How to increase stats?

I keep seeing people with 500+ stat horses, and i honestly don't understand how they get that many!? Please can someone tell me their secrets to increasing their horses stats, as i can't figure it out (apart from treats and training)

Breeding.

I raise my horses until they're 20 and breed them at that age so the offspring will have the highest stats possible. The stats keep raising and raising through generations. Otherwise it's tack, treating, and training!

Showing is a major way to get stats, if you can't afford to show your horse then you can put it into riding schools which also give stats.

Treating, training and showing/riding school, - every day. A store horse with 100 stats can easily reach 500+ through it's lifetime.

Like others have said treating, training, showing/riding school everyday. It takes time.

It's best to show when your horse is at least 50% to it's next level {N1 to N2}. So if your horse has 110 stats, do the riding school until they reach 125+ stats. I personally do riding school until my horse is 5 stats away from the next level, sometimes 10 stats away. Yesterday, I had a mare that had 149 stats{almost N2} and entered shows. She placed in 9/10 shows and earned 20 stats. I had another gain 13 stats yesterday.

It's all strategy.

There are 4 ways for a horse to gain stats:
1. Being fed treats
2. Winning 1st, 2nd, or 3rd place in a show that has at least 5 entries
3. participating in Riding School
4. Getting a Stat Boost after 10 days of training

To my knowledge, the most stats that a horse can gain in a single day is 60.
That would happen only if a horse won 10 placings in shows and earned +3 stats from all of them (incredibly unlikely - probably around 1 in 1 billion chances of this happening), if they got a 20 point stat boost (possible at the Na level and above), and if they got +10 stat from a high value treat like an Easter Bouquet.

however, most horses gain around 5 stats a day (about 35 a week)
A 3 year old, 100 stat store horse could easily reach 500 stats by the time it retires, and if you breed it with another equally well-statted horse, you'll get a 0 year old with ~300 stats, who you could then get to 800 stats by retirement, etc.