Shiorin

Given <136 hit rating, is there a (relatively) easy way to relate crit power to hit rating?

I realize this is a "complicated" question requiring modelling of a combat system we don't have the source for. My question is which is superior, Lightwarden's Band(+18 agi, +38 ap), or the Ring of Shadow Deeps (+13 hr, +21 crit, +24 ap) for me right now.

Based on just the crit and ap the band is 0.5% better, but since I'm still under the magical never-miss level, I assume the hit rating picks up some of that.. the question is.. enough to favor wearing it?