Legacy Points are points you get when people cheer you on during a boxing match. They are accumulated at the end of the match. The winner will recieve 80% of the Legacy Points, while the loser recieves 20%. And whether you win or lose, your legacy points will never decrease. These cheers by viewers also gives boosts of energy to the fighters.
To view your legacy points, put on your gloves and the statistics of your points will show up.