What, then, is the best stat to determine putting skill, or is there one?
Years and years ago, Golf Magazine had an article about how to measure your putting in a round of golf, comparing it your total score for the round. Specifically to give you a putting score measured against par.
The formula gave the golfer points based on the length of their first putt, a +30 foot putt got 2 points, a 2 foot putt got 1 point, etc. The theory was that you should ALWAYS make the 2 foot length putt in 1 stroke (par for this length putt would equal 1 point) while you should make the 30 foot putt in 2 strokes (par for this length putt would equal 2 points).
The table looked something like this:
Length of Putt Points
0 - 2 feet 1.0
2 - 4 feet 1.1
4 - 6 feet 1.2
and so on ...
So you would add up your total putts for the round divide it by the total points based on the length of the first putt and multiply that number by 72 (par).
The resulting score should be compared to your total score for the round and rationalized to determine if your putting helped or hurt you achieve the score for the round.
As an extreme example, let's say the length of everyone of your first putts was 35 feet and you 2 putted each one, you would have a putting score for the round of "even par" 72. A very good putting round. If your total score for the round was an 80 ... that means your putting helped achieve that score.
To use this system you have to remember to step off the length of your first putt which actually helps you realize that you are closer or farther from the hole then you think and mark it on your scorecard.
I used this method in conjunction with other stats (GIRs, ParSaves, 1-putts, etc.) to analyze the round.