I'm doing a project on free throw percentage in basketball where I want to create a formula to calculate Z Scores* for the free throw shooting of basketball players. I want to take into account free throw percentage and free throw attempts, so I don't want to find their z-score simply based on their percentage. Basically, I want to make sure that 8 out 10 shooting registers a higher Z-score than 4 out of 5 shooting. EXAMPLE: The player in question has the following stats: - Average of 2 free throws made per game - Average of 8.67 free throws attempted per game - Average free throw shooting percentage of ~23% The league has the following stats - Average of 12.28 free throws attempted per game - Average free throw shooting percentage of -47% - Standard deviation of 8.5% Normally I would assume that we can calculate the standard deviation like so - (player_avg_ft% - league_avg_ft%) / (league_stddev_ft%) = Z Score (.23 - .47) / .085 = -2.82 Z score = However, the tricky part is that we need to account for volume. A player that averages 10/10 free throws is worth much more than a player that averages 3/3 free throws. My thought was that we can add a multiplier to account for volume like so Z Score * (player_avg_ft_attempts / league_avg_ft_attempts) = Volume Adjusted Z Score = -2.82 * (8.67 / 12.28) = -1.99 Volume Adjusted Z Score I know that this is not the mathematically correct way of doing it (I just made this up). How can I calculate Z Scores that account for shooting volume? A friend told me that the correct z score should be closer to 2.65, but wouldn't tell me how to calculate that. I don't know if this is the correct number either though. I'm doing a project on free throw percentage in basketball where I want to create a formula to calculate Z Scores* for the free throw shooting of basketball players. I want to take into account free throw percentage and free throw attempts, so I don't want to find their z-score simply based on their percentage. Basically, I want to make sure that 8 out 10 shooting registers a higher Z-score than 4 out of 5 shooting. EXAMPLE: The player in question has the following stats: - Average of 2 free throws made per game - Average of 8.67 free throws attempted per game - Average free throw shooting percentage of ~23% The league has the following stats - Average of 12.28 free throws attempted per game - Average free throw shooting percentage of -47% - Standard deviation of 8.5% Normally I would assume that we can calculate the standard deviation like so - (player_avg_ft% - league_avg_ft%) / (league_stddev_ft%) = Z Score (.23 - .47) / .085 = -2.82 Z score = However, the tricky part is that we need to account for volume. A player that averages 10/10 free throws is worth much more than a player that averages 3/3 free throws. My thought was that we can add a multiplier to account for volume like so Z Score * (player_avg_ft_attempts / league_avg_ft_attempts) = Volume Adjusted Z Score = -2.82 * (8.67 / 12.28) = -1.99 Volume Adjusted Z Score I know that this is not the mathematically correct way of doing it (I just made this up). How can I calculate Z Scores that account for shooting volume? A friend told me that the correct z score should be closer to 2.65, but wouldn't tell me how to calculate that. I don't know if this is the correct number either though