Yes I agree, the higher octane allows for maximum compression to be obtained prior to spark detention hence the more advance timing allowing for maximum stroke to be achieved, as SST said it's not making more power using premium but it allows the engien to produce its near maximum efficiency, which ties into 73sharks statement of getting better mpg..
The however is exactly what shark stated it's a trade-off.. in everyday driving I use regular, road trips and towing I use premium.

 

I just notice better drivability. This weekend its will be 115 degrees here so ill likely start filling up with premium during summer months.

 

I take it you live in a desert environment if you are seeing 115. The performance improvement is likely influenced by the lower humidity ( but not lack of) and lower morning temperatures...
I have noticed that in the spring when the air is cool 65-75 degrees and low humidity 30's% range the engine loves it! throttle response is great and she seems smoother... there is a near perfect balance for moisture and air molecules to blend with the atomized fuel for the optimal performance...
high humidity actually displaces room for oxygen in the combustion chamber, cooler temps but not too cold, allow for the air coming into the combustion environment to be just right for the mixture...
some moisture is important for pre-ignition control
I know it sounds crazy, but there is science to it...

 

Yes winter months here are fantastic and throttle feel great even with 87 octane. Summer temps on 87 octane the girl feel sluggish and not so peppy. The last few fill up I have used high octane and Bessy gets her pep back.

 

Cooler air is denser and allows more fuel to be used resulting in a little more power. That's why among other reasons that boosted engines use an intercooler.

I think my mpg increase on pure gas was due more to the lack of alcohol than the octane increase.

 

I always fill up with high octane A/C in the summer months