Judging from the manual
- A loss of effectiveness reduces a vehicle's movement speed (manual p.15). It is calibrated in a way that at 50% effectiveness, a vehicle moves only at 75% of its max. speed.
- Fire Combat: The effectiveness of a vehicle affects its firepower (it modifies the fire value, p. 36). There is no effect on its defensive power in fire combat - the resilience of a vehicle is only determined by its armor value and by whether the vehicle is immobilized or not.
- Assault (p. 56): When it comes to determining a vehicle's offensive assault power, a vehicle's weapons and - unless immobilized - its armor value matter. If the vehicle's effectiveness should also taken into account, then the manual forgot to mention it. The defensive power of a vehicle in assaults depends entirely on its armor value and on whether it is immobilized or not.
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So, to sum it up, it seems as if effectiveness only affects the movement speed and the fire power of vehicles. But it neither affects the defensive parameters of a vehicle, nor its performance in assaults.