I've got a manual, and a sport button (although it's a 3.0 Z4 - the button probably didn't come on the 2.2, or if it did it might not have been standard - someone on here might be able to confirm this) - I think all it does (in terms of the throttle) is switch to a slightly different map so that when you press the throttle for a given amount of travel, the engine speed rises more than if you had the button switched off. I can't comment on the delay in throttle response as mine seems ok, but I've never driven the 2.2 - I know the 2.0 4-pot actually wasn't bad, not as quick to accelerate as a 2.5/3.0 (to be expected) but I didn't notice a delay in response i.e. push the pedal, engine speed rises. Other members may be able to say more on it...