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Almost all gasoline engines made in the last 10 years have fairly high compression ratios. This improves fuel economy and performance. Due to the large range of loads, altitudes etc, that the engines run at, variable cam and ignition timing are used to prevent detonation and provide optimal fuel economy. This means that bumping from the 87 to a higher octane results in better power, especially at sea level. For naturally aspirated engines, the gains are usually small, maybe a couple percent. The higher the compression ratio the bigger the gains.
Forced induction causes the adjusted compression ratio to rise with the boost level. Cramming more fuel/air into the cylinder means more power, but with lower octane fuel the ignition needs to be retarded significantly. Higher octane fuels allow the engine to run optimal ignition and cam timing. In some cases the gains can be as much as 10%.
The EcoBoost uses fuel to stave off detonation, which is why they get better fuel mileage on premium vs. regular.