The End

 I started this blog in August of 2008, with a challenging goal: to shoot an even par round of golf.  I knew at that time that my game was probably good enough, but I was never quite able to hold it together for a full 18 holes.  I hoped that by writing publicly about it I would get some motivation, and maybe this would be a nice golf journal to look back on someday (which, frankly, it is).

I was 30 years old then.  I'm 43 now.  And the game isn't getting easier.  I haven't written anything in almost 6 years.  There have been some close calls, but between life and kids there just hasn't been time or enough impetus to share it.

So I'm writing today to say this will be the last entry in this journal.  Because today I shot even par.

Without further ado, here's the blow-by-blow.

COURSE: Granite Links Golf Club (Milton-Quincy)

STATS: Par 71, Blue Tees 6379 yards, rating 71.6, slope 132

WEATHER: Overcast and about 50 degrees with steady 10 mph winds out of the northeast, and gusts upwards of 15-20 mph 

1st Hole (Milton 1, par 4) - A challenging opening hole, which today was made all the more difficult since I arrived only 5 minutes before my tee time, and I actually sprinted down to the tee box and had to ask the nice threesome in front of me if they wouldn't mind me jumping out in front of them -- I was playing solo and trying to get around quickly.  They were gracious enough to let me go.  So with only a quick couple of practice swings I launched a 3 iron off the tee and pulled it left.  I got a good bounce around the fairway bunker and settled in a decent lie in the rough.  Still rushing a bit to be sure to get quickly out of the way of the other group, I took aim with an 8-iron and just tried to hit a smooth shot to the front pin location.  There were some grounds crew members working on the bunker left of the green, which is sometimes a magnet for me.  But this time I hit a nice slight draw which settled just 5 feet short of the hole.  1 putt birdie.  SCORE: -1

2nd Hole (Milton 2, par 3) - A fairly straightforward par 3 with a deep green that can play anywhere from 145 to 175 yards depending on the pin location.  Today it was middle, and my 7-iron settled in pin high on the right side of the green.  Routine 2 putt par.  SCORE: -1

3rd Hole (Milton 3, par 4) - Easily the toughest hole on the course, it requires an accurate tee shot of about 240 yards, followed by a lengthy all-carry approach over water to a well protected and multi-tiered and sloped green.  Par is always a good score.  I hit a hybrid a little off the toe but still found the fairway, leaving 190 yards to the back-right pin.  A little draw plus the wind brought my 6-iron to the front of the green, leaving a 60+ footer.  My "lag" was over-cooked and actually hit the hole, bounced out, and finished about 10 feet past.  But I made the testy come-backer for par.  SCORE: -1

4th Hole (Milton 4, par 5) - A reachable par 5 that was playing straight downwind today.  First swing with the driver and I hit a good one, actually carrying the first fairway and bouncing up through the rough into the second fairway.  The approach is well uphill, and I hit a 9-iron a little fat, coming up short of the green.  

Here's where I should pause and say that I've been taking some lessons this winter.  Last week I played a round that was a bit of a mess -- I hit a lot of good full shots, but my wedge game was awful.  So in my last lesson we focussed on half- and three-quarter wedges, and let's just say it paid off: 58 degree to 6 feet, and another birdie.  SCORE: -2

5th Hole (Milton 5, par 4) - Running parallel to the 4th and back into the wind, this is a hole where a great drive can leave a short pitch shot and a birdie chance.  I did not hit a great drive.  On the second shot the ball was below my feet, but I hit a decent 7-iron to just short of the green.  My chip also wasn't the best but at least left an uphill putt, and I happily got up and down for par.  SCORE: -2

6th Hole (Milton 6, par 3) - Generally a tough par 3 with a tricky green, particularly when the pin is back left, which it was today at 190 yards, though down-wind.  I hit 7-iron again, and pushed it a bit, pin-high but missing the green right.  From that angle the green runs uphill until about 10 feet before the hole, then back downhill and severely right to left.  I felt my only option was to try to flop it and get it to stop quick...and I nearly holed it.  Tap-in par.  SCORE: -2

7th Hole (Milton 7, par 4) - A short par 4 that is sometimes reachable, but played longer today into the wind.  I hit a good drive to the safe part of the fairway, which left the exact shot that was a disaster the last time I played: a 60-70 yard pitch.  My distance control wasn't perfect, but at least it went straight, and I had about a 20-footer for birdie.  Par was good enough.  SCORE: -2

8th Hole (Milton 8, par 4) - There are a lot of different ways to play this hole, but most members try to hit the tee shot over the left fairway bunker, which leaves a more direct approach shot and takes the massive right-side sand area out of play.  I chose that route today and hit 3 wood to about 95 yards out.  Another wedge opportunity, and again I was happy with the result, hitting the middle of the green.  2 more putts for par.  SCORE: -2

9th Hole (Milton 9, par 5) - I have the hardest time hitting the fairway on this hole.  Being fair to myself, it's a difficult tee-shot where you have to pick a line with a specific carry distance; anything left of that will run down a steep slope and perhaps out of play, and a good shot that goes a little right might also find trouble.  But I consistently make the big mistake and hit a pull-hook left that gets into the trouble.  Today, though, was atypical: I hit the center of the fairway.  The 2nd shot is significantly uphill (about 2 clubs worth), and with the wind today the green wasn't reachable.  I hit a poor lay-up into the fairway bunker left, and although I got out of there fairly well I was still short of the green in 3.  My pitch shot was good, and left only about 6 feet, but the putt was never high enough.  SCORE: -1

10th Hole (Quincy 1, par 5) - Although there is a lot of trouble if you hit it offline at Granite Links, there are only a few areas that are out of bounds, and one of them is the road left of Quincy #1.  It's pretty far left to get there, but there's a big ravine with thick fescue and brush between that and the fairway which is mostly unplayable in the summer.  I hit my drive just a little left -- not flirting with OB, but in the summer I would have been searching for a while.  Instead today I found a decent lie and a clean swing, and I was able to advance a 7 iron back into the fairway.  It wasn't great from there -- 9 iron well short of the green, then a pitch shot that flew too far, and 2 putts from 20 feet.  SCORE: E

11th Hole (Quincy 2, par 3) - There are three tough par 3's on the Quincy 9, and this one is probably the hardest.  Even playing downwind it was a 5-iron for me, and a decent shot still found the green-side bunker.  I was short-sided, and went a little long with a 58-degree, then 2-putted for bogey.  SCORE: +1

12th Hole (Quincy 3, par 5) - After 3 straight bogeys I felt like I needed to get one back here.  I liked hearing Justin Rose talk about how he tried to play a match against the course in the 2nd round of the Masters last weekend, and right now in my match I was 1-down.  I absolutely piped a drive down the right side of the fairway, but the longer you hit it on this hole the more the fairway slopes right-to-left, and my ball ended up all the way across to the rough on the left.  Still, after 309 yards off the tee I had just 170 left, all uphill.  My 5 iron found the front of the green, and 2 putts meant my match against the course was back to even.  SCORE: E

13th Hole (Quincy 4, par 4) - This is a ski-slope downhill hole that plays significantly less than the scorecard distance.  I hit what I thought was a good drive but the wind grabbed it and I ended up well right, into the 3rd fairway.  That's a fine place to be, though, and I hit an okay 9 iron that also got caught up in the wind, and was left with a long 70 footer.  I hate 3-putts.  SCORE: +1

14th Hole (Quincy 5, par 4) - This is closer to a par 4-and-a-half, uphill and long from the back tees, though from the blues it's more playable.  I hit exactly the drive I wanted to, but it turned out my target was off and I ended up in the right rough.  My pitching wedge from there rode the wind all the way to the back of the green, but I managed a good 2-putt this time.  SCORE: +1

15th Hole (Quincy 6, par 3) - The 6th on Quincy is all about club selection, short but significantly downhill.  Today it was also down-wind, which I didn't love with a back pin position since flying over the green is basically dead.  I went with a smooth pitching wedge...and nearly holed it.  The pitch mark was 6 inches from the hole, and I had just about 5 feet for birdie.  SCORE: E

16th Hole (Quincy 7, par 4) - I play this hole really well.  It's a short risk-reward type par 4, easily drive-able, but the shot toward the green is blind and anything right or short of the target is out of play or at least unlikely to be found.  But for some reason I just have that blind shot grooved, and I average under par.  I went with 3-iron to be sure I wouldn't be short, and ended up a little long and left of the green (which is the safe miss).  My pitch shot was tricky -- a downhill lie playing back uphill to the green -- and I came up short, then putted from the apron and made a 4 or 5 footer for the par.  SCORE: E

17th Hole (Quincy 8, par 3) - This is another downhill par 3, but much longer than Quincy 6.  The green is massive, and I like to think of it like 4 different greens depending on where the pin is.  Today's location was in what I would consider the front-left of the back-right green; or, I guess, "middle."  With the wind at my back 7-iron was all I needed, and I tried to make the same smooth swing I had made back on #15, but I pushed it just a bit.  It hit the right edge of the green and bounced straight right...and into the woods.  Fortunately, I again got lucky with some early season conditions and had a clean lie that I was able to get back onto the green, and 2-putts from 40 feet was just fine this time.   SCORE: +1

18th Hole (Quincy 9, par 4) - Well, this was it.  1-over through 17, needing birdie, standing on the 18th tee, and playing dead into a gusting 15-20 mph wind.  The best line is basically straight at the green, even though from the tee box it looks like all the playable fairway is off to the right; I hit a low drive about 225 yards down the left side of the fairway, right where I was aimed.  The pin was tucked in the back right portion of the green, which sits in a little bowl, and most shots that get back to that location will funnel toward the pin.  I had about 100 yards, and felt good about a 50-degree wedge into that wind.  Ball contact was good but up in the air I had some butterflies that the wind was going to be too much, and it wasn't going to be enough club.  Fortunately I saw it disappear over the little hill in the green, which meant it was in the bowl...and when I got up to the green I saw my ball sitting pin-high, about 7 feet away:

SCORE: EVEN PAR

And that was that.  The long journey is complete.  All-in-all the round was very solid, with 5 birdies and 5 bogeys, no penalties, and of course a little luck.  But I finally halved the match against the course.  

(Now I have to go win one.)

The Fitting | The New Sticks

I made the decision over the winter that I was going to make an equipment upgrade this year.  I'm more than happy with my irons, but my hybrids were old and outdated, and in the past year I've found that I haven't hit them with the same consistency I used to.  Moreover, my driver had a lot of swings in it, and it seemed like it was time to take advantage of some of the new face and shaft technology available.

With that in mind, last weekend I went to Joe & Leigh's Golf Performance Center in Easton, MA for a fitting.  Joe & Leigh's has been famous a few times; it was the site of Golf Digest's cover article a few years back touting the benefits of club fitting for all players, and also was where Jim Furyk famously bought a used putter that he had in the bag when he won the Tour Championship and FedEx Cup in 2011.

My current driver is a Titleist 907 (so 8 years old).  After doing my homework (primarily on mygolfspy.com's Most Wanted Driver list and data set), I settled on testing the new Titleist 915 D2 and D3; the Callaway Big Bertha Alpha DBD; and the Cobra Fly-Z+.  I also wanted to get in a good number of shots with my old driver on the launch monitor just to see if making a change was really worthwhile.

You can see the map of all the shots I hit below (excluding severe outliers).  You can see right away that my old driver (the 907) is still a pretty good club, with the best drive hit at over 300 yards and just right of center.  But all the shots are right of center, which highlights the problem I have with it -- keeping it straight.

With even just a cursory scan of the shots, the Cobra quickly stands out for having the 4 longest drives of the day, all of which are relatively on-line.

It doesn't take a long look at the detailed view to determine that the Cobra Fly-Z+ is the easy winner.  Both the D2 and D3 Titleist models are maybe a little bit more consistent in terms of accuracy -- but not by much -- and the Cobra is easily the longest.  Not only that, but set up on neutral and with the Grafalloy Blue 75 shaft my fitter set me up with, I was hitting a slight draw (manifest by mild negative side spin) instead of the old power fade (see the high positive side spin on the 907) that hasn't been as consistent as I would like.

After deciding on the driver, it was relatively easy to pick the matching Fly-Z+ and FlyZ fairway wood and hybrid -- both are adjustable within a 4-degree range, and both were carrying 10-15 yards longer than my current 1-hybrid and 2-hybrid.

I ordered everything custom from the Cobra website that night.  Just 3 days later the wife sent me this via text:

Can't wait to really put them in action.

The Hole-in-One Odds

I've never had a hole-in-one.

I don't check my Facebook feed that often, but I happened across this post today:

Unfortunately that means I now hate that guy.  I also hate my dad (3 aces in the last decade) and my brother (x2).  At this rate I won't have anyone to golf with that I actually like in a few years.

The odds of making a hole-in-one are surprisingly hard to find.  A lot of that probably comes from the fact that it's an infrequent enough event that it's hard to study.  But Golf Digest has been trying to keep track and published some of the data in 2013.  According to their numbers, a "low handicapper" has about a 5000:1 chance on a par 3 (pros: 2500:1; high handicappers: 12,500:1).  If there are 4 par-3's on a standard track, then a low handicapper should have about a 1 in 1250 chance of writing "1" on the scorecard in any round.

But of course not all par-3's are created equally, and it stands to reason that it's a lot easier to make an ace on a 90 yard pitch than it is trying to fly in a 3-iron 220 yards over a wetlands preserve.  I couldn't find much data out there about different odds for different distances; the only odds I found were for "average golfers" on a 200 yard hole -- 150,000:1.

Using those numbers I estimated the odds for a low handicapper on a 200 yard hole at about 62,500:1.

Now I play most of my golf on my home course, which has 7 par-3's over 27 holes, ranging from 140 yards (from the blue tees) to 242 yards (from the black tees); the majority, are in the 170-200 yard range.  I'll spare you the details, but if we assume I play about 50% of my rounds from the blue tees and 50% from the blacks, then my true odds of getting a hole-in-one in any given round are about 1564:1.

So...if I play 20 rounds a year it will only take 78 years to guarantee an ace.

Sigh.

The (US) Resorts

There's almost 100 inches of snow on the ground in my front yard, and so naturally the only thing on my mind is...golf.

The new Golf Digest list(s) of "America's Greatest Courses" is out.  Obviously any one ranking of courses is going to be incomplete and imperfect, but this is the one that carries the most weight in the golf community.  For 2014-15, they have five different rankings: the Top 100, the "2nd 100" (i.e. numbers 101-200; why it's not the "top 200," I don't know), the Best in State, the Best in Canada, and the Top 100 Public.  The Top 100 itself is dominated by courses that are private (1-2-3 are Augusta National, Pine Valley, and Cypress Point, which are all famous both for their awesomeness and their exclusivity), and there isn't a public course until #7 (Pebble Beach).  You don't see another public until #18 (Pacific Dunes).  I've only played one course on the list: #43, Bethpage State Park (Black).

Ultimately it's the Top 100 Public list that I'm most interested in.  This year I happened to take note of the courses from the same property or resort that show up on the list -- probably because the AT&T Pebble Beach Pro-Am was on TV at the time, and they were playing on 3 of the top 100.  So this got me thinking: what are the best golf resorts in the country using the top 100 rankings as a metric of quality?

As best as I can tell, there are six resorts that have more than one course in the Top 100 Public ranking:

Pebble Beach: Pebble Beach Golf Links (1), Spyglass Hill G.C. (11), and The Links at Spanish Bay (49)
Bandon Dunes: Pacific Dunes (2), Bandon Dunes (7), Old Macdonald (12), and Bandon Trails (14)
Kohler/American Club Resort: Whistling Straits (Straits) (4), Blackwolf Run (River) (16), Whistling Straits (Irish) (47), and Blackwolf Run (Meadow Valleys) (72)
Pinehurst Resort: No. 2 (5), No. 4 (59), and No. 8 (80)
Streamsong Resort: Streamsong (Red) (18) and Streamsong (Blue) (24)
Turning Stone: Atunyote G.C. (52) and Kaluhyat G.C. (82)

Limiting ourselves to those criteria (more than one course in the Top 100 Public), then we can use the scores within the rankings to determine which is the most desirable resort to go to (from a strictly golf perspective).*  I looked at the numbers three ways: the average score across the courses at each resort (more uniformly high quality = better), the total score for each resort (more courses = more variety = better), and the top ranking course at each site (a standout "must-play" course = better).

*This doesn't quite tell the whole picture of these resorts, as we're only looking at the courses that are ranked in the top 100.  Pinehurst, for example, has 6 additional courses that may all be of high quality, but not quite good enough for the rankings.

I look at the those 3 characteristics as all being equal.  To compare the resorts, I took the z-score for each category and added those up to get a total score.  Here's how it breaks down:

PEBBLE BEACH			BANDON DUNES			KOHLER
COURSE	GD SCORE		COURSE	GD SCORE		COURSE	GD SCORE
Pebble Beach	67.6226		Pacific Dunes	65.1785		Straits	64.7478
Spyglass Hill	62.7138		Bandon Dunes	63.4556		River	61.0936
Spanish Bay	57.6485		Old Macdonald	62.4879		Irish	57.7387
			Bandon Trails	61.5480		Meadow Valley	56.5514
AVERAGE	62.6616		AVERAGE	63.1675		AVERAGE	60.032875
TOTAL	187.9849		TOTAL	252.6700		TOTAL	240.1315
TOT Z-SCORE	2.264		TOT Z-SCORE	2.914		TOT Z-SCORE	1.223

PINEHURST			STREAMSONG			TURNING STONE
COURSE	GD SCORE		COURSE	GD SCORE		COURSE	GD SCORE
No. 2	64.2727		Red	60.7601		Atunyote	57.5788
No. 4	57.1474		Blue	60.1842		Kaluhyat	56.0961
No. 8	56.1970
AVERAGE	59.2057		AVERAGE	60.4722		AVERAGE	56.83745
TOTAL	177.6171		TOTAL	120.9443		TOTAL	113.6749
TOT Z-SCORE	-0.335		TOT Z-SCORE	-1.746		TOT Z-SCORE	-4.321

In both the average and total ranking categories, Bandon comes out as the clear winner -- unsurprising, since all 4 of it's courses fall in the top 14 overall; that's strong enough to place first in the total ranking.  Pebble Beach carries the "top ranking course" category, but that isn't enough to overtake Bandon overall.  Kohler finishes 3rd; having a 4th course on the list helps out here, since the numbers are otherwise very similar to Pinehurst.  With just two courses each, Streamsong and Turning Stone can't quite keep up with the bigger names, though they still have very strong averages.

Naturally, when it comes to resort destinations there are other things to consider beyond just the golf. The setting at Pebble Beach -- including the accommodations and the other activities available -- could easily be argued as enough to push it back ahead of Bandon.  On the other hand, it's hard to ignore the cost:

Cost figures are based on peak season rates.

Here it's quite clear that Bandon has a huge advantage over Pebble; in fact it appears that Bandon and Streamsong are relative steals compared to the other resorts.  And this doesn't even take into account the cost of accomodations, which is nearly twice as much at Pebble as it is at any of the other sites (and hotel reservations are required to make a tee time).  Bottom line: at this point, if I could go anywhere, it's definitely Bandon.

Also not factored in here is the cost of a caddie, which may not be required at every course, but where available they are certainly recommended.  (As far as I can tell, caddies are not available at Pebble or Turning Stone.)  When you factor that in, something very interesting happens:

Amazingly, they all fall nearly exactly on the trendline of the aggregate data -- in short, it costs just about $6 per Golf Digest point to play golf at each of these resorts.  

Two lessons learned here: (1) You probably can't go wrong at any of these resorts, and (2) Golf Digest's "America's Greatest Courses" probably drives the cost of golf far more than we realize.

The Quarry Hills Invitational

One of the absolute pleasures of membership at a golf club is the opportunity to bring guests to enjoy a nice round at your home course.  And the pinnacle of guest hosting is definitely the member-guest tournament that nearly every club hosts over the summer.

Being honest, these events are basically opportunities for clubs (and their members) to showcase everything they've got in one big "my club is better than yours" contest.  But that doesn't mean they're not a lot of fun.  I previously wrote about part of my experience at my friend Kevin's member-guest (and the closest round I ever had to even par), which is just a fantastically run tournament; this year I had Kevin as my guest at the Quarry Hills Invitational at Granite Links.

Kevin hits his 2nd shot -- 4th Hole, Milton 9, Granite Links Golf Club

The Format
The event is played in 2-man teams, slotted into flights of 6 teams based on combined handicap.  I was playing as an 8 and Kevin as a 10, which put us as the top seed in the 4th flight (of nine).  On the weekend, each team plays a 9-hole match against the other 5 teams in their flight, with each hole being worth 1 point (you get 1 point if you win the hole, 1/2 point if your halve the hole, and 0 points if you lose the hole).  Additionally, on the Friday before the weekend there is an 18-hole better-ball event (at 90% handicap) for "bonus points" -- 2 points for the low team in the flight, 1 point for 2nd, 0 points for 3rd and 4th, and -1 point for 5th and 6th.  At the end of the weekend, the team with the most points wins the flight, and each flight winner then plays in a shootout to determine the overall champion.

Day 1: Better-Ball
Before we started, I told Kevin I thought we needed to shoot 6-under to win the flight.  It was a shotgun, and we started on the 5th hole on the Milton 9 and each made routine pars, so we got off to a good start.  From there we really played well as a team, with at least one of us putting up a good score on each hole; I shot 82 and Kevin 87, but together (with our strokes) we managed exactly what I had set as our goal -- a 6-under 65.  Along the way I found my putting stroke,* with just 26 putts for the round, making both a few long ones and several 4-8 footers.  Unfortunately, my prediction about the score we needed to win the flight was way off -- we were 3rd, with groups having shot 61 and 63 ahead of us!

*Side note: I put a new putter in play before the tournament started.  I realize this screams of desperation, but in truth, it wasn't really a new putter -- it's the same one I have in my bag down in Florida.  I love that putter, and happened to see it on sale at Golfsmith earlier in the week.  As you'll see, this was a great decision.

Day 2: 27 Holes (3 matches)
Saturday we played 3 matches covering all 27 holes of the club.  It was an awesome (and full) day of golf.  We got off to a rocky start, losing our first 3 holes, but battled back to halve the first match; then halved the second match; and finally won 5-4 in the 3rd match.  The key to the day was definitely our putting; we both hit it all over the place, but were very consistent on the greens.  Kevin made a 20-footer on the 9th of the 1st match to save the halve; I made a testy 15-footer on the 1st of the 2nd match for birdie.  But the 3rd match was where it really all clicked -- I had 7 putts through the first 6 holes, getting up-and-down 3 times and making two long ones for birdies.

Really, it was a great putting weekend all-around.  I had been struggling a bit with the flat stick this year, which I mostly attributed to my lack of play.  As I said, I decided to put a new putter in the bag this weekend.  I don't know if it was because of that, or the fact that the greens were rolling absolutely perfect, or that I actually played several days in a row -- or some combination of all of the above -- but I was seeing lines on the green like it was a video game.  It felt like everything had a chance to go in.

Here are my short-game stats for the year before and after the new putter:

Short Game Performance YTD (prior to new putter)

Short Game Performance at QHI (with new putter)

There's a little bit of fiction to those numbers since some putts were conceded and there were a few holes where I was out of play and didn't finish the hole -- but not many.  The vast majority of those 1.52 putts/hole represent made putts.

The kicker, though, is that it was putting that was ultimately our undoing.  We both missed 2-footers on the 8th hole of our 3rd match that would have garnered us an extra half-point.  And then there was day 3...

Day 3: 18 Holes (2 matches)

We finished day 2 in second place in our flight, but a distant 6 points out of the lead.  Our matches that day were against the 3rd and 1st place teams, so we needed to be on top of our game.  We started well, each making par on the first hole of the day.  On the 2nd hole (the par 3 #7 on the Granite 9) we cost ourselves a 1/2 point, as we were both on the green and both 3-putt (I hate 3-putts, even when the pin is in an impossible position on a steep slope), ending up with a halve.  We halved the next as well before we each made sandy-pars to steal a full point on the 9th.

The next hole (Granite #1) featured two of the best shots of the tournament.  The hole is a par-5 that plays severely downhill; most players hit a lay-up off the tee, and then must choose whether to lay-up again or hit a 200+ yard downhiller to go for the green.  It's an intimidating-looking hole, especially for those who haven't played it much, because it looks like there is trouble everywhere (in reality, the fairway is enormous).  Kevin struggled with it all weekend, and he did not make a committed swing on his tee-shot, pushing it well right and out of play in the woods.  After a drop and a layup short of the first hazard, he was left with about 260 yards in.  At this point in the match-play format there was no reason to play conservative, so he pulled out the 3-wood and let it rip... and rolled it just about 3 feet past the hole.  It was awesome.

Granite #1

Unfortunately, although that was the best shot I saw all weekend, he wasn't even the closest to the hole on the green, as our opponent hit his drive down the left side to the narrow strip of fairway, getting all the way down to a flat area that leaves just about a 7-iron into the green.  And he stuffed his next one inside Kevin's ball.  So despite Kevin's amazing par, we lost the hole by 2 shots.

We battled right back, though -- I halved with a par on #2, and then made a 15-footer from just off the green for birdie on #3 to get back to 1-up in the match with two holes left.  Both the other member and I made par on the par-3 4th; but then on the last hole Kevin and I both mis-hit our approach shots and had to battle to get up and down for pars.  Those weren't good enough, though, as we watched our opponents roll in a birdie to (yet again) halve the match.

So that left just one more match, and we were up against the leaders in our flight.  We actually had gained a half-point, so we needed 7-1/2 points in order to win the flight.  And we still had a 1-point lead for second (and therefore, the money).  We started this one on Milton #7, a potentially-drivable par 4, though with the wind in our face that was unlikely.  Kevin and I both hit good drives and put ourselves in decent shape to make birdies; but for the second hole in a row we watched our opponent make a nice putt and we weren't able to match.  We did get that point right back on #8 when everybody missed the green and I was the only one that managed to get up and down for par.  Everybody parred the 9th, but our opponent's guest was getting a shot there, so now we were back down a point.  We halved the next two before Kevin won us another point on #3, and I took home #4 to put us up 4-3 with two holes to play.  At that point 1st place was already out of play, but 2nd was a strong possibility.

On the par-4 5th I hit my drive well left, actually down into a bunker on the 4th fairway; my shot from there was never found, essentially putting me out of the hole.  But Kevin was on the green in 2, albeit a good 50 feet from the hole.  From the other positions on the green, it was likely that par would yield a half point.  It was a tricky downhill putt that required a precise line since it could really break either way depending on the line... but it ended up being speed that was the putt's undoing, as he ended up about 20 feet short.  Suffice to say, we headed to the last hole back to even in the match.

But 2nd place was still out there, and Kevin was the only one in our group to hit the green on the 188 yard par 3.  I was in the fescue on the right, but was able to get my pitch onto the green, leaving about 20 feet for par.  After our opponent's guest essentially put himself out of par contention, I was next to putt, and again I felt sure that I was seeing the line perfectly.  As soon as I hit it I was sure it was in, tracking perfectly uphill and slightly left to right... except it just skirted by the right edge.  Bogey.

Kevin's putt was all about speed again -- he had to go uphill over a ridge initially, but the last 5 feet were going to be back downhill.  He hit it just a bit too hard, and left a good 10 feet coming back; he, too, made bogey.  All we could hope for was a halve, which would require a miss from the other member on an 8-footer on the same line Kevin just had.  His putt?  Oh, it only did a full 360 around the cup before falling in.  We lost the match 5-4....

...and finished 1/2 point out of a tie for second place.  Ouch.

Final Analysis

Considering neither Kevin nor I have played much golf this year, I'm pretty happy with how we played.  We certainly were well-placed in the 4th flight since we ended up halving everything -- 3 matches were 4-1/2 to 4-1/2, and the other two were 5-4.  Obviously the missed opportunities on the last two holes hurt, but really I go back to the 8th hole of our 3rd match on Saturday (when we both missed 2-footers that would have won the hole) as the one that got away.

It was definitely a great weekend.  The course was in absolutely perfect condition, the weather couldn't have been better, and the atmosphere amongst the guys was what really made it fun.  I can't wait for next year.

The SCC June Invitational: Round One

This year I have the distinct pleasure of playing in my first member-guest tournament as a guest of my friend Kevin at his home course, Springfield Country Club. It is an arguably ridiculous five day affair. Today was the seeding round, played as four-ball (aka best ball of 2-man teams) using gross scores.

We were the first group off the 10th tee, with a 7:30am tee time. Here's how the round played out...

10TH HOLE

A short, sharp dogleg left. The smart play is to hit a 180 yard shot off the tee, and then a short iron into the slightly elevated green. I hit 5-iron but pulled it left; fortunately I managed to have a good view of the green with only about 100 yards in. I hit a gap wedge to about 18 feet. Kevin played it about the same, with a pulled iron off the tee, then a wedge to maybe 20 feet. His birdie try just missed; mine was in the center of the cup. A good start. TEAM: -1. MY BALL: -1. 

11TH HOLE

A tough par 4 that plays uphill and therefore a lot longer than the distance on the scorecard. The tees were up, though, which made driver the fool's play. I again pulled my tee ball, a 15 degree hybrid into the tree line. Kevin also followed me to the left, but he had a clean shot at the green, whereas I was going to have to hit a punch through a narrow window if I was going to advance the ball at all. Kevin ended up flying the green; my 6-iron punch got through clean and left me with about a 30 yard pitch to a crowned back pin. I hit a decent shot, but still had about 12 feet for par...and made it. Kevin had a little more trouble from his position and made 6. TEAM: -1. MY BALL: -1. 

12TH HOLE

A reachable par 5 that plays -- interestingly -- across a road. Both Kevin and I hit 275 yard drives down the center, and then we both hit hybrid across the road to the landing area short of the green; Kevin had about 75 yards left, and I had a delicate pitch that would need to carry the bunker on the right of the green. Kevin's shot was aggressive and ended up on the back of the green -- not where you want to be on a green that slopes severely from back to front. I hit a quick-checking pitch that stopped about 2 feet from the hole on the high side.  Kevin's try ran (unsurprisingly) past the hole, but I managed to cozy in my quick tester for a second birdie. TEAM: -2. MY BALL: -2. 

13TH HOLE

The 2nd of two back-to-back par 5's, this one is less likely reachable though actually easier to go for it because there isn't really any trouble in front of the green. We again hit matching 275 yard drives, but terrible shots from there -- I fanned a 1-hybrid way right, into the 14th hole rough, and Kevin hit one fat, leaving 100 or so into the green. My 54 degree wedge found the front of the green, while Kevin's next shot was off the back edge. I was in after 2 putts; Kevin finished with bogey. TEAM: -2. MY BALL: -2. 

14TH HOLE

Playing at just about 180 yards, this should have been an easy 5-iron, but I hit it thin and ended up in the green side bunker on the left. Kevin hit a beautiful 5-iron with a little draw pin-high, with about 8-10 feet left. My bunker shot went right over the stick, and it took 2 to get down for bogey. Kevin's birdie try dove left at the last second, and so we settled for his tap-in par. TEAM: -2. MY BALL -1. 

15TH HOLE

This is a long uphill dogleg right par 5. Kevin popped his drive up a little and was in the right rough, blocked out a bit. My drive was almost to the corner of the dogleg, but leaked a little right at the end and wandered into the first cut of rough; I also didn't really have an angle to go at the green. Kevin's next one carried through the fairway into the left rough, while my 5-iron came up about 50 yards short of the green in the center of the fairway. From there I hit a nice pitch that landed next to the pin and ran 5 feet past; Kevin hit a good looking 7 iron that somehow came up short and in the bunker. He took 3 to get up and down; my putt did almost a full 360 around the cup but somehow did manage to fall in for another birdie. TEAM: -3. MY BALL: -2. 

16TH HOLE

A long par 4. I hit a good drive 265 yards down the center, while Kevin pulled his a bit and nearly got to the woods on the left side, leaving no clean shot to the green. He hit a good punch that actually almost got there. I hit 8-iron that landed in the center of the green and somehow spun 20 feet back to the front fringe. Kevin had a tough lie in the rough and needed a chip and 2 putts to get in; I lagged up to about a foot and made par. TEAM: -3. MY BALL -2. 

17TH HOLE

A difficult par 4 because of the treacherous green the slopes severely from back to front. I hit hybrid past the dogleg corner into the 1st cut of rough on the left; Kevin hit driver to the right side of the fairway. I had about 95 yards to the pin (which was front-right) and the lie was a little heavy so I decided to hit a full gap wedge. It flew to about 5 yards past the pin, and then started to come back toward the hole...and then past the hole...and then off the green...and then 50 feet down the hill of the false front. Kevin saw that happen and decided to hit a dead wrist wedge to take the spin off and managed a perfect shot to about 6 feet that held its position. I got up and down for par. Unfortunately Kevin's trick right to lefter wasn't meant to be. TEAM: -3. MY BALL: -2. 

18TH HOLE

Both the 18th and the 9th holes are long uphill par 3's. This one plays a little shorter, and my 5-iron made the front right of the green. Kevin hit hybrid and didn't make a committed swing, leaving it short and right in the rough. His chip ran about 10 feet past, and so did my poorly-read lag putt. We both missed the comeback. Ugh. TEAM: -2. MY BALL: -1. 

1ST HOLE

The 1st is a straightforward short par 4 -- reachable at about 285 yards, but risky with protective bunkers on both sides of the front of the green. We each hit 4 irons in the fairway, then 100 yard wedges to about 20 feet. 2 pars. TEAM: -2. MY BALL: -1. 

2ND HOLE

A short downhill par 3 over water that was only about 100 yards with the tees up a bit today. I hit a 54 degree wedge that landed about 5 feet past and right of the pin, and for the 3rd time in 5 holes I watched my ball spin 20+ feet back, this time to the very front of the green. Kevin wound up in the bunker that sits in back of the green; his bunker shot left him about 15 feet. I had a tricky uphill right to left putt that was along a ridge line, so I hit it firm and ran 3-4 feet past. Kevin's par try skirted past the hole and ran down that same ridge leaving a long comeback for bogey (it wouldn't go). I made my par. TEAM: -2. MY BALL: -1. 

3RD HOLE

A long par 4 that falls off the right side, requiring a good drive that favors the left. I hit it on the screws 295 yards in the fairway; Kevin was nearly as good, just about 20 yards back. We both hit short of the green with a front pin; I could have putted mine but didn't like the way it was sitting and elected to chip instead -- and nearly holed in, leaving just a tap in for par. Kevin made 5. TEAM: -2. MY BALL: -1. 

4TH HOLE

By now I was clearly feeling it, and on a hole that doesn't require a driver I still took a rip at it and hit a power fade to the center of the fairway, just 40 yards from the center of the green. Kevin played the opposite, hitting hybrid to the 150 yard marker. His shot ended up on the right fringe; my pitch came up a little shorter than I wanted and left about 15 feet. 3 shots for Kevin made bogey; I 2-putt for par. TEAM: -2. MY BALL -1. 

5TH HOLE

A gradual dogleg left where driver is a difficult play. I hit 1-hybrid to the right side of the fairway; Kevin's shot was nicely down the left side. The green is elevated and the pin is difficult to see from below; we both hit wedges that looked awfully good, but both shots were 20+ feet from the hole. 2 pars. TEAM: -2. MY BALL: -1. 

6TH HOLE

Unquestionably the most difficult hole on the course: a 408 yard downhill, narrow, gradual dogleg left that has hazard on both sides, plus a brook that starts about 100 yards from the green and crosses the fairway 40 yards in front. The ideal shot off the tee is about 230-260 yards to a flat area between 2 ski-slopes that can potentially take your ball on a trip off course quickly. I hit 2-hybrid into that sweet spot. Kevin hit an iron off the tee but left it off to the right in the rough (but not the hazard). From there he punched down to the flat area. I had 175 in, all downhill, and hit 7-iron to the left center of the green. Kevin hit his thin and ended up in the left rough -- he eventually made 6. I had a routine 2 putts for par. TEAM: -2. MY BALL: -1. 

7TH HOLE

A short-ish dogleg left par 4 where you must favor the right side off the tee -- the left side slopes off to a hazard area. We both hit left -- Kevin into the hazard, but still with a playable lie; I got a little lucky and stayed in the rough with a clean shot at the green. Kevin punched out, and then hit one to the back of the green; I hit a 9-iron to almost pin high. The hole was precariously placed just over a ridge from me, but I managed to lag to tap-in distance. Kevin also 2 putt for his bogey. TEAM: -2. MY BALL -1. 

8TH HOLE

A very difficult par 5 that requires a lay up off the tee, then a carry over a wetlands hazard to an uphill fairway. If you hit 2 good shots, then you still probably will have 150-200 yards in. I hit 3-iron into the left rough. Kevin hit hybrid to the left fairway. My lie was not good, but I needed to pick up some distance so I hit 2-hybrid, which spun out right and crashed into a grove of trees. (I hit a provisional at that point that would prove to be unneeded.) Kevin chunked his next one a bit, but did manage to safely carry the hazard. I had a limited window when I found mine, but was able to hit a low 4 iron punch to about 30 yards short of the green. By this point, by the way, it was pouring rain, and I lost track of what Kevin did (I think he made bogey). I hit what I thought was a good pitch, but it didn't get nearly as close to the hole as I wanted; my 18 footer skirted past the left edge from there, but I made the 3 footer coming back. TEAM: -1. MY BALL: EVEN. 

9TH HOLE

Uphill par 3. 185 yards today. Pouring rain. And I'm at even freaking par with one hole to play. 

Deep breath. 

4 iron. Just hit it smooth. 

Kevin would later say that the calm confidence that I had the whole round had clearly evaporated as I stood over the ball. 

I will freely admit: I choked it. The only truly bad shot I hit all day. A thin pull hook, well left of the green and down a hill into thick rough. 

Still, all it would take was a flop shot (over a bunker) and a putt to reach the goal. I hit the shot I wanted, and got absolutely no roll out, so 15 feet was what stood between me and even par. I read it as just a hair left to right, but Kevin's putt (from a little deeper on the green than mine) ran hard to the right, and so I gave it a little more credit than I initially planned....and it never broke. Tap-in bogey. (Kevin also made bogey, I think.)

TEAM: even par. MY BALL: +1. 

I could make a million excuses, but the truth is I just hit a terrible shot on the last tee. I can't play much better than I did -- all aspects of my game were clicking. (In retrospect, my long iron play could have been better overall.) The good news is I get to get back out on the same course tomorrow to take another run at it. 

As for our team performance, the course became unplayable due to the weather not long after we finished -- as a result only 15 groups actually finished, and the scores were wiped out (seeding instead will happen based on combined handicap). 

But we were the low score by 3 shots. 

The Swing Analysis (2013 Edition)

"I figured it out!"

I've said that probably two dozen times over the years with reference to my golf swing.  My brother has said it at least that many to me.  Our dad has easily doubled that.

We're always (eventually) wrong.  But that doesn't mean it's not worth working on.

This year's "I figured it out" moment came courtesy of a Sean O'Hair tip in Golf Digest.  You can see the video version below.  What he says isn't revolutionary, but it's the imagery of the hands and clubhead being on train-tracks on the take away that really clicked for me:

My problem historically has been what O'Hair refers to as "sucking in;" that move gets the club too far inside, and I have to make a big adjustment to get on plane at the top of the swing.  Sometimes that works, but sometimes it doesn't; just depends on my timing.

So for the past month or so at the range I've been rehearsing the "train tracks" take away over and over.  Below you'll see some video of my swing with this mental image at the forefront of my mind:

7 iron

Driver

A couple of things I learned from this: (1) this is definitely better, less of a wrap-around take away than I've had previously, and leads to a controlled but powerful weight transfer (especially with the driver); and (2) no matter what I think I'm feeling, the video tells a different story -- I'm still too far inside.

7-iron swing sequence - click to make larger

Ultimately I think I'm doing a better job with the first 25% of the backswing, but then I go right back to rotating the club as I continue backward as opposed to lifting it.  The past 2 range sessions (after these images/videos) I've been focusing on the full backswing, and I feel it becoming ingrained.  The question now is how long I can keep it that way before the old habits creep back in.

The Amendment

I need to make an amendment to the last post on my short game statistic.  My brother (the math teacher) pointed out that making an "arbitrary" assignment of 5 putts saved as "perfect" didn't make a whole lot of sense after all the intricate calculations that came before that.  He recommended using normative data for strokes gained-putting to assess how the adjustment should be made.  Unfortunately, I didn't have normative data for strokes gained-putting.

So... I decided to go straight to the source.  I emailed the guru himself, Mark Broadie, and asked if he could help out.  And he graciously sent along the distribution of PGA strokes gained-putting ranging from +5.5 to -5.5.  Based on that, I was able to asses that (a) it is indeed normally distributed, and (b) the standard deviation is about 1.735.

One problem with that, though -- although I refer to the number as an estimated shots gained-putting, what I'm really trying to calculate is something more like "shots gained from short game shots."  So putting-only distribution doesn't quite fit (obviously there are fewer putts in a round than there are total short game shots including putts; therefore the range should be a bit bigger).  Fortunately, Broadie's research comes through again here, as it turns out an average round's short game play can be split into about 75% putts and 25% short game shots.

Based on all that, here's the final calculation for short game score:

SG = 0.75 + [(SGP*0.75)/1.735] * 0.1

where SG = short game, SGP = estimated shots gained-putting

That yields a short game score of 0.750 (or 75% efficient) when SGP = 0, and goes up or down by 10% for every standard deviation above or below the PGA mean, adjusted for the added short game shots.  Ultimately this works out close to my original "arbitrary" assessment, but it's definitely more precise -- and I like that.

Using this calculation, by the way, obviously changes my short game scores that I had reported in the previous post.  Here are the updated values:

Red Tail Golf Club (SGP +0.672) -- short game score 0.779 (down from 0.784 by original method).

Butter Brook Golf Club (SGP +3.213) -- short game score 0.889 (previously 0.911).

Fox Hopyard Golf Club (SGP -6.145) -- short game score 0.484 (previously 0.443).

The Must Plays: 2013

This is happening right now:

That means two things: (1) no golf for me any time soon, and (2) more blog posts for you!

So let's review last year's "must-play" list and delve into the courses I'm looking to get to this year.

First up, the courses from last year's list that I made it out to.  It was good year as "must-plays" goes, as I made it to 3 of the 5 courses on the 2012 list, plus one from the 2012-2016 list.

MUST PLAYS 2012: COURSES PLAYED

1. Wintonbury Hills Golf Course, Bloomfield, CT.  I played this one very early in the season, just after opening.  I really can't say enough about this course, a varied design that plays fairly open on the front side, and more tightly through the forest on the back.  It's the perfect stop half way between Boston and New York.

2. Meadow Brook Golf Course, Richmond, RI.  I ended up here on a last minute decision -- I had spent a night in Providence and was thinking of heading down to the Connecticut casinos for some poker, but at the last minute decided play 18 instead.  The course comes as advertised: "7400 yards from the back tees with rolling fairways and multiple elevation changes throughout, allowing golfers to use every club in their bag."  It still needs a little bit of maturing, and there is one notable oddity -- the first tee is quite a distance from the pro shop -- but it has the potential to be the prime choice for golf and gamble trips in the future.

3. The Ailsa Course, Turnberry Resort, Ayrshire, Scotland.  As perfect a place as I've ever been.  If you haven't read about it yet, click here.

4. The Oaks, The International Golf Club & Resort, Bolton, MA.  I had put this one on the 5-year list, but suggested that I would try to get there in 2012 because it was newly semi-private, and there's always a chance it would go back to full-time private.  I actually ended up playing there twice, 10 days apart.  It immediately vaulted to one of my favorite courses, a perfect mix of challenging but still fair, with fantastic conditioning and a tremendous hole variety -- not to mention some of the best views of the Worcester Hills and Mt. Wachusett around.  I cannot recommend this course enough.

Although it was an awfully good year for courses played, there will still be some carry-overs this year.  Before we get to the this, let's review the rules again:

• "Must plays" for the year (or the next 5 years) cannot be courses that I played last year.
• "Must plays" for this year should all be fairly local so that it's realistic; must plays for the 5-year list can be a bit more extended.
• I want to be somewhat pragmatic.

MUST PLAYS FOR 2013

1. The Springfield Country Club, West Springfield, MA.  As I mentioned last year, my friend Kevin (of Asher Invitational fame) joined here last year, but unfortunately I didn't get a chance to play.  That will change this year as I have been invited to their member-guest, a 5 day (!) affair.  Can't wait.

2. Shaker Hills Country Club, Harvard, MA.  Shaker has long been one of my favorite courses (and still features my favorite hole, the par-5 16th).  That's why it was shocking to hear that the course was shuttered and sold at auction last spring.  Fortunately, the buyers didn't decide to turn it into a movie production studio, and instead have been at work renovating the course and clubhouse.  I'm looking forward to getting back there this year to see the updates.

3. Taconic Golf Club, Williamstown, MA.  Golf.com ranks it as the #39 on their "Top 100 You Can Play" rankings; Golf Digest has it ranked as the #19 course overall in the state of Massachusetts.  I was fortunate enough to play there back when I was about 18 years old, and really I was too naive to appreciate it then.  But, lo and behold, when I looked at the schedule for The TOUR of Greater Boston, there it was, marked down for October 7.  I'll be there.

4. Acushnet River Valley Golf Course, Acushnet, MA.  Another carry-over from last year's list.  It's too good a course to go ignored, and now that I know there's a pro-level Titleist fitting facility nearby it's a no-brainer -- I think it's time for new wedges.

5. The Black, Bethpage State Park, Farmington, NY.  In the words of Jack Shephard, "We have to go back!"

MUST PLAYS FOR 2013-2017

1. Chambers Bay, University Place, WA.  I've said it once, and I'll say it again -- this course is #1 on the list until I play it.  It seems like some of the buzz for the course has died down recently, but I'm sure it will pick up again soon enough with the U.S. Open coming in 2015.  My post-Scotland obsession with links-style golf has only enhanced my desire to get there.  It will happen.

2. Cabot Links, Inverness, NS.  The only new course on the 5-year list this time around; this one is my newest obsession.  Not only is it Scottish-links, its in Nova Scotia ("New Scotland").  And the early reviews are spectacular.  Unfortunately, it turns out to be more difficult to get to than I had hoped (apparently there no longer is a Boston-to-Halifax ferry), but I'm convinced that the wife can be swayed to go away for another "unique" vacation.  

3. Pine Barrens, World Woods Golf Club, Brooksville, FL.  Too close to my parents' house to not get there.  It's only a matter of time.

4. Ballyowen Golf Course, Hamburg, NJ.  This is the 3rd course on this list which advertises itself as being born "in the Scottish tradition" or to actually have a picture of a man wearing a kilt playing the bagpipes on its website.  I may actually have a problem.

5. Boston Golf Club, Hingham, MA.  The reviews (ranked in the 70s on both the "top 100" courses lists).  The secrecy.  The proximity.  This: 

If anybody knows a way to get on there (or any members who want to invite me), just let me know!

The Short Game Statistic

This, by the way, might as well be a mathematics thesis paper.  I'm not saying I'd get a good grade, I'm just saying I spent a lot of time on it, and the math is complicated.  If that's not interesting to you, I suggest you stop reading now.

For those of you still here, I brought up a statistic I simply referred to as "short game" in my last post.  What I've attempted to quantify in one number is how effective were the shots taken within 20 yards of the green and on the putting surface for a given round.  It is essentially the complement to my previously described "shot efficiency" statistic.  I played around with a number of different formulas over the past several years, but last year I settled on one that I think works well.

First, a few assumptions:
1. If we are striving for even par, then using PGA tour data as a gold standard upon which "perfect golf" should be measured is reasonable.
2. Putting itself is an adequate measure of total short game (both putting and chipping/pitch shots/bunker play) since the closer your short game shots get you to the hole, the fewer putts you should have.

The PGA Tour uses "strokes gained-putting" as their #1 putting efficiency stat.  The basis for this is the work of Mark Broadie, a researcher at Columbia University, who determined the average number of putts for a PGA Tour pro from any given 1st-putt distance (see his paper here).  For example, the average PGA pro takes 1.5 putts to get in from 8 feet; 1.87 putts from 20 feet; and 2.06 putts from 40 feet.  Strokes gained-putting simply measures an individual player against the expected average for each of their putts; so if Phil Mickelson drains a 20 footer, he "gains" 0.87 putts against the average for that hole.  The total gains (and losses) for each hole are added up to provide a score for the round, and a player's average per-round score is their strokes gained-putting number for the year.  Last year Brandt Snedeker led the tour with 0.860 strokes gained-putting per round.

Now utilizing that statistic requires a precise measurement of the first putt distance for each hole; something that is not practical for the amateur golfer playing without the benefit of ShotLink technology.  So what we need to determine is a way to estimate the average 1st putt distance for a given round; and that brings us to the complicated math.

Mark Broadie has done some other research that comes in handy here, including the average distance from the hole for PGA pros on shots from 20-60 yards and 100-150 yards.  Using that, I determined a best-fit equation to describe the theoretical average 1st putt length:

P = (A/1.9259)^(1/1.2159)

where P = 1st putt length, and A = approach distance

Next, though, I needed to come up with an average approach shot distance (outside 20 yards) for a given round to plug in as "A" in the equation above.  This required several steps:
1. First I calculated the average distance per shot for the round -- this is essentially the same as the shot efficiency, except I eliminated penalty shots since those ultimately do not impact the short game play.  So avg distance per shot = course yardage / (score - putts - penalties).
2. Next I calculate the average rating per hole for the course; simply course rating / 18.
3. Then I calculate the percentage of the total distance that should be attributable to tee shots.  Based on the USGA standard to determine course rating, that factor is 2.39 (in other words, the tee shot is worth 2.39 course rating points).  So if the average rating per hole is 4.0 (i.e. a course with a rating of 72), then the percentage of the rating attributed to tee shots is 2.39/4 = 60%.
4. The inverse of that number (in the example, then, we are talking 40%) is the percentage of total distance that *should* be accounted for in approach shots to the green.  I multiply that number by the average shot distance calculated in step 1 to get a theoretical average approach shot distance.

In sum:

A = (1-T)*(PISE)

where A = avg approach shot distance, T = avg tee shot distance, and PISE = penalty-independent shot efficiency

So now we have our dependent variable to plug into the first equation above, thus determining the average 1st putt length for a given round.  One last step, though -- we need to compare that to the expected putts from that distance based on the PGA averages; rather than looking at a chart for each putting distance, I determined the equation for putts to hole from any distance (2-90 feet) as:

PP = 0.3759ln(P) + 0.6933

where PP = predicted putts, and P = avg 1st putt length

Confused yet?  Let's look at an example.  Last August, playing in the TOUR of Greater Boston Club Championship at Red Tail Golf Club, I shot 83 with 30 putts.  The course rating is 71.9, played over 6698 yards.  I had 1 penalty shot.  So:

A = (1-(2.39/[71.9/18]))*(6698/[83-30-1])

A = (1-.598)*(128.8)

A = (0.402)*(167.45) = 51.78 yards per average approach shot

and

P = (51.78/1.9259)^(1/1.2159)

P = 14.96 feet average 1st putt distance

Based on the probable putts equation, the average tour pro will take about 1.704 putts to get in from that distance; over 18 holes that comes out to 30.672 putts/round.  I took 30 putts, so my calculated strokes gained-putting for the round is +0.672.

Lastly, I wanted to put this on a similar scale to the shot efficiency data.  So I arbitrarily set the expected putts value at 75% (since that's the "average"), and 5 putts saved as 100% and 5 putts lost as 50% -- essentially assigned letter grades of "C" "A" and "F" to those scores respectively.  Using that scale, a score of +0.672 yields a short game score of 0.784.

________________________________________

Extremely complicated, I know; but once you have the formulas plugged into an Excel file, all you need is 5 data points from the round -- yardage, course rating, score, putts, and penalty shots.  And here's the thing: it works.  The numbers match up well with my subjective impressions of how well I chipped and putted for most of the rounds that I've measured.  My best short game round last year was in mid-August at Butter Brook, where I shot 85 but had just 27 putts -- 3.213 strokes gained-putting, for a short game score of 0.911.  One of my worst was during the first round of the Asher Invitational at Fox Hopyard, a round in which I hit 69% of fairways and 50% of greens, but shot only 89 after 37 putts (including four 3-putts) for an abysmal 6.145 strokes lost-putting; short game score 0.443.  Sometimes you just know when something is right, and this one feels that way.