Growth cannot be determined by age at all. Growth at a certain age is totally dependent on how hard a horse is 'pushed'. Horses fitted for sales and for show are fed for early growth. They will have their mature height several months to even years ahead of horses fed grass hay, pasture and other low protein, high fiber diets. Horses that run out and are not fed supplements and high protein diets will get as big they would have gotten if they were pushed. It just may take them a couple more years to do it.
As far as genetics goes -- it depends on individual horses. I have a stallion that is 15.1. He got a little big for reining and cutting, but he is a super cow horse and can handle anything on the end of a rope. He is very deep in the heartgirth and he sires very few foals that are smaller than he is, even out of small mares. Some, out of mares that stand 15.0, hit 16 hands. We are riding two now. We figured out very quickly that if we wanted little cow horses, we had to breed tiny cutting mares to him.
Different stallions are more 'prepotent' than others. If I cannot go out in any pasture and pick out the foals of a certain stallion, he is not prepotent enough to work for me.
I also tried the coronet to mid knee measurement on a good many of the horses I measured. I found it only worked about 60% to 70% of the time -- at best. It was not so accurate in big horses with short cannon bones and low set hocks - exactly what I have always liked in a horse. It also makes a difference on horses with very long pasterns. That is so variable in horses.
I think there is definitive proof that geldings get taller than stallions of the same breeding. Testosterone has been shown to make the epiphysis' of the leg bones close earlier -- thus, geldings castrated prior to 18 months of age will grow taller than horses not castrated.