Ill reference this thread for the various equations.
This info is on many different forums. I found a spreadsheet on some site a while back that uses to do all the rmp/speed ratios. To determine the final drive ratios just multiply the transmission ratio x rear gear.
Multiply these by the 3.15, 3.73, or 4.10 to get the final drive.
You can see that after 1st the automatic is set up to be more of a grand tourer than a sports car. Even with a 4.10 rear 3-5th is still steeper in the manual with 3.73s
btw, thanks for the wielding tip. I hadn't ran across that thread before
This chart is flawed with the way you're reading it comparing the ratios of the auto and manual.
Trust me I have personal experience here. Going to a steeper rear gear in the auto is not the answer. Start with a good tune and go from there. The next step would be a converter. But no more than a 3.31 gear. It won't help at all. Many have thought differently only to later realize the error in their ways.