91 vs 89 Octane for 2011 BMW 535i engine

Nothing makes me more angry than for a person to use a lower octane gas in a car that requires premium. I like to run my old Oldsmobile on higher octane gasoline because I jumped the timing up for better performance. I siphon gasoline from cars that I know require premium fuel. When I have gone to the trouble of siphoning fuel from a car that requires premium and the cheap skate owner has used a lower octane gasoline, and my engine starts to ping, it really makes me see red. I don’t want to destroy my engine just because you don’t care about your engine.
Seriously, in the old days, I used to set up my timing and use premium gasoline. I got better mileage and performance and the improved mileage made up the difference in cost. I know that one can’t adjust the timing in modern cars–this is done with the computer. I would guess, however, that the improved mileage using the higher octane on a car that requires the higher octane fuel will justify the added cost.