The Amendment

I need to make an amendment to the last post on my short game statistic.  My brother (the math teacher) pointed out that making an "arbitrary" assignment of 5 putts saved as "perfect" didn't make a whole lot of sense after all the intricate calculations that came before that.  He recommended using normative data for strokes gained-putting to assess how the adjustment should be made.  Unfortunately, I didn't have normative data for strokes gained-putting.

So... I decided to go straight to the source.  I emailed the guru himself, Mark Broadie, and asked if he could help out.  And he graciously sent along the distribution of PGA strokes gained-putting ranging from +5.5 to -5.5.  Based on that, I was able to asses that (a) it is indeed normally distributed, and (b) the standard deviation is about 1.735.

One problem with that, though -- although I refer to the number as an estimated shots gained-putting, what I'm really trying to calculate is something more like "shots gained from short game shots."  So putting-only distribution doesn't quite fit (obviously there are fewer putts in a round than there are total short game shots including putts; therefore the range should be a bit bigger).  Fortunately, Broadie's research comes through again here, as it turns out an average round's short game play can be split into about 75% putts and 25% short game shots.

Based on all that, here's the final calculation for short game score:

SG = 0.75 + [(SGP*0.75)/1.735] * 0.1

where SG = short game, SGP = estimated shots gained-putting

That yields a short game score of 0.750 (or 75% efficient) when SGP = 0, and goes up or down by 10% for every standard deviation above or below the PGA mean, adjusted for the added short game shots.  Ultimately this works out close to my original "arbitrary" assessment, but it's definitely more precise -- and I like that.

Using this calculation, by the way, obviously changes my short game scores that I had reported in the previous post.  Here are the updated values:

Red Tail Golf Club (SGP +0.672) -- short game score 0.779 (down from 0.784 by original method).

Butter Brook Golf Club (SGP +3.213) -- short game score 0.889 (previously 0.911).

Fox Hopyard Golf Club (SGP -6.145) -- short game score 0.484 (previously 0.443).