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Greens hit in Regulation is defined as:

The percent of time a player is able to hit a green in regulation (greens hit/holes played). A green is considered ‘hit’ if the birdie shot on the hole is taken from the green.

Here are a few examples:

A player plays a par-3 hole and misses the green on the tee shot. The birdie stroke is the second stroke on a par 3, and since this is played from a lie other than green, this is not a green hit in regulation.
A player plays a par-3 hole and hits the green on the first shot. Since the second shot (the birdie shot) is played from the green, this is a successful green hit in regulation.

Pros:

Provides a data point on overall ball-striking. It is very difficult to have a great ball-striking day without hitting many greens.
Provides a measurement on how many birdie putts a golfer has.

Cons:

It’s a binary statistic meaning that it only measures whether or not the criteria for a GIR is satisfied or not, but fails to capture nuances.

A green hit to 100ft from the hole, and a green hit to 1 inch from the hole are both worth the same = 1 green hit in regulation, despite the shot hit to 1 inch being exponentially better than the shot hit to 100ft.
A green missed by 1 inch is worth the same as a green missed out of bounds or in a penalty area, despite the fact that the green missed by 1 inch is exponentially better than hitting the ball out of bounds.

If you hit a bad tee shot and need to punch out sideways, this ‘robs’ you of the ability to be able to hit a green in regulation. The tee shot quality affects your ability to measure greens hit. You can therefore be in a situation where you are hitting great approach shots, but bad tee shots, so your GIR value becomes really bad. If you just look at the stat

Recommendations

As with many of the ‘traditional’ golf stats, they do tell a story, but only part of the story. They are really useful to use as supplementary variables and help narrow down what is actually happening, but only with help from other data points. We would recommend that you also look at Strokes Gained Approach, and if possible, Strokes Gained from different distances in order to narrow down exactly what is happening to the shot hit approaching the green. The Strokes Gained variables isolate the shots hit from around the green on their own, without being influenced or affected by other things that it isn’t designed to measure.