In the USA Pool League (USAPL) 8-ball match format, players are awarded one point for each ball pocketed and 7 points for the 8-ball. So the player who wins a game always gets 14 points, and the player who loses a game gets between 0 and 7 points. Fargo Ratings predict the likelihood of each player winning a game, so it is straightforward to use Fargo Ratings to predict which player gets 14 points, but Fargo Ratings is silent on the number of points the losing player is expected to get for a loss.

Fortunately, this can be determined from statistics on tens of thousands of 8-ball games played by players of different skill. The average score for a losing player is a little more than 4 points. But by drilling down a little more it is determined that a player earns more points when losing a game against a weak opponent than by losing a game against a strong opponent. A strong opponent is more likely to run out leaving many of your balls on the table. A weak opponent is more likely to win the game when you have tried and failed to get out and consequently have few balls on the table. This dependence is accounted for in the USAPL matchups.

Fair USAPL matchups are determined by the rate each of the players is expected to earn points, so the only thing needed to determine the actual matchup is the length of the match, and that is determined by the desired number of games, or the desired length in time of the match.

If p is the probability a player wins a game and q=(1-p) is the probability the same player loses a game, the expected points earned in a game is p14 + q(points per loss), and points-per-loss depends on the opponent’s rating.

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