That Miss State study that showed doe preference for larger antlered bucks is truly fascinating, and I great study. However, in the wild, many other factors come into play. One of the best "successful breeder" research projects I've ever seen was conducted on a large military reservation in Oklahoma. Every year for several years, researchers would go into the field at fawning time and live-capture newborn fawns and take blood samples. These samples were used to sequence each fawn's DNA. All deer harvested during special hunts on the property had DNA samples taken. Researchers would also comb the property every spring to collect every dropped antler they could find, also to extract DNA. What they were able to produce over time was a massive "family tree" for most of the deer using the property that would show which buck sired each fawn.
For me, the three findings from this massive research project that stuck out were: 1) Most bucks sire very few fawns each year. I think the average was only one per buck. Just a few bucks produced several offspring in a single year. I believe the top for any one buck was 6 offspring in a year and that was a statistical outlier. 2) Even when the buck age structural is "normal," with mature bucks present, bucks of all ages successfully breed; even yearling bucks. However, successful breedings are "skewed" towards the older age-classes. In essence, mature bucks produce more fawns per buck than young bucks do. 3) Because they had the dropped antlers of many of the bucks, they could look at antler size compared to successful reproductions. They found larger-antlered bucks for their age-class did not produce more offspring than smaller-antlered bucks of the same age. In fact, the top breeders were generally average to slightly below average for their age antler-wise.
Social dominance among bucks is driven by body weight and personal disposition. The bigger bodied, bad-attitude bucks end up being socially dominant.