Thomas Shey
Legend
Sorry, dude. You've lost me.
Let me use an example where it worked pretty well, even though its a system I fell out of love with.
Mutants and Masterminds, though evolved from D&D3e, is philosophically a relative of Champions; its effect based, point built and class and level (at least in the sense its used in normal level systems) free.
One of the things you do is buy your Accuracy in combat. There are degrees of breadth in how you do it (so you can specialize or not).
So let's say you have a Superman expie and a Batman expie at the same power level. The Superman expie buys his Accuracy at +8 and his Strength (which he'll use for damage when not using his heat vision) at +12. Batmanoid buys his Accuracy at +12, buys his Strength at +6 (which is within the high end human range) and buys an extra +2 damage to represent martial arts.
Both of them buy Power Attack. Power Attack allows you to take a penalty of up to -5 on your attack to add a bonus of up to +5 on your damage.
The difference is, the Superman type is probably only using this to, say, punch out giant robots and other things with no defense worth mentioning. The Batman equivalent, on the other hand, starts with a high enough attack that against a lot of easy-to-hit-but-tough opponents he can afford to throw it all to damage and still have a fair chance of hitting.
In terms of basic damage, he's still well below the Superman equivalent, and hit maximum is well below him. But in terms of practical ability to deliver damage, he's not that bad off.
Since I know you're a Hero guy, you get something not dissimilar with Haymakers, and a number of other supers games have something similar.