A system according to the principles of the present invention includes a firing fraction module, an offset generation module, and a firing fraction module. The firing fraction module determines a firing fraction based on a driver torque request. The offset generation module randomly generates an offset. The firing control module adds the firing fraction to a running total each time that a crankshaft of an engine rotates through a predetermined angle, adds the offset to the running total, and executes a firing event in a cylinder of the engine when the running total is greater than or equal to a predetermined value.