ZDC / BBC Stability for Relative Luminosity

I've made a plot of ZDC (E && W) integrated over bunch crossing / BBC (E && W) integrated over bunch crossing for several (1216) runs starting after run #10122050 (after which Hank's made some important timing adjustments):

It's important to notice that boards 4 and 6 "track each other".  Also, each vertical striation corresponds roughly to a fill.  If you were to zoom into one of these, you would see that each "strip" curves to the right; e.g., fill 10712:

We would like for this ratio to be "flat"--but exactly how flat must it be for the needed precision in the relative luminosity (~ 10-5) ?