The old horseman's saying is, "Stamina from the mare, speed from the sire".

I will attempt to decipher the following from a paper that lends more credence that good runners are more influenced by females from a stamina and speed point of view.

Muscle biopsies contained large accumulations of mitochondria with bizarre cristae formations. Biochemical analyses revealed a very low activity of the first enzyme complex in the mitochondrial respiratory chain (NADH CoQ reductase). The exercise intolerance and muscle stiffness in this horse were attributed to a profound lactic acidosis resulting from impaired oxidative energy metabolism during exercise.

The bolded statement is referring to a single gene in mitochondria, therefore inhereted from mom, that was producing the enzyme called NADH CoQ reductase, one of a number important enzymes important in exercise found in mitochondrial DNA.
In this case, the enzyme was of form that caused a severe lack of ability of a horse to exercise. So in my mind, there have got to be forms of various enzymes in mitochondria that should enhance the ability to exercise. It should be easy to find these forms. So one might have a dud of a mare that could not run due to some injury (nongenetic), yet she might carry an outstanding set of cellular respiratory genes so that her progeny should be able to run fast for long distances (given the right musclature and other things that go into running).
The genes in the mitochondria have to play a large role in the very basics of running. Of course various genes that control muscle conformation, etc... are a 50/50 proposition from dad and mom.

I would love to know what goes on in big breedng operations and if they have some sort of research projects along these lines. I have found nothing about it. Seems to me it would be pure folly not to put some money in to this research.