To start,automatics,they tend to be slow as hell,there is a lot of lost power. The reason it is a 4spd auto is because it is meant for fuel economy,it may be a spoty model but an automatic is made for highway cruising and getting the most mpg's,not racing around a track. To validate your thinking,yep a 6 spd has tighter ratios enabling much much quicker acceleration but usually that 6th gear is meant for the highway and a low rpm cruising speed,but you will go thru 1 2 and 3 real quick. You line up against a 6spd version of your ride with the same mods and it will blow you away,but,you will spend a lot less money at the pump going to and from grandmas house. So,as an older guy now at 38 I can say this...kids,if ya want to go fast,do not get an automatic,and do not get one thinking you will swap in a manual because the time,energy and cost will make that dream never come true.
