Unless you're fairly talented with hand release and ball speed changes, once you need to move inside due to oil depletion and drying outsides, you often have to go with a weaker drilled, polished and/or pearlized ball. (with the large number of coverstocks these days we don't always have to go to pearlized balls when we move inside any more.)
So, as one example, if you start off with a dull/matte or lightly polished solid/hybrid drilled with a 4" - 4.5" pin-PAP, maybe at or below your fingers ( possibly a 60x4x60 or 60x4x40 drilling), to move inside effectively, one often needs to move to a highly polished 1/2 - 1 stage weaker (maybe hybrid, maybe pearl) coverstock, with a 5" - 5.5" pin-PAP, with maybe the pin at or above the level of the fingers, (possibly a 50x5x30 or a 60x5.5x25 drilling).
Concrete examples:
You start off with a Brawler and drop down to a Ringer.
You start off with an Arson Hybrid and drop down to a Cobalt Vibe
You start off a Crossroad and drop down to a Freakin Frantic
You start off with a Disturbed and drop down to a Shatter