While the previous method I posted to calculate PER was the best formula for use in the NCAA, the FIH offers more statistics in their box scores. This allows the formula to not be so offense-heavy and allows for a better comparison of defensive players as well.
The three factors being added to this formula are blocks, interceptions, and tackles. All three statistics count as positive factors in this formula.
Calculations
The weight of these variables was not easy to determine for the formula.
While creating the original formula, I found the correlations between specific factors and goals scored. When I ran the same test for the data set, two factors had negative correlations and one was slightly positive. Because of this, using those correlations as the factor would make each of these variables a negative.
While math wants to make these factors negative, we know that they are beneficial to the game.
My next step was to figure out what sports have similar statistics and what they do with them. I looked at the original basketball PER formula, but it does not really translate.
Since soccer is the closest sport to field hockey in terms of gameplay, I searched how they weigh these variables. The only source available was a breakdown of fantasy soccer scoring. For fantasy soccer, each of these variables is weighted as 0.5.
Most of the variables in the article are much higher than those used in this formula. Both goals and assists are worth 5 times more in fantasy soccer, shots were about 3 times higher, and cards were a little over doubled.
Given this information, and the knowledge that the correlation believes these variables have little to no positive impact, 0.5 is too high for this calculation. My next step was to adjust 0.5 by the three differences in weights we already know, by 2, 3, and 5.
Dividing 0.5 by 3 results in 0.167. Remember how earlier I said that one factor was positive? Interception resulted in a correlation of 0.167. Given this, I determined the factor for all three to be 0.167.
Defensive saves were removed from the formula since that is not a statistic on the website.
When adjusting the unadjusted PER to PER, I adjusted the average player PER to 10 from 5. The NBA uses 15 for their formula, however, that is too high for this equation. The average PER of a professional player should be higher than a collegiate player, hence the change.
Updated Formula
unadjusted PER = (Goals x 2) + (Assists)+ ( SOG x 0.6) + (Tackles x 0.167) + (Interceptions x 0.167) + (Blocks x 0.167) - (0.5 x Green Cards) - (Yellow Cards) - (Red Cards x 2)
Then to adjust it =
PER = uPER x (10/league average PER)