If the target is affected by an effect that slows down by 20%, its speed will change by the formula movement_speed*0.8.

If the target is also affected by the same effect, the slowdown remains the same, just the action timer is updated.

If the target will be affected by 2 different slow-down effects (e.g. 20% and 30%), they will be multiplied. The result is movement_speed*0.8*0.7.

If the slows down effects are cumulative (like Ice Arrows with 10% slows down), they will also increase to their limit: movement_speed*0.1*0.1*0.1.

If the target is affected by both cumulative and normal effects, they will also be multiplied. So, if Swordsman is a unit with Ice Arrows and Witch effects, the slowdown will work like this: 12*0.3*0.1*0.1*0.1*0.1 and so on up to the Ice Arrows cumulation limit.