I've been reading up and trying to understand batteries. If I'm getting this correctly, a lower mah battery would need a higher C rating in order to be able to give up the same amount of energy per time. For example, both a 2500mah 50C battery and a 5000mah 25C battery would discharge at up to 125a, but the former one would last half as long. Am I getting that right?

Second, a system will only draw as much energy as it does, right? Meaning, just because you put a higher capacity battery with a higher C rating in a car doesn't mean it's going to go any faster (given the same voltage). Right?

With that in mind, could a lower mah battery with a higher C rating give the same punch up until it starts fading?

If you want to know why I'm asking, one of the reasons is because I've developed the habit of topping off batteries before heats, but then end up at the end of the night with a battery that still has most of its juice left and takes quite a while to discharge down to storage. It also seems that once a car is set up for racing, you don't want to run it for too long per session. That makes it tempting to get batteries with smaller capacity to race with.