In 2013 the best average proximity to the hole on approach shots was 31 feet, 3 inches (Jim Furyk). To be sure, he had a lot of shots within 15 feet or less but not nearly as often as I might have guessed.
I think GIR for the average or above average amateur golfer is an excellent predictor of scoring. L.J. Riccio, PhD (a frequent contributor to Golf Digest) did a statistical analysis of amateur goflers and found GIR to have a strong relationship to scoring. Perhaps once one gets into the realm of + handicaps the data is not as valid. Also, there are going to be amateur outliers who rarely hit a green and score wonderfully and others that hit lots of greens and don't seem to get the job done. On average, however, GIR is usually tied to scoring pretty closely.
Yes - I like Riccio's stuff. But I think even he acknowledges that it breaks down at the upper end where players tend to bunch around 11-13 GIRs. At that level I think you you get all sorts of interference - depending on course conditions and player strategy - that can mask relatively small differences in ball striking.
If you want more accuracy to the pin and better scores, here are two tips. Before taking a swing to a green look at where the pin is. There are A) Ok pins, B) difficult pins and C) sucker pins- decide which one you are shooting at and avoid shooting at B and C, next what ever club you think you should be using, swallow your pride and use a stronger club, maybe choking down a half inch and swing at 80%-the swing should feel fluid and not forced. The ball will go straighter, better contact,a little further and land softer. The biggest difference from a 20 handicap and a low single digit handicapper on approach shots is low handicappers hit the ball beyond the hole, the high handicappers do not use enough club and often leave the shot short. why is this so bad? think about it.... 1) traps and water are typically in the front or front R and L- rarely in back. 2) greens typically slope back to front as does the fringe & fairway in the front of the green typically is sloped towards the golfer both which prevents the ball from releasing forward for a steep decent angle for higher handicappers. 3) ask yourself, especially if you are familiar with the course " where do I want to miss?" and "where do I want to putt from" before hitting your shot.
Trust me you'll hit better quality shots AND closer to the hole for more likely 2 putts
Cheers. All good stuff to take into account. I do remember getting a bit of a shock the first time I saw the course map at my club, to see the depth of the greens and therefore the number of different clubs that you could hit into them.