Arguably the most important discovery in statistical analytics in basketball. 

A possession ends

(1) by making a field goal attempt;

(2) by missing a shot and not getting the offensive rebound;

(3) by turning the ball over;

(4) by going to the line for two or three shots and either making the last shot or not getting the rebound of a missed last shot.

Two teams in any given game are essentially limited to the same number of possessions.

Basic Possession Formula=0.96*[(Field Goal Attempts)+(Turnovers)+0.44*(Free Throw Attempts)-(Offensive Rebounds)]

More Specific Possession Formula=0.5 * ((Field Goal Attempts + 0.4 * Free Throw Attempts - 1.07 * (Offensive Rebounds / (Offensive Rebounds + Opponent Defensive Rebounds)) * (Field Goal Attempts - FG) + Turnovers) + (Opponent Field Goal Attempts + 0.4 * Opponent Free Throw Attempts - 1.07 * (Opponent Offensive Rebounds / (Opponent Offensive Rebounds + Defensive Rebounds)) * (Opponent Field Goal Attempts - Opponent FG) + Opponent Turnovers)).
This formula estimates possessions based on both the team's statistics and their opponent's statistics, then averages them to provide a more stable estimate.