Yes, there is scientific data that proves the Wizards will be a better team with Caron Butler taking more shots than Gilbert Arenas. The Truth will indeed set the Wizards' offense free.
Considering I’m much more of a writer than a statistician, my take is based more on the poetics of the matter rather than the probable outcomes presented in the numbers. First, Arenas was far happier and bolder taking shots in the free-wheeling Eddie Jordan offense. He had the money, the scoring output, and the game-winning DAGGERS to justify free-falling into a 6-22 night on any given night.
Butler, with his size and skill from mid-range, has much more opportunity to hold opponents at his mercy. He’s strong enough to handle guards and quick enough off the dribble to make most small forwards work hard defensively (which, Butler says, very few enjoy doing).
Arenas is a better shooter and playmaker than Butler, but he doesn’t open the floor up for Butler. Because most guards would prefer to sag off Agent Zero on a cold shooting night, the three-point line is ripe for Butler even if his drives to the hoop are taken away.
Conversely, most teams would have to respect Butler in the post because he has a good repertoire with his back to the basket. A spacing game between Arenas and Butler opens up the opportunity to drive to the hoop, or get a poorly-contested jump shot. The same goes for Antawn Jamison on the opposite side of the floor.
The Wizards have always been a dangerous team, just not a smart one. Between the maturation of Arenas and the organization of Flip Saunders, it may be enough to seriously contend in the Eastern Conference.