the less a high performance engine knocks, the more power it can make. The octane *does not* give any engine more power, but by reducing knock, up to 10% "more" power can be obtained - but only in very high perf engines. If you're running a 13.5-14.0:1 compression ratio, knock will rob a lot of power. Reducing knock gives power back, thus contibuting to the idea that octane produces power.

Same idea goes for water/alchohol injection. Water does not produce power, indeed, it robs power, but sometimes, in extreme engines (in other words, the fun ones), the reduction in knock allows for more power production than is lost in the heat of vaporization of water. In these cases, it makes sense to add water injection to "increase" power. The alchohol is only included to eliminate freezing the tank. Uusually a 50/50 blend is best.

In WWI, the Air Force obtained "gains" of over 800 hp in their P-52's (I think, or P-51's) that were supercharged at high altitude and had huge knock problems. The addition of water cooled the intake charge enough to reduce knock to the point that the engine was allowed to perform as designed - with 800 more hp than without the water injection.