.5'% reduction of the original movement speed.

Every haste or slow effect (except for boots,, and the passive on ) is given as a percentage. The firsts to be calculated are the hastes, followed by slows and diminishing returns (if any) afterwards. Remember that due to how percentage works, a champion affected by a 20% haste and a 20% slow still has a reduced movement speed.

Stacking
Slowing effects follow particular rules regarding to stacking:
 * Slow effects derived from items do NOT stack, even when coming from different champions. Only the strongest slow gets applied in this case.
 * Attacking a champion with the buff when the target is already affected by that slow, will reapply the debuff resetting its duration but will NOT increase the slowing amount. The same holds true for the  summoner spell.
 * If a champion is affected by multiple slows, the strongest effect will be fully applied, while the others are applied with a 65% reduced effectiveness.

Items
Increases the movement speed of a champion by adding a percentage of their base move speed (ordered by movement speed increase)
 * +8% Movement Speed. +76 Magic Resistance, +40 Health Regen per 5 sec, UNIQUE Passive: Restores 0.35% of your champion's health every second. 2610 Gold.
 * +10 Attack Damage, UNIQUE Passive: Your champion gains 5 damage per stack, receiving 2 stacks for a kill or 1 stack for an assist. This effect can stack 20 times; you lose a third of your stacks if you die. At 20 stacks, your champion's movement speed is increased by 15%. 1369 Gold.
 * +8% Movement Speed. +20% Attack Speed, +10% Critical Strike. 1195 Gold.
 * +7% Movement Speed. +350 Mana, +80 AP, +30 Magic Resist, UNIQUE Passive: 100% chance when an ability is used that your next physical attack deals an additional 100% of your Ability Power in damage. This effect has a 3 second cooldown. 3470 Gold.
 * +15% Movement Speed. +55% Attack Speed, +30% Critical Strike. 2895 Gold.
 * +12% Movement Speed. +30 Attack Damage, +30 Ability Power, +30% Attack Speed, +15% Crit Chance, +250 Health, +250 Mana, UNIQUE Passive: 25% chance on hit to slow the target by 35% for 2.5 seconds; on cast, increases your base Attack Damage by 150% for one attack. 4070 Gold.
 * +30 Attack Damage, +15% Critical Strike, UNIQUE Passive: Reduces cooldowns by 15% and +20 armor penetration, UNIQUE Active: Gives 20% movement speed and +50% attack speed for 4 seconds. Attacking enemy units with melee attacks increases the duration by 2 to a maximum of 8 seconds. 60 second cooldown. 2687 Gold.
 * +330 Health, +30 Health Regen per 5 sec +15 Mana Regen per 5 sec. Unique passive: Reduces ability cooldowns by 15%. Unique active: Nearby champions gain 40% movement speed for 3 seconds (60 second cooldown) 2200 Gold.

Summoner Spell

 * Your Champion ignores unit collision and moves 27% faster for 10 seconds.
 * revives your champion instantly at the spawning pool and increases movement speed by 225%, diminishing to normal over 12 seconds.

Mastery

 * mastery increases the movement speed of your spell by 6% and its duration by 1.5 seconds.
 * Increases your movement speed by 10% for 5 seconds after dodging an attack.
 * Increases your base movement speed by (1/2/3)%. (Note: Despite the description, this doesn't affect base movement speed and simply works like other percentage bonuses.)

Runes

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

Champion Abilities

 * grants him (16 / 20 / 24 / 28 / 32)% increased movement and (30 / 38 / 46 / 54 / 62)% attack speed for 8 seconds.
 * grants her (15 /17.5 / 20 / 22.5 / 25)% increased movement if she hits a champion.
 * grants him (15 / 25 / 35)% extra movement speed for 12 seconds as well as heals him for 40 / 55 / 70 % of his max health.
 * grants her (50 / 75 / 100)% attack speed and (20 / 25 / 30)% movement speed for 10 seconds.
 * creates a directional draft for 5 seconds which increasing the movement speed of allies passing through it by (20 / 25 / 30 / 35 / 40)%.
 * grants him (8 / 10 / 12 / 14 / 16) attack damage and (3 / 4 / 5 / 6 / 7)% movement speed passively. When activated it grants Gangplank (14 /18 /22 /26 /30)% movement speed and (20 /28 /36 /44 /52) attack damage. Nearby allies receive (7 /9 /11 /13 /15)% movement speed and (10 /14 /18 /22 /26) attack damage.
 * grants him (15 / 20 / 25 / 30 / 35)% increased movement for 3 seconds.
 * passive increases the movement speed of all allied champions by 3% while she's alive.
 * passively increases her movement speed by (8 / 10 / 12 / 14 / 16)% and enables her to pass through units.
 * increases her movement speed and an ally's movement speed by (10 / 12 / 14 / 16 / 18 / 20)%. The amount is doubled if she uses a charge on the spell.
 * increases an allied champion's movement speed by 12% for 10 seconds.
 * grants him a flat bonus to movement equal to his base movement speed (after any other bonuses are calculated) and the ability to move through units for 4 seconds.
 * steals (14 / 17 / 20 / 23 / 26)% movement speed from the target for 4 seconds.
 * increases his movespeed by 40% for 6/9/12 seconds.
 * passive grants her an additional 25 movement speed after not taking any damage for 7 or more seconds, increasing each second up to 70 maximum bonus speed.
 * grants her 20 movement speed in cougar form.
 * grants 15% movement speed for 2 seconds when moving through brush.
 * increases his movespeed by (15 / 20 / 25 / 30 / 35)% while in the trail it or the enemy champion leaves.
 * grants an allied unit (25 / 35 / 45 / 55 / 65)% increased attack speed and (11 / 12.5 / 13 / 14.5 / 15)% increased movement speed for 15 seconds. If cast on an ally, Nunu also gains the effect of Blood Boil.
 * increases movement speed of allies moving through it's area of effect by (25 / 30 / 35 / 40 / 45)%.
 * grants her (17 / 19 / 21 / 23 / 25)% increased movement speed for 5 seconds when activated.
 * grants him an increasing bonus to movement speed while active.
 * grants him (10 / 15 / 20 / 25 / 30)% increased movement speed for 1 second. When in the "Danger Zone" this amount is increased by 30%.
 * grants him (35 / 50 / 65) increased movement speed while active.
 * grants her and nearby allies 25% extra movement speed and a percentage of attack speed (a third for her allies) for 15 seconds.
 * grants nearby allied champions bonus movement speed (8 / 11 / 14 / 17 / 20). On activation, it grants an additional burst of speed (6 / 8 / 10 / 12 / 14)% for 1.5 seconds.
 * increases his movement speed by (10 / 14 / 18 / 22 / 26 )%. If Teemo gets hit by a champion or turret while Moving Quick, he gets knocked out of it. 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 (20 / 30 / 40 / 50 / 60)% attack speed, (20 / 25 / 30 / 35 / 40)% movement Speed, and (20 / 25 / 30 / 35 / 40)% CC reduction while on it.
 * grants him (15 / 18 / 21 / 24 / 27)% increased movement speed for (2 / 2.5 / 3 / 3.5 / 4) seconds upon activation.
 * gains 40 Movement Speed when moving towards an enemy champion. After activating she gains 120 Movement Speed for 8 / 10 / 12 seconds when moving towards an enemy champion instead.
 * senses enemy champions under 50% life within (1500 / 2300 / 3100 / 3900 / 4700) distance of him; while he detects a low-health enemy, he gains (20 / 25 / 30 / 35 / 40)% increased movement speed.
 * increases an allied champion's movement speed by 55% for (2.5 / 3.25 / 4 / 4.75 / 5.5) seconds.

Neutral Buffs

 * The buff gives 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.