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My sense about total energy is akin to what partsnut said. If you consider the idea of a 2 to 1 relationship between 1 extra energy unit expended early resulting in 2 units of energy lost at the end, then a too-early pace for a horse should result in a slower time, thereby giving a lower energy total due to a flabbier 3rd fraction. If the horse runs at a pace where it does not need to expend extra units of energy to keep up, then it can run to its ability and thereby produce a higher total energy time.
I suppose what I'm saying is that total energy is somewhat a function of the pace the horse ran against. Of course, this idea is probably a bit elastic as it depends on the class of the horse.
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