i used to work for westech fuel, who was this state's local authority/service provider on testing, maintaining, and purifying gasoline, and diesel. I know gasoline, i also have spent my life at the racetrack giving me a real-life knowledge of the tendancies of gasoline
Octane level is not a "power" level, it is a compression level measurement.
close, it is a measurement of heat needed to ignite/speed it burns
which can be directly tied to compression, but not expressly
on a combustion chamber where less ambient heat (usually from heat via compression) is available to aide in ignition, a lower octane fuel is needed which burns faster, and at a lower heat.
on a combustion chamber with more ambient heat (heat from higher compression for example) a higher octane rating is needed to slow the burn down/control it from igniting from combustion chamber instead of a spark plug, i.e. pre-ignition/detonation/"pinging"
which is a result of the combustion pushing harder against the face if the piston faster(harder) than the piston can be pushed downward, or even in cases of severe pre-ignition when the piston is still coming up.
its all about the speed it burns
this is also why timing on lower compression engines needs to fire so far before TDC, so that the slower burning fuel can get ignited, and started uniformly combusting by the time the piston reaches TDC. And why timimg on higher compression engines doesn't need to be so far advanced, and will even pre-ignite if set at timing suited for lower compression.
also to support this if you talk to racers who know,(or even com-cams tech-line) they run more advance timing with shorter rear end gears, and less advance with taller rear end gears because a shorter rear end gear allows the piston to be pushed out of the way by the combustion easier, thus counter-acting the pre-ignition that would be present at that same level of timing, and taller rear end gears.
http://en.wikipedia.org/wiki/Octane_rating
Octane ratings are not indicators of the energy content of fuels. (See section 4 of this page and heating value). It is only a measure of the fuel's tendency to burn in a controlled manner, rather than exploding in an uncontrolled manner.