Critical Ring is replaced by what?

If you have under 171 total attack, a 5atk ring can replace it.
If you have under 229 total attack, a 6atk ring can replace it.
If you have under 286 total attack, a 7atk ring can replace it.

Shouldn't str also be a factor? Or more accurately shouldn't it go off your entire range, not just your w.atk?