There has always been a belief that using a 10" wheel will make a car rev much higher for a given final drive ratio and speed.
I just did some calculations on the rolling radius of 10", 12" and 13" wheels with all the usual tyre sizes:
145/80 x 10 Nominal Rolling Radius 9.567"
165/70 x 10 9.547"
145/70 x 12 9.990"
165/60 x 12 9.890"
175/50 x 13 9.940"
So it can be seen that the difference between the smallest rolling radius and the largest is a mere 4.64% and that is with new tyres. So in reality it makes virtually no difference. The highest profile is a 12" wheel with a 145/70 tyre fitted. Some tyres, such as a 145/70 x 10" winter tyre will have a higher rolling radius due to the greater tread depth.