You cannot gain power from some kind of magic juice. Normal hp variation from run to run on the same dyno can be more than 9 or 10 horsepower.

Want to free up horsepower? Go to a lighter oil. You'll gain power. Then you'll watch your motor come apart eventually.

Austin, there is no magic formula to horsepwer that you can buy in a bottle or a pill over the counter. These are mechanical contraptions. Guys build horsepower the old-fashioned way for one reason:

That'* the only way to actually get horsepower because it doesn't come in a bottle.

Minus

I've been looking and several oil brands claim the same thing, I think they just free up horse power by creating less friction and resistance, therefore, making the engine run smoother and creating more power.

Most modern oils have friction modifiers allowing them to make that claim. You're not going to make any huge power differences with ANY oil. I have heard some good things about Royal Purple, but not enough to justify the price. Our motors love just about any oil.

There are many brands of high performance and racing oils available. All of them behave in different ways, and yes...there are some that will increase the power of the engine...temporarily only!!! The gains will go away as the oil breaksdown and experiences cycles.
For a daily street driven car, I use Shell Rotella T, 10W30 oil (non-synthetic) or Shell Rotella T 5W-40 (Full Synthetic). Yes, it is a Diesel engine oil, however, it contains detregents to keep the inside of the engine clean, and also has a higher contents of Zinc which helps all friction surfaces such as cams and bearings. If you switch to Rotella for the first time, you will be for a surprise since the oil will darken due to the fact it will disolve and remove any old sludge. So, if you switch to Rotella for the first time, do two oil changes at 1,500 miles. After that, switch to your normal schedule. You will be surprised when you remove the valve covers and intake and see a clean engine with no sludge.
For racing only, I recommend both Redline and Royal Purple.

I would assume this would dictate an oil change between races, too?

What dictates the oil change is the type and class of racing and how much blow-by the engine has. Blow-by will contaminate the oil with fuel and dilute the oil.