User:Irismus/SandboxPage



Movement speed (sometimes abbreviated as Move Speed or $$ms$$ ) is the speed at which a unit can move over a second. The default movement speed caps are at on the low end, and  on the high end, which can be bypassed by only a few abilities. Only units capable of moving can have a movement speed. This means granting a non-mobile unit movement speed with an ability does not allow them to move still. A unit's movement speed can be increased by abilities, items or talent. Some items grant passive speed bonuses to the wielder.

Commands
There are several different orders which make the unit move.

Move Command
The default move command is bound to mouseright or M, it can also be bound to a hotkey. Targeting the ground with this command makes the unit move to that point, or until unable to get closer to the point (i.e. target is out of reach). During a move command, the unit does not automatically attack enemies on the way.

Follow Command
The follow command is merged in with the default M move command, and is executed with the same keys. To follow a unit, the move command has to be targeted on the desired unit to follow. Targeting an allied unit with the move command makes the unit follow the allied unit, until a new order is given or until the targeted unit dies. The follow range for most units is 100, meaning a unit ordered to follow another unit attempts to stay within 100 range of the targeted unit. Mobile ward type summons (such as ) have a follow range of 250. In order to follow enemy units, the hotkey must be used, since mouseright on an enemy automatically orders an attack on it.

Patrol Command
The patrol command makes the unit move back and forth between its starting location and the targeted point, until it is given another order. A unit can be given multiple points to patrol. When doing so, the unit moves to the targeted points in the same order in which they were given. Upon reaching the last point, it moves back in reversed order. Just like the move command, the unit will automatically attack enemies it crosses while patrolling.

The default hotkey for the Patrol Command is blank.

Attack-move Command
The default Attack-move command is bound to A, it can also be bound to a hotkey.

Identical to the move command, with the difference being the ordered unit attacking any enemy they cross while moving. This order can be given by giving an attack order onto the ground. To do this, the attack hotkey must be used. If the unit crosses no enemies during an attack move order, it essentially acts as a move order. When an enemy gets within the unit's acquisition range, it goes towards that enemy and attacks it. If the target can no longer be attacked for any reason (dies, becomes ethereal or invulnerable, turns invisible or loss of sight over target), the unit resumes moving towards the targeted point, continuing from its current location. It does not trace its way back to where it left the path to attack an enemy.

Total Movement Speed
Calculating the total movement speed of a unit involves using a few values and a multiplier.
 * If a Set Movement Speed value is present, the set value overrides the unit's original base movement speed.
 * If the Set Movement Speed value is absolute, the absolute value is now the unit's Total Movement Speed.
 * Absolute Movement Speed can only be affected by haste and abilities that modify minimum movement speed limit.
 * Flat movement speed bonuses (items, abilities and talents) are simply added to the base movement speed of the unit.
 * Movement speed percentage based bonuses and slows get all summed up, and then applied to the unit's base movement speed as a multiplier.

Movement Speed Multiplier ( $${ms}_{Mu}$$ ) is defined as


 * $${ms}_{Mu} = 1 + \sum_{i=1}^n (a_{i}) - \sum_{j=1}^m (r_{i}) $$

With  being the bonus and   being slows movement speed percentage values respectively.

Total Movement Speed is defined as


 * $$\sum{ms} =

\begin{cases} \mid ms\mid & \quad \text{if } \!\! & \mid ms\mid &= \top \\ (ms_{B} + ms\sum_{i=1}^n f_{i}) \times ms_{Mu} & \quad \text{if } \!\! & ms_{Set} &= \top \, \rightarrow \, ms_{Set} = ms_{B} \end{cases}$$

With  being the Absolute Movement Speed value,   the Set Movement Speed value,   the Base Movement Speed and   the Flat Movement Speed values.

Stacking Restrictions
However, most item-based speed bonuses have stacking restrictions. Passive movement speed bonuses from items are separated into groups. The movement speed bonuses of the items in their groups do not stack with each other or with multiple of themselves, but do stack with the bonuses from items from the other groups.
 * Group 1: Boots
 * Group 2: based items.
 * Group 3: itself.
 * Items that do not belong in any of the groups above fully stack with each other, with multiple of themselves, and with all other item bonuses, including.
 * Bonuses from abilities and talents have no such restrictions and stack with all other bonuses.

Examples
A maxed level with  has, a  and. She is currently affected by a level 4. What is her current movement speed?
 * Example 1


 * Flat movement speed values:
 * 's base movement speed:


 * Percentage movement speed values:



has a theoretical movement speed of from abilities and items in this calculation example, but it gets capped at, so long she is not affected by anything that unlocks the maximum movement speed.

The same from the previous example is now also affected a level 4, along with the level 4. What is her current movement speed?
 * Example 2


 * Flat movement speed values:
 * 's base movement speed:


 * Percentage movement speed values:



has a theoretical movement speed of, which again gets capped at. This example shows that the movement speed cap is ignored by the calculations, meaning the strong slow of is not applied to her actual current movement speed of, but gets subtracted from the percentage-based movement speed bonuses before being applied to the sum of the flat movement speed values.

Base Movement Speed
Every unit capable of moving has a base movement speed ( $$ms_{B}$$ ) value. This value is fixed, and can only be altered by very few abilities.

Heroes
The following list shows the base movement speed of all heroes, and their movement speeds with any of the items based on

Set Movement Speed
Set Movement Speed ( $$ms_{Set}$$ ) sets a unit's movement speed to a fixed value for the duration. The units are still fully affected by flat and percentage-based movement speed changes. The movement speed is still bound to the minimum and maximum movement speed limits. If a unit is affected by multiple abilities in this list, the lowest value takes priority.

The following abilities are able to override a unit's base movement speed, setting it at a certain value.

Absolute Movement Speed
The following abilities set a unit's movement speed to an absolute value ( $$\mid ms\mid$$ ). No other values can change them, with the only exception of abilities that increase the minimum movement speed limit, which includes all Hastes.

Absolute Movement Speed is defined as


 * $$\mid ms\mid =

\begin{cases}

\sum{ms} \quad & \text{if } & \mid ms\mid &= \top \\ \text{min}(ms) \quad & \text{when } & \text{min}(ms) &= \top \\ ms_{Haste} \quad & \text{when } & ms_{Haste} &= \top

\end{cases}$$

Movement Speed Limits
By default, the lower limit for movement speed is at, while the upper limit lies at. These values are the same for all units and cannot be exceeded by flat or percentage movement speed bonuses or reductions. Base movement speed changes cannot exceed these either.

Minimum Movement Speed
The following abilities are able to change a unit's minimum movement speed, preventing it from ever being lower than the set value. If a unit is affected by multiple abilities that change the minimum value, the higher value takes priority.

Maximum Movement Speed
The following abilities are able to change a unit's maximum movement speed (of ), allowing it to reach even higher values. If a unit is affected by multiple abilities that change the maximum value, the higher value takes priority.

Haste
Hastes increase a unit's minimum and maximum movement speed to a specific value. Hasted units cannot be slowed below the hasted value.

Modifying Movement Speed
There are several properties that affect a unit's movement speed in different ways.

Flat Movement Speed Changes
These abilities increase or decrease a unit's movement speed by a constant value.
 * These bonuses and reductions can not exceed the minimum and maximum movement speed limits.
 * These are applied before percentage-based movement speed bonuses and reductions.

Items
These items passively grant the wielder a flat movement speed bonus.

Percentage Movement Speed Changes
Percentage Movement Speed Changes can not exceed the minimum and maximum movement speed limits and are applied after flat movement speed bonuses and reductions. There are stacking restrictions for items, but no restrictions on stacking percentage movement speed bonus from abilities.

Items
These items passively grant the wielder a flat movement speed bonus.

Recent Changes
Скорость передвижения 移动速度