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Base stats are the 6 main stats a horse has. These are the ones that display on their page in the Stats table if you buy either Traits (colored stars) or Hidden Stats (exact numbers). Each of these stats can range from 1-10 points, making a total possible "Potential" of 60.
Together with the doubled-stat style factor, these can make up a very large portion of your horse's PR. However, especially in horses with lower potential, other factors will actually have equal or more bearing into the PR than these do. The maximum possible PR is over 200, so potential is certainly not the only important factor.
Breaking: A stat that determines how quickly your horse moves out of the starting gate.
Early Speed: A stat that determines how much speed your horse shows early in the race.
Rating: A stat that determines the ability of a horse to control their speed at the jockey's request.
Versatility: A stat that determines the ability of a horse to adapt to changing situations in races.
Acceleration: A stat that determines how quickly your horse can gain speed.
Late Speed: A stat that determines how much speed your horse shows late in the race.
A horse's maximum stats are determined at birth. Through training, they will improve their current stats and potential until they eventually max all of their stats. This maximum is based upon several factors, including Stat Genes, parent producer quality, and Bloodline. For horses who are purchased from the Horse Trader or Pro Shop (Goldbloods), stats are based directly on stat genes. However, you can improve your horse's max stats through using Oracle, buddyworking, and sometimes buying a horse from sales.