Circle of Putting Equivalence

PGATour.com has unveiled their new putting statistic, catchily titled "strokes gained - putting." This is an attempt to describe which players have, uh, gained the most strokes compared to field average with their putting. So if you make a putt that they estimate the field would have made 80% of the time, you get +0.20 strokes gained from putting; if you miss a putt the field would make 40% of the time, that's -0.40. It's a perfectly reasonable way to approach the idea of creating a more comprehensive putting statistic; indeed, if done right it is the authoritative way to judge a good putting performance. But there's a problem I have with it, which is that it's very intangible. Theoretically there's no reason we couldn't do this for driving, or iron play, too: on a given hole, you can look at the difference between hitting the fairway and missing the fairway in stroke average, look at the field's fairways-hit percentage, and calculate a strokes-gained from driving accuracy. But we don't, because we like to be able to say, so-and-so hit 63% of fairways. It's all very well and good to say that someone gained 3 strokes from putting in their round, but it's very much a construct. Problem is, most of the simple putting stats are actually quite bad proxies for putting prowess; putts per GIR is heavily influenced by proximity to the hole, and putts per round is heavily influenced by GIR%. But I have an alternative fancy putting stat which, I think, is much more easy to feel on an intuitive level: the circle of putting equivalence.

The circle of putting equivalence is defined as follows: what is the smallest distance which, if a player had holed every putt from inside that distance and missed every putt from outside that distance, would have resulted in the same overall score? The idea is to find a distance which the player had the same number of missed putts that were shorter than that distance as holed putts that were longer than that distance; the "smallest" requirement is just to make it well-defined, because there's likely to be a gap based on what putts the player happened to have. Obviously longer is better. For instance, assume that a given player hit every putt they missed to a foot from the hole and made all those one-footers, and had the following eighteen lengths of first putt in their round: 3', 4', 5', 6', 8', 10', 15', 17', 19', 21', 25', 28', 32', 34', 42', 45', 52', 60'. Now suppose that, of these eighteen first putts, they sank the ones from three, four, six, eight, fifteen, and nineteen feet. Then their putting equivalence distance would be ten feet and one inch: they missed two putts shorter than this, the five- and the ten-footer, and made two putts that were longer than this, the fifteen- and nineteen-footers. This player took 30 putts on the round, and if they had made everything of 10 feet or shorter and missed everything longer than 10 feet they would have taken 30 putts.

The only difficulty is how to judge a three-putt from inside the circle: for instance, say that the ten-footer had been three-putted instead of two-putted. If that putt had been made, it would've saved two strokes; however, you get to the same place by counting one stroke saved from making that putt and another stroke saved by making the three-footer or whatever that was missed to create the three-putt. Arguably this is a slight change from the original definition, since we're looking at the made/missed equivalence instead of the "same score" equivalence, but I'm pretty sure it would ultimately get you to the same place since you need two putts holed outside of the line to balance out a three-putt from inside the line any which way. (If you hit from inside the line to outside the line and then miss that one, I'm not sure how that works out.)

This strikes me as a really good way to judge quality putting. It's also something that would be trivially easy to calculate using ShotLink data, but I doubt they'll ever do it. I'd be really curious to see the results, though, and especially to see the correlation with their new Strokes Gained - Putting stat.