Most guys shoot better when they are open.
I remember seeing the statistic that Ray Allen hits over 70% of 3's when he is "wide open." I guess the 3-point contest percentages would be a pretty good indication of that (the rhythm benefit would offset the fatigue factor).
EDIT:
I guess I was thinking of this:
Sacramento Kings player offensive production by shot contestedness from 82games.com
The guy charted out every shot the team took all year and ranked the level of costedness of each shot. Stojakovich is the one that was pretty shocking.
The one thing that I'm not sure of is how many of those "uncontested shots" were layups off fast breaks vs. 3-pointers, etc.
But looking at Stojakovich, it looks like he made 10 3's and 13 2's on the season when he was deemed wide open. So even if all his 2's were bunnies, he must have still shot lights out from the perimeter when left open.