Questions about advanced Horse breeding

After 1500hrs of documenting every bred attempt successes and fails. I have still not managed to get a full understanding of how to improve the base stats through generations. Talents and traits I have well understood and can more often then not produce the offspring I want for talent reproduction.

What does not seem to happen is the overall base quality of the horse minus the talents and traits improving.
What I had originally guessed (as this was nothing like ARK breeding) was base stats were rolled under a law of averages -
i.e The closer the stats were the better chance the babies stat would go forward Vs the bigger the difference between the stats the greater chance for a completely random roll going backwards.

I have not found a confident enough trend after 100 generations to really consider the law of averages as a viable way to look at progressing my horse lines base stats.

Has anyone found success in progressing the base stats of a horse? I have started to note a small amount of red tier horses popping up on the market and after thousands of fresh tames my only guess is this is well bred with knowledge I don't have.

As a breeder in many other games this is driving me crazy.

Note before anyone mentions enhanced breeds I do know about them I have done a lot of them and 1 thing I noticed is unless you keep successfully enhance breeding each generation the stats will not pass on I am interested in improving my base stats without gambling mutating stats into often dead ends after 2 or 3 generations.