# A Quick Note on Adjusted Save Percentage

Different goaltenders face different distributions of shots from across the ice due to the offenses they face and the defenses in front of them. We adjust save percentage by re-weighing the components according to the league-wide distribution of shots, so that the value better translates between different goaltenders. This is similar to stratified sampling in survey methodology, and also goes by the name benchmarking.

With our danger breakdown, standard save percentage of Saves/(Saves + Goals) is expressed as

Sv% = (Saves_low + Saves_med + Saves_high)/(Saves_low + Goals_low + Saves_med + Goals_med + Saves_high + Goals_high)

The adjustment is to re-weigh every danger-based save percentage by the league-wide distribution of shots on goal in each zone:

AdSv% = (S_l/(S_l + G_l) * AllShots_l + S_m/(S_m + G_m) * AllShots_m + S_h/(S_h + G_h) * AllShots_h ) / (AllShots_l + AllShots_m + AllShots_h)

If the shots faced by the goalie have the same ratio as the league average, then their unadjusted and adjusted save percentages will be equal.