>> hot rod boats using auto engines ran them in reverse rotation to that of their rubber burning cousins. Why is that?
Well, not necessarily. It is not that you want it rotating contrary to what it was, more likely it is that you want it rotating in a specific direction: the direction you want the prop rotating.
So now you ask, why do you want the prop rotating in one direction and not the other. Well, if you have twin props (and twin motors) you need them rotating in opposite directions. This is mostly the case of any boat with any amount of power. You will have two similar motors rotating in opposite directions.
If you have a single prop (like my boat) then you have a phenomenon which I am not going to explain in detail but it is the fact that the prop does not push the boat only forward but also sideways. When moving ahead it is much less noticeable and easy to compensate but when you are maneuverng and have no way through the water and engage astern, the boat has a very marked tendency to “walk” sideways. So, what happens is the boat will turn much better in one direction while turning very badly in the other. If you know and learn this you can use it to your advantage but if you don’t and try to turn the boat to where it does not want to go, you’ll make a mess. My boat’s prop turns clockwise (viewed from astern) and I believe that is the most common arrangement. It will turn left very easily but will turn right with difficulty or not at all.
If the convention is that props turn right and your motor turns the other way, you may want to reverse that.
Note that the convention is that the direction of rotation of the prop is as viewed from astern and looking forward while you describe the rotation of the motor as you are looking at it and facing astern. My motor and prop rotate in opposite directions because the gear box reverses it. So, my prop rotates right and my motor rotates right (I told you they rotate in opposite directions).