I know that you move slower when using your basic attack. I also know that jumping has no speed penalties. Is this the same when running backwards or sideways?
If true, what is the speed difference between each direction?
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From the Wiki
The Backpedal penalty is applied when walking backward. The Strafing penalty is applied for moving sideways. The Basic Attack penalty is applied while using basic attacks and for a short time afterwards. None of these penalties are shown in the movement speed counter. Some abilities such as Medusa's passive allow one or more of these penalties to be ignored.
According to community experiments:
Backpedal penalty = 40% reduced Strafing penalty = 20% reduced Ranged Basic Attack penalty = 50% reduced Melee Basic Attack penalty = 35% reduced
Note: Movement speed reduction from the mentioned above sources can be compounded, but cannot exceed 50% reduction (e.g moving backwards while attacking will only reduce the player's movement speed by 50%).