Both are important, but it can depend on your breeding and gaming strategies.
- With good birth genetics your horse can run sooner.
- With bad birth genetics he will run later, when he is at his maximum (because he won't have any chance to win before).
But it's difficult to have both : good birth genetics AND good max genetics !
So players created are 2 different kinds of breeding :
- "Precocious breeding". Precocious horses have extremely good birth genetics. They only run during their 1st year, and at the beginning of their 2nd. After that, their max are lower then the other horses and they're retired from races, only used to breed.
They are really good at races at 1 year old.
- "Usual" breeding. The aim is to have the best final genetics. These horses usually start to run after 3yo (because as you understood, before, precocious win all the races).
- (And between these 2 kinds of horses, as training became longer, there are "half-precocious" horses, who are better when they are 2 yo.)