The New Statistic, Part II

Last spring I wrote about a new statistic I devised called shot efficiency.  The idea was to try to analyze ball striking for a round, using a few simple numbers (course rating, yardage, score, and putts.  [See the post for the full formula.]  One of the flaws inherent in the formula is it doesn't fully account for how challenging a course is to play -- something that is fundamentally accounted for in the "other" part of the USGA course rating system, the slope.

The USGA suggests that the best way to determine how difficult it is to score on a given course or set of tees is to use the bogey rating.  Here's how they explain it:

This rating is the evaluation of the playing difficulty of a course for the bogey golfer. It is based on yardage, effective playing length and other obstacles to the extent that affect the scoring ability of the bogey golfer. To figure out this number, other than from looking at this database, the bogey golfer should take the Slope Rating®, divide it by the set factor (5.381 for men, and 4.24 for women) and add that to the Course Rating. The result is a target score for the bogey golfer, and is a truer yardstick of the challenge that lies ahead for the particular set of tees. Example: 96.3- which predicts the bogey golfer's average of his ten best (out of twenty) scores would be approximately 96.3 from this particular set of tees.

So how can we use this to adjust the shot efficiency formula?  The first step I came up with is to determine what I'm calling the course adjustment factor (CAF):

CAF = BOGEY RATING / STD BOGEY RATING

 where:

BOGEY RATING = [SLOPE / 5.381] + COURSE RATING

STD BOGEY RATING = [113 / 5.381] + COURSE RATING

I use 113 as the "standard slope" as that is the USGA definition of an average difficulty course.  From there I simply multiply the calculated shot efficiency by the course adjustment factor to yield the adjusted shot efficiency (ASE).

As an example, let's look at 3 rounds that have the same shot efficiency score to see how the adjustment impacts the rating.  As it turns out, I shot 79 in all 3 of these rounds, making it an even more ideal comparison:

1. 4/29/09 at Butter Brook Golf Club (Black Tees, 6702 yards, 72.6 rating, 133 slope).  I shot 79 with 30 putts, for a SE of 0.737.  The CAF comes out to 1.046, so the ASE is 0.771.  By the conventional metrics I hit 54% of fairways and 50% of GIR.

2. 8/2/09 at Brookmeadow Country Club (Gold Tees, 6585 yards, 71.7/123).  Again shot 79, this time with 31 putts, again the SE being 0.737.  The CAF for those tees is 1.017, so the ASE this time is 0.749.  The standard stats: 29% fairways and 44% greens.

3. 3/6/11 at Nancy Lopez Legacy CC in the Villages (Black Tees, 6906 yards, 73.2/135).  Shot 79 with 29 putts for (again) a SE of 0.737.  Here the CAF is 1.057, for an ASE of 0.779.  In that round I hit 50% of fairways and 33% of GIR.

Obviously these three rounds are all quite similar, but the intuitive difference that comes from the course difficulty is fairly represented by the subtle difference in the adjusted shot efficiency.  

Here's an even better example: in my 2008 round at Bethpage Black, I shot 94 with 36 putts, for a SE of 0.687.  The Black is largely considered one of (if not the) most difficult courses in the country, with a rating (at that time) of 76.6 and a slope of 144.  It's a great course to empirically understand how the slope rating works; even though the course is incredibly long, it plays even longer because of elevated greens, thick punishing rough, and the maniacally placed bunkers -- hence a high slope rating.  So when you apply the course adjustment factor (the highest of any course I've played at 1.123), the ASE jumps all the way up to 0.771.  And that's fair -- there's no way you can say an 84 at Braintree Municipal (rated at 70/123) has an equal shot efficiency to 94 at Bethpage, but that's how the calculation works out.  After applying the course adjustment, the difference in the 2 rounds is almost 10% (0.771 vs. 0.686).

On a final note, here are my top 5 rounds by adjusted shot efficiency over the past 3 years:

1. Butter Brook (7/17/11): score 73 (+1), SE 0.926, ASE 0.969.
2. Cane Garden (5/18/10): score 80 (+8), SE 0.868, ASE 0.925.
3. Granite Links (7/29/10): score 76 (+5), SE 0.851, ASE 0.913.
4. Red Tail (7/25/09): score 75 (+3), SE 0.851, ASE 0.911.
5. Butter Brook (6/23/10): score 74 (+2), SE 0.860, ASE 0.900.

Up next in the statistics category, I'll try to tackle the other part of the game: short game/putting.  

The Aerated Greens

Masters weekend.  It always inspires me to get out on the course, even in the sub-par conditions that New England weather usually gives this time of year.  But here in 2010 things have been different; although we had drenching rains for several weeks, we've also had warm temperatures, and so it was mid-60s and sunny when I got out for my third round of the year early on Masters Sunday (i.e. before the TV coverage started).  Did I have an even par round in me this early in the year?  Here's what unfolded....

Pinehills Golf Club (Nicklaus Course), Plymouth, MA - April 11, 2010

I've played the Nicklaus course 5 times before, and I have never played poorly on it.  Never.  I shot 74 (+2) the first time I played it.  "It suits my eye," as they sometimes say.  But this was the 3rd round of the year, and -- I'll be honest -- I didn't really keep my skills up at the range this winter in the way that I did last year.  So I didn't have high expectations.  And to top that off, the greens were aerated 6 days before my round, so putting wasn't going to be smooth.  I was there to have fun and enjoy being outside.

It turns out the round was slightly better than I expected.

1 A nice gentle 384 yard par-4 from the Blue tees.  After a pretty terrible range session before the round (which consisted of mostly pull-hooks with the driver), I was tempted to hit an iron and just get out there.  But like I said, I was there to have fun.  So driver it was, and though it wasn't my best shot it did find the fairway about 270 yards out, leaving a 53-degree wedge into the green.  I pulled the approach a little but still hit the target, leaving about 30 feet in for birdie.  As I said before, the greens were aerated that week -- they weren't in terrible condition, but still a bit bumpy -- and my 1st putt came up about 4 feet short.  The 2nd one bounced straight left about 2 inches before reaching the hole.  I hate 3 putts.  Score: 5.  Round: +1.

2 A par 5 that for some reason I always drive the ball left, and I did it again here.  I ended up in the rough behind a tree, forcing a punch out, though I was able to advance the ball to about 145 yards short of the green.  I hit a nice 8-iron in to about 15 feet and 2 putt for par.  Score: 5.  Round: +1.

3 A long and challenging par 3, measuring 221 yards, with a large bunker that protects the front center of the green.  I hit 2-hybrid dead at the stick (the ball mark was about 2 feet in front) and ended up on the back of the green.  My 30 footer just scooted right of the hole at the last minute, and I tapped in for par.  Score: 3.  Round: +1.

4 The fourth is a nice dogleg left par 4, with a carry over a waste area on the approach to the green.  I hit my drive a little more left than I wanted to (and almost rolled into the waste area), but actually ended up with a great angle for another 53-degree wedge approach.  Hit the center of the green and 2-putt.  Score: 4.  Round: +1.

5 The 5th is probably my favorite hole on the course, if only because I've played it well in the past.  I hit an ideal drive (first time I really felt comfortable with the driver all day) 290 yards down the center of the fairway, again leaving a gap wedge to the green.  Stuck it in there at about 10 feet, but missed the birdie opportunity and settled for par.  Score: 4.  Round: +1.

6 A nice, slightly uphill dogleg left par 5 that clocks in at 521 yards.  The fairway is protected by bunkers shortish left and longish right -- I carried the left bunkers to leave an ideal approach shot.  My 4-iron found the right fringe, and I easily 2-putt from there for birdie.  Score: 4.  Round: E.

7 The first time I played this hole I came the closest I've ever come to a hole-in-one (a topic for another blog?).  This time... not so much.  My 8-iron came up well short of the green; from there I made a nice pitch up to about 4 feet... but missed the putt when for the 2nd time in the round my ball bounced straight left on an aeration hole.  Score: 4.  Round: +1.

8 A 361 yard par-4 that plays tough because the green is capped more than most on this course and protected by a deep bunker on the right side.  I found the rough left of the fairway on the tee ball, and then the aforementioned bunker greenside.  I got out fine, but had 20+ feet for par and had to settle for bogey.  Score: 5.  Round: +2.

9 Like the 5th, I've always seemed to play this hole well.  That was the case again here as I smashed a drive 275 yards right down the middle, leaving just a 60-degree wedge in, and I stuck that to about 5 feet.  No bounces left this time.  Score: 3.  Round: +1.

10 After a quick hot dog, I got right back to driving the ball well -- this one was my best of the day, 305 yards down the middle.  Another gap wedge to the middle of the green and 2 putts for par.  Score: 4.  Round: +1.

11 A sharp dogleg left par 5 that measures 514 yards on the scorecard but plays a lot less than that if you can cut the corner.  I was playing with a member at Pinehills who said that when Jim Rice plays there he actually goes straight at the green and often has less than 50 yards left after his drive.  I wasn't quite so bold, but did manage to get over the trees and leave about 195 yards.  With the pin back and the wind in my face I hit 2-hybrid and found the back of the green.  I like 2-putt birdies.  Score: 4.  Round: E.

12 A tough par 4, playing 436 yards with an approach that is essentially all-carry over a valley between the end of the fairway and the green.  I hit my first poor drive in a while -- a pull left, reminiscent of the range earlier.  I had about 185 in from the rough and hit 5-iron just onto the front; it had a little cut spin and then took a slope down to the far right of the green (pin was left), leaving a long 50 footer back up the hill.  I ran that by the hole 10 feet and missed the come back.  I hate 3-putts.  Score: 5.  Round: +1.

13 A 181-yard par-3 with a somewhat shallow green.  I hit 6-iron pin-high but about 20 feet left.  For the only time all day, though, the putt found the center of the cup.  Score: 2.  Round: E.

14 My nemesis hole on the course.  I have never made par.  It's a short par-4 (just 312 yards) but you can't see the green from the pin because the sight line is protected by a huge mound and there are bunkers on both the right (short) and left (long) of the fairway.  On top of that the green is well-bunkered and very shallow.  I hit 2-hybrid off the tee and pull-hooked it into a bush.  Punched out -- barely; I still didn't have a line to the green.  Had to punch it again, this time down in front about 30 yards from the flag.  My pitch with my 60-degree hit the stick and bounced away 20 feet.  2 putts.  Score: 6.  Round: +2.

15 An all-carry 166 yard par-3 over a large waste area.  I hit a perfect 9-iron (with the wind) to about 6 feet.  Didn't make it.  I'd like to blame the aeration, but I think it was the stroke.  Score: 3.  Round: +2.

16 A dogleg left par 5, and at this point I knew I would probably need eagle here -- 17 and 18 are two of the tougher par-4's on the course.  But 16 is a great opportunity.  The tee is highly elevated, which gives a big advantage to any effort to cut the corner.  The wind was favorable.  In a similar situation in the past I'd managed to get my drive to the 150 yard markers.  I picked my line and gave a great swing -- just a little draw, high trajectory... but pulled just a shade more than I wanted.  There was no way to know if it made it or not, so I ended up hitting a provisional out safely (sort of -- it was in the fairway trap straight out).  When we got around the corner there was no ball in the fairway, which meant I didn't make it.  I did find it, just past the tree line, presumably after trickling through a few branches.  I was able to advance it but had no shot at the green; ended up in a bunker about 50 yards out.  From there I hit the green and made a long lag up to tap in distance for par.  Score: 5.  Round: +2.

17  Birdie-birdie?  It would take a better drive than I hit.  The pull-hook was back, and I was blocked out behind a mound and trees.  I hit a low 7-iron to well right of the green, then chunked a pitch into a bunker, but did get up and down from there.  Score: 5.  Round: +3.  Mission: Failed.

18 At least I didn't fold.  Perfect drive down the middle, 290 yards.  Easy gap wedge to the front of the green.  2 putts.  Score: 4.  Round: +3.

Was it another "round that could have been?"  Of course.  (Aren't they all?)  Without aeration marks, would I have made 3-4 more putts?  I think I might have.  I know this -- I have never hit my irons that well.  I hit 14 greens -- 3 more than I have ever hit before.  I drove the ball great in the middle of the round, but so-so on the bookends.  If only for that damn 14th hole.

It is going to happen.  Someday.