Statistics on non-static AC vs. attack bonus?

[RangerWickett]

I'll admit, I'm no good at multi-die statistics, so can someone help me out?

How do you determine the odds of hitting if you roll both for attacking and for AC (using the optional rule in the DMG that your AC is d20 + modifiers, instead of 10 + modifiers)?

 

[Stalker0]

The average odds of hitting someone should be exactly the same, as the average does not change. However, the variance would change a great deal.

Edit: Actually it is a little different. In this case, the average AC is 10.5 + mods not 10 (with a d20 roll). So all hit probability are adjusted by 2.5%