If you have a performance vehicle (usually a european made car; sorry this doesn’t include what i personally call “performance cars”), like a Mercedes, BMW, Jag… basically any expensive european car, then it will most likely take a higher octane gas. If you put the specific type of gas you are supposed to, then your gas mileage should remain where they say it is, and will run much cleaner and smoother.
If you put the wrong octane in a car, say a lower octane in a higher octane required car, well… not a good idea, but higher octane cars run at higher compressions, thus require the higher octane gas to run properly, if you run under octane, then chances are it won’t run clean, and will put a dent in your gas mileage.
If you put higher octane in a low octane car, then you just plain shattered your gas mileage for the most part, and are an idiot for paying the higher price in the first place.