Well the problem is marketing numbers versus engineering numbers. I don't know the forumula off hand to give you the answer you want, but in general, engines with higher compression tend to do better with higher octane fuels in both power and mpg (in the case of atkinson cycle engines, power is sacrificied for efficiency so high mpg but not more power).

There are cars that are more tailered towards lower octane gas and get better power/mpg by using the recommended fuel octane rating such as the HCH.

The atkinson cycle engine (like found in the prius) tends to be on the higher side of compression ratios, which to me means in order to really take advantage of this engine, you need to use higher octane fuel. But the problem is higher octane fuel tends to be more expensive, so marketing kicks in and says you can use regular because you end up saving more even though you might get better mpg using higher octane fuel, but from an engineering point of view, the recommended octane level will be higher than what is listed.

So there is going to be an ideal octane rating for every engine for efficiency and one for power. The problem is those numbers are rarely published.