Has there ever been a proper study of tire width to horsepower on these cars?

https://www.roadandtrack.com/car-culture/a18334/scion-fr-s-tire-transformation/

I went 225 all around and there is definitely a difference in traction and control on corners at high speed. Even stock. It's not just aesthetics and it hasn't seemed to slow me down any, even with heavier wheels.

Not the most scientific of tests, but when I put my supercharger kit in on the stock shoes, it definitely kicked loose more than I wanted. The traction control light was always lighting up.

I now have summer compounds in 245 width on the rears and while I can still peel out when I want to, it is much more grounded.

That said, I changed several variables here, so it's not exactly scientific.

Personally I went with 255r18x9.5 1. for looks as a DD, 2. for extra grip (all about that grip lyfe and better braking) and 3. because I plan on going FI in the future and figured I might as well get the wheels/tires now so they're ready when i get the $$$ for FI.

I might go up to 265 on my next set of tires so they fill out the wheel instead of having the little stretch look the 255s do.

Boy I'm hoping someone corrects me if I'm wrong, but from what I understand, size doesn't really matter much... It's more about tire compound and overall weight. Going to a wider tire doesn't increase friction because your contact patch doesn't actually change in surface area, it just changes shape. The only way to actually add more friction, is to get a stickier tire compound or lower your tire pressure to increase your contact patch size (the latter of which is obviously a bad idea for a street car). However, if you also don't spend the money to get wheels made from a lighter material, big wheels will add unsprung weight which is bad for everything.

I know a lot of people go with super wide tires for looks. Its the same reason we get people who claim you need to tuck the top of the tire under the fender.

I dont know if anyone has actually done anything scientific in this regard, but i know that most people i have met that do AutoX or track work run 225s to 255s. I personally find the grip levels on 225 PS4S tires to be plenty for normal driving as well as some spirited canyon carving. For performance, compound is more important than width. I find most people just do a bit of trial and error to find something that works for them. My recommendation is usually to go that route unless you are tracking the car and dont have enough grip even with the sticky compound.

You're not going to find any scientific test of this, but your assumptions are correct. Wheel slip is minimal with 215 tires, so any tire size greater than 215 will slow you down in a straight line because of the increased friction. I'd be curious to see drag times with even narrower tires to see whether 215 is the optimal size, but no one really cares because these cars aren't built for straight line speed.

You obviously have more grip for turning and braking with wider tires, so people are willing to sacrifice straight-line speed for that. What's best is really personal preference. Personally I keep to 215 for stock power. If you go FI, 245 seems to be safe to keep from excessive wheelspin.

All I can add is that I’ve got 245’s on 9” wide wheel because that is what is the max allowance for STX class in autox (and I’m basically stock power level). My buddy with 225’s on 8” wide wheel (same re-71 tires) is occasionally faster than me, so I’m willing to bet anything wider than 245’s has diminishing returns on stock power levels