Chris,
You are right and wrong, as are Mike and I. But Mike and I are more correct than you are. While width does effect sideall height, the 2nd number (aspect ratio) effects the sidewall height twice more than the width.
225 x 0.45 = 101.25
215 x 0.45 = 96.75
4.5mm difference
225 x 0.45 = 101.25
225 x 0.40 = 90.00
11.25mm difference
Therefore the common belief and used practice is to increase or decrease the 2nd number (aspect ration) to determine sidewall size.
In addition, it's smarter to change sidewall size.
Why? Because you do not sacrifice width for height. By doing so you get less rim protection on your wheels, increasing the chances of damaging/bending a wheel - especially "curb rash".
