Regarding the looking to the dam for stamina thing, I may be completely wrong here (nothing new for me, ha ha ha...sigh...) but I believe the gene for the large heart is carried on the X chromosome so it tends to show up through the dam. Secretariat had a heart what, almost three times the size of an average horse heart, which is why he could run so long so fast. But that characteristic, being on the X chromosome was something he could only pass on to his daughters, who could then pass it on to their sons and daughters both. He is generally regarded as having been a better broodmare sire, right?
Anyway, my guess is that is why people look to the dam's side for stamina. Not that every dam has that particular gene, of course.
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