Engines with high compression ratios and/or many boosted engines (turbocharged or supercharged engines) can benefit from higher octane fuel. Octane measures the fuel's resistance to self-ignition. From basic thermodynamic theory and the ideal gas law (pressure * volume = n * R * temperature where "n" is a constant based on the air + fuel chemical composition and "R" is one of those universal chemistry/physics constants) compressing an air+fuel mix as the piston goes up (reducing volume while substantially increasing pressure) forces the air+fuel mix temperature to rise to keep the equation balanced. Turbocharged and supercharged engines use mechanical devices (the turbo or supercharger, duh) to pre-pressurize the air going into the engine. More air going into the engine = more potential horsepower. But boosting the incoming air pressure also subjects it to that ideal gas law, raising the intake air temperatures before the piston-induced temp increase. Intercoolers cancel some of the turbo/supercharger created temperature increase but can't cancel the piston induced temp increase. If the air+fuel mix gets hot enough the air+fuel will self-ignite (rather than waiting for the
spark plug to do its job) leading to engine-part-damaging detonation if too severe. If the temperature is not quite up to the self-ignition value then the
spark plug will still start the combustion process... but now the combustion will happen too quickly leading to pinging or mild knocking. The amount of air in the cylinders, compressed by the piston, is a function of the throttle (gas pedal) position: low throttle means little air is actually inside the cylinder so there isn't much to compress and thus peak pressures stay low. But "wide open throttle" or "pedal to the metal" lets in as much air as the cylinders can handle (and turbo/superchargers shove in even more air compared to non-boosted engines) so there are many more air molecules in the cylinders... so there's more to compress and thus pressures and temperatures will be much higher prior to the spark.
Modern engines use a "knock sensor" (which is really just a microphone screwed to the side of the engine) to detect pinging/knock/detonation vibrations... when the knock sensor output exceeds a specific magnitude the engine control computer takes action to protect the engine. That action typically includes retarding the ignition timing a bit - so the spark is later in the 4-stroke cycle - which reduces the combustion temperatures. This works only if the issue is pinging or minor knock; if severe detonation is present reducing the ignition timing won't matter as the air+fuel has self-ignited before the spark occured. The only "fix" is to add more fuel on the next 4-stroke cycle, diluting the air+fuel mix. The extra fuel molecules, which are FAR heavier than air molecules - will absorb some of that temperature increase, lowering the peak temperature to hopefully something less than the self-ignition temp. On turbocharged and supercharged engines, the engine computer can reduce the boost pressure to reduce the air temp increase caused by the turbo/supercharger and to reduce the total amount of air in the cylinders during the compression stroke which reduces the air+fuel temps too. Both fixes reduce the horsepower produced however.
The self-ignition temp is a function of several things including the ambient air temperature - on a hot desert day its easier to raise the air+fuel temp to the self-ignition temp compared to starting with near-freezing temps. And octane is a major player as well. On boosted engines the turbo/supercharger boost process raises the temp quite a bit; the
intercooler negates some (but not all) of that temp increase. Simple air-to-air intercoolers work best on cold days; water-to-air intercoolers are more complex but less sensitive to ambient air temps.
In the old days, ignition timing was set by simple mechanical means - you may remember "centrifugal advance mechanisms" and "vacuum advance mechanisms" on distributors. Modern engines replaced those rather imprecise mechanical gizmos with computer calculations. As you drive, the engine computer plays high-low with the ignition timing a little bit, advancing it little by little until the knock sensor starts detecting vibrations at which point the computer backs off timing a bit. The more ignition timing the engine can use - without pinging/knocking/detonating - the better the MPG in general... Though there is an upper limit to how far the timing can be tuned for various other reasons. So engine computers play this high-low game, tweaking the ignition timing ever so slightly every few dozen miles. It takes a while for the engine computer to iterate to the "best possible" ignition timing for the current atmospheric pressure, ambient temperature, and fuel octane. If you measured MPG while driving on regular octane gas, and then pumped in high octane fuel, you might not see a measurable difference until you've driven dozens of miles. And this iterating happens mostly at steady-throttle conditions. When asking the vehicle to accelerate quickly, or when coasting, the iterations generally stop and the computer uses fixed/stock timing computations. Now, will that MPG increase (on premium fuel) be enough to offset the higher cost of premium fuel? Maybe, maybe not. That's what Consumer Reports and other sources base their conclusions on. If you drive sedately all the time - never working your engine very hard - you never get a whole lot of air+fuel into the cylinders in the first place so the compression stroke won't cause the mix to reach the self-ignition point. Thus regular or premium fuel will result in similar ignition timing tweaks as both fuels likely reach the upper tuning limits. Ergo no difference in engine performance or MPG between the two fuels. But if you accelerate hard often, climb hills frequently, tow stuff, or just have the vehicle fully loaded - anything that makes you use more than "sedate" amounts of throttle pedal - then the amount of air going into the cylinders will be much higher... perhaps high enough where high octane fuel will allow more timing tuning than lower octant resulting in better MPG. One of the limits on how much ignition timing tuning the computer can do is to protect against a high-throttle use. I.e. if you drive sedately 99% of the time, the computer still has to leave ignition timing margin for that 1% when you mash-the-gas-pedal to merge onto a crowded freeway or whatever without leading to detonation.
Normally aspirated engines (no turbos/superchargers)
designed to run on just regular octane fuel have only moderate compression ratios. Using high octane fuel is a waste on these engines as they simply don't get close to the high cylinder pressures and near-self-ignition temperatures during the piston compression stroke thanks to the lower compression ratio.
The story changes a lot for direct injection engines. After all, the whole point of direct injection is to NOT have fuel in the cylinders during the piston's compression stroke. With just air in the cylinders - no fuel - there is no chance of self-ignition. Injecting the fuel at the last possible moment actually cools the compressed air a bit (the fuel is at ambient temperature, not the compressed temps) - which means that air could have been compressed a bit more while keeping the final air+fuel temp just below the self-ignition point. This extra allowable compression yields about a 4% MPG improvement which is why many modern cars use the more expensive direct injection design. Even so, as the fuel is injected at the last possible moment, it can still self-ignite if the compressed air is hot enough. Higher octane fuels let that compressed air be a little hotter... so high octane helps MPG even in direct injected engines.
Now that I've put everybody to sleep... the TL;DR answer is "if you routinely work your engine hard, high octane fuel may provide sufficient MPG and/or horsepower improvement to offset its higher costs." Lower compression normally aspirated engines can't push the cylinder air temps high enough to warrant the increased self-ignition temperature of high octane fuel so using high octane on those engines is silly. Also, for some gas brands, the high octane "premium" gas has the best or highest levels of fuel additives. Those additives help keep your engine innards clean. So future maintenance costs might be lower, offsetting the higher fuel costs.
mike c.