Risk-Reward at The Masters: Round 1,2 Statistics -- Plus 2003, 2005, 2007

[Mark Bourgeois]

Eric

Again, it's not simply about the eagles or the birdies, it's about the distribution.  If in 1991 18 eagles were recorded then you have to balance that against the "cost," such as the number of double-bogeys, or bogeys if as you say it played like a par 4.  If nobody scored bogeys, then I agree: the risk-reward was out of whack then and needed to be fixed.

Jeff, as far as 13 goes, it's not doing terribly on the risk-reward front -- certainly not as screwed up as 15.

Lemme take another crack at this.

I. Cumulative play of the par 5s in Round 2
6 eagles = 1.6% of all scores on par 5s
115 birdies = 30.7%
204 pars = 54.5%
35 bogeys = 9.4%
13 double-bogeys = 3.5%
1 triple-bogey = 0.3%

So:
standard deviation of 0.22 strokes (same as R1)
scores within +/- 1 shot of par = 94.7% of all scores
birdies and pars = 85.3% of all scores

The distribution moved a little in the right direction, but statistically speaking there's no change.

II. Cumulative play for R1+R2
8 eagles = 1.1% of all scores on par 5s
241 birdies = 32.1%
412 pars = 54.9%
65 bogeys = 8.7%
22 double-bogeys = 2.9%
2 triple-bogeys = 0.3%

So:
standard deviation of 0.22 strokes
scores within +/- 1 shot of par = 95.7% of all scores
birdies and pars = 87.1% of all scores

And: the pros are scoring roughly 3 double-bogeys for every eagle. More on that below...

III. Cumulative play on par 5s for 2003, 2005, 2007, 2008 (% of total scores on par 5s) (It would be better to compare to pre-"Hoozio" changes but sorry this is all I've got.)

Eagles =                 1.0%,       1.2%,       1.4%,        1.1%
Birdies =                 28.8%,    32.9%,    29.8%,      32.1%
Pars =                     55.9%,     54.4%,     54.3%,     54.9%
Bogeys =               11.6%,      9.4%,       11.9%,     8.7%
Double-bogeys = 2.0%,       1.5%,        1.7%,       2.9%
Triple-bogeys =    0.7%,       0.5%,        0.8%,       0.3%

Frankly, none of these distributions suggest The Masters in the Naughties has been much about risk-reward.

IV. A simple way to compare the distributions is to calculate the number of eagles per double-bogey. Call it the "Risk-Reward Index."
2003 = 0.48
2005 = 0.82
2007 = 0.86
2008 = 0.36

A perfect balance would be 1:1, or 1.0.

So why the complaining with 2007?  Its index rates better than 2003 and 2005 -- although, it needs to be said again, a better comparison would be data from pre-Hoozio.

Not only that, 2007 totaled 18 eagles -- 45 percent more than in 2003 or 2005.

It's not about the total number of eagles!  It's about their distribution across the days of the tournament, their ratio to risk (double-bogeys) -- and their distribution across the holes.

V. Distribution across holes
The problem in a nutshell was 15 -- not the only problem, but by far in 2007 the worst-scoring par 5 on the Risk-Reward Index.  And this "trend" appears to have continued into the 2008 tournament.

Risk-Reward Index, 15th hole
2003 = 0.83
2005 = 1.00
2007 = 0.33 (versus: 2=2.50, 8=1.00, 13=0.82)
2008 = 0.14 (versus: 2=0.00, 8=0.25, 13=0.75)

It will be interesting to see if this trend continues on the weekend. So far the field has scored no eagles on 2 and just 1 on 15.  This out of 188 chances on each hole.

Getting back to 2007, one thing that went wrong (from a "golf theater" perspective) was the field scored only 61 percent of its eagles on the back, versus 73% in 2003 and 86% in 2005.

In fact, half of 2007's eagles came on just one hole: the 13th.  But even that hole fell short of ideal: it scored 0.82 on the Risk-Reward Index.

It paid to lay up on 13 and definitely 15.

Mark

[Pete_Pittock]

Mark,
How do you statisticalize Justin Rose's play at #15 on Friday. He lays up and ends up with a snowman.

[Mark Bourgeois]

Pete

Just count your blessings you don't have him in a Calcutta.

Mark

[Mark Bourgeois]

Mark,
Google 1934 masters.
There's a fascinating article on Golfobserver by Bobby Jones analyzing what happened in 1934 vs. what was intended.
Anecdotally it supports your theory (at least in the case of Horton Smith-the winner)

Jeff

Thanks for that -- I'd never seen it and you're right, it's fascinating!

One thing to keep in mind about the brassie / spoon "comparison" is those players hit to a different green of different firmness / agronomic conditions.

The New York Times said, "The long hitter may go for as long a carry as he wishes and thus reach the green with a long second shot..."

Also, Bob does write at the conclusion of that article, "I think the most deadly, boring holes on a golf course are those prodigious affairs that can be reached with three ordinary shots but never with two excellent ones.  I think a par 5 should always be of the kind that can be played as a great par 4 if the player is man enough to do so.  Holes like this give the big hitter a chance to do his stuff."

Too bad he didn't give us his ideal Risk-Reward Index!

Mark

[Jim Nugent]

Mark is correct.

The sign of a great strategic course, one that tempts players to take risks to obtain lower scores, is a spread of scores at both the high and low ends.

A tightly set up US Open course tends to have scoring bunched around par.

Bob

Does the field birdie or eagle 33% of par 5's at the U.S. Open?  I doubt that.  And that's including all the old-timers at the Masters, who dilute those averages downward, but don't play the Open. 

I wonder also if the spread of scores at ANGC was wider in the 1990's than now.  Without having exact numbers in front of me, seems like during the 1990's scores overall were lower.  Did that simply mean the spread, or distribution, shifted lower? 

Stated another way, perhaps the course just played easier in the 1990's.  There wasn't more risk, but there was a lot more reward -- because many players could hit short irons/wedges into so many holes.  Even some par 5's.  More low scores, fewer high ones.  Would like to see the actual numbers.   

The trees and/or rough and/or new tees are really taking a toll on driving distances.  Tiger is averaging under 290.  Back in 1997, with the old ball, the old equipment, didn't he average well over 300?

Clubhouse leader Immelman's scorecard so far looks rather Zach Johnson-esque. His 8-under total has been achieved by being -1 on the Par 5's (a single birdie, on 15 yesterday)...

Actually the difference between Immelman so far this year and Zach last year is night and day.  Johnson played the par 5's in 11 under.  If Immelman keeps on his current pace, he will play them in 2 under. 

 

[Mark Bourgeois]

Jim

I can't speak for anyone else but I certainly don't think the 1990s necessarily are the benchmark.  For me the benchmark is creating ideal risk-reward holes.

Your comment about 33% birdies or eagles gave me two thoughts:
1. No, of course the Open doesn't have that many eagles (or par 5s!) but their purpose on the par 5s is dramatically different from the purpose at ANGC --  at least, the purpose Bob Jones stated.  The USGA wants its par 5s to be true three-shotters.  ANGC par 5s are not supposed to be that -- well, that's not what Jones wanted.  Check out the quote from the 1934 article in a prior post.  Also, here's what Jones wrote about 15 in 1959:

The fairway of this hole is quite wide. The short rough on the left is far removed from the line of play, and there is no demarcation on the right between the fairway of the 15th and that of the 17th. The tee shot may be hit almost anywhere with safety.

It is nevertheless of considerable importance that the line of play be along the crest of the hill, a little to the right of the center of the fairway. This fairway, being on high ground, usually provides more run to the ball than most other holes of the course. It is also more exposed to the effect of any wind which may be present. Two tees, front and back are provided so that the length may be adjusted within wide limits according to playing conditions.

The design of the green causes it to be most receptive to a second shot played from the right center of the fairway. The greater depth of the putting surface is on the right side. The left side is quite shallow, considering the length of the second shot, and the most severe hazards lie here. A ball played over the green on this side may very well run down into the pond at the 16th hole. It is usually the better part of wisdom to play the second for the main body of the green even though the hole may be cut on the left side.

Under almost any conceivable conditions, the second shot to this hole suggests precarious possibilities. With the wind against, the player must decide whether his power and the state of the game warrant an effort to reach. With a following wind he may have to consider whether he will be able to hold the green, even though it be well within reach.

Billy Joe Patton's magnificent bid to be the first amateur to win the Masters ended when he tried to reach this green from the rough on the left. The ball finished in the pond. The resulting 6 was one too many. Had he played safely for a 5, he would have tied with Snead and Hogan.

A few takeaways there.  First, clearly under normal conditions he expected a fair number of golfers to go for it in two. And more importantly from a risk-reward perspective, if you look at the graphic of the hole from 1959, virtually no trees on either side exist.  He wanted golfers to make the decision.  He didn't want trees to make the decision.  Second, the reward is birdie / eagle; the risk is bogey.

Third, the powers that be had no easy choices to preserve risk-reward on this hole: only 20 yards have been added in 50 years.  They can't go back any farther.  But trees and rough -- it's just so unimaginative, and screws up the risk-reward equation by stripping the thoughtful kind of decisions from contestants. It doesn't provide the best test of their "temperament."

What about these options (instead of trees and rough):
A. Shrink green dimensions and / or regrade green. Make it more of a fallaway, or sharpen the grade from right to left.  Changing the green complex might be what Jones might have done; he wrote in 1934 and again in 1959 that the way to "stir up" pros was by introducing "subtleties" on the greens and not by lengthening.
B. Regrade slopes around green or position water behind green.
C. Regrade fairway to effectively lengthen.

2. On the risk side, are double-bogeys really the right cost for eagles? The more I think about Jones's quotes, the more I think the right offset for reward needs to include some proportion of bogeys in addition to the double bogeys.  I think the risk-reward many of us seem to be thinking about are the second shots on the par 5s: whether to go for it or lay up.  If you go for it and miss into a water hazard, I would think the most-likely outcome is pitch plus two putts.  That's the real risk, yes?

The Risk-Reward Index probably is better expressed as something like: (eagles) / (a percentage of bogeys + double-bogeys)

Arbitrarily choosing 10% as the percentage of bogeys, here's how 15 has scored on the Adjusted Risk-Reward Index (Index rank among par 5s in parentheses):

Year
2003 = 0.58 (1)
2005 = 0.68 (2)
2007 = 0.19 (4)
2008 = 0.12 (2)

Maybe 2007 was just an aberration and 2008 isn't the picture that will develop over the weekend.

On the other hand, here's a benchmark for comparison -- the 13th:
Year
2003 = 0.32 (2)
2005 = 0.79 (1)
2007 = 0.61 (2)
2008 = 0.60 (1 - ugh!)

Mark

[Mark Bourgeois]

Re 15, there's also Kelly Blake Moran's suggestion:



Kelly, as a sane person you're probably not reading this, but it seems like the trees at 3 and 4 are to challenge the drive off the tee; how do they affect the options / decisions available to the competitor?

Can you explain how the hole might play if the trees at 3 and 4 didn't go in?

What if bunkers were put there, of a depth that gave the golfer a chance of going for the green in two, but with significant risk?

Thanks!
Mark

[Phil McDade]

I wonder if this intelligent group of statistics experts would indulge me by reviewing a few more stats and answering a few questions?

First, please review the stats on the following web pages:

http://www.masters.org/en_US/history/records/alltimestats.html

http://www.masters.org/en_US/history/records/eagles.html#most_e_f_tourn

http://www.masters.org/en_US/history/records/scoring.html

What went on in 1974?  Why does that year stand out as having 1) 4 holes with low tournament scoring average records that still stand;  2) Bruce Crampton, a fireballing risk-rewarder iirc, who made the most eagles ever in one tournament by an individual--record still stands;  3) Maurice Bembridge (?) who shot the first-ever 4th round 64 (which by the way has been equaled several times but not since 1988—why?  No juicy risk-reward pin placements on Sunday since 1988 or ?)

Why are Ben Hogan, Nick Faldo, and Jim Furyk among the all-time birdie leaders with 22 birdies each in one tournament?  Because they hit it with precision or because they knew how to take advantage of the risk-reward equation that Augusta USED to offer, and apparently no longer does?

What was going on in the 1950s?  Scoring average highs were set on 10 holes in tournaments in the 50s that still stand!  Did I miss a earlier period in Augusta history when they had rough and trees?  289 was the winning score in ’56 and ’57, just like in ’07 when all the moaners and whiners—I mean learned commentators—said Augusta was irrevocably ruined.

Do you want to go back to the glory days of “roars” like 1991 when 18 “eagles” were scored at 15?  Or will you consider that 15 then was a par 4 masquerading as a par 5 and “eagle” is really a misnomer—shoulda been “birdie.”

I await your learned conclusions on these and any other wisdom you glean from Masters official statistics!

Eric:

My sense is that without knowing two crucial factors involved in scoring -- weather conditions and pin positions -- it's tough to generalize about differences in scoring through the years.

Along those lines, Augusta has always seemed to me to have two interesting characteristics. One, it's a course that under good-to-ideal scoring conditions, is always close to the edge in terms of scoring differential on any given hole. That is, extremely well-struck shots can yield low scores, but slight mishits can be punished by high scores. Unlike, say, a typical US Open par 4 where birdies are rare and pars/bogies are the norm, several holes at Augusta (notably 10, 11, 12, 13, 15, 16) can yield big differentials in scoring in similar conditions, depending on shot execution. Secondly, Augusta's greens seem to be greens that have potential pin positions that, again, can potentially yield big differentials in score. 16 is a notable example -- the traditional Sunday pin position can funnel balls to easy birdie range, but leaving a tee shot on the upper back tier of that green can make a two-putt quite difficult. The greens, because of their slope and Masters-level speed,  seem to have some benign pin positions and easier ones.

Secondly, I noticed the low number of all-time birdies-per-tournament in 2001, the year before the major course changes and lengthening in 2002. I think it was that Masters that led to the significant changes seen today. Remember that Augusta was essentially the same length -- @ 6,900 yards -- for nearly its entire tournament history until the significant lengthening that came about several years ago. Technology certainly accounts for some of the birdie-fests, most of which occured from 1990 on (the four that weren't were four players -- Hogan, Jack, Floyd and Seve -- in their absolute primes of their careers.)

[Mark Bourgeois]

Phil

Your post sent me to take a quick look at the cumulative stats for the par 4s so far in the tournament -- where an interesting risk-reward picture seems to be developing.

The par 4 that's given up the most number of birdies (30) is the 3rd. But this hole -- regarded as the least-changed since inception -- has given up nearly the same number of bogeys (32).

If the Risk-Reward Index for par 4s is the ratio of birdies to bogeys, it has struck a perfect balance.  It has given up the most birdies but in perfect proportion to bogeys.  (It is playing to an average score of 4.0532 -- the par on the card!)  The caveat of course is the tournament's only halfway done and last year the ratio wasn't perfect: 38/54. (Don't know how that compares with other par 4s in 2007, though.)

In contrast to the 3rd, the other par 4s so far have displayed a significantly different Risk-Reward Index, by dead-reckoning it looks in the neighborhood of 0.33.  Not every (or even most?) par 4s should have balance -- the 3rd counts these days as a short par 4, right?  Still, the 10th for example has given up 9 birdies against 51 bogeys, a Risk-Reward Index of 0.18.  1,4 and 7 appear to have similar ratios.

The numbers for the 7th, as a former bookend short 4 to the 3rd, in particular are striking for the contrast to that perfectly-balanced hole: 14 birdies, 57 bogeys.

Mark

[JESII]

Todays green speeds are the number 1 reason guys would be less likely to go for #13 with a fairway wood than you might have seen origianlly...at least using Jones' words as a baseline for the aggressive player reaching with a spoon...

Miss the gree just long and you're trying not to chip it into the creek...

[Jim Nugent]

Todays green speeds are the number 1 reason guys would be less likely to go for #13 with a fairway wood than you might have seen origianlly...at least using Jones' words as a baseline for the aggressive player reaching with a spoon...

Miss the gree just long and you're trying not to chip it into the creek...

Sully, as Tiger proved a few years ago, even hit the #13 green long, and you may be trying not to putt it into the creek...

[JESII]

Good point...

[Phil McDade]

Mark:

The 3rd is one of my favorite holes at Augusta -- highly under-rated, in part because it's not often shown on TV. I think it helped ruin Tiger's chances for a recent Masters, because it tempted him into a drive that led to poor 2nd-shot position. Looks to be ne of the few risk-reward par 4s left at Augusta, perhaps?

[Mark Bourgeois]

I remember that. I think it was important to Mickelson's victory in 2004. I've watched groups go through and although the viewing on the green end isn't great - credit the fantastic complex for that - the pros must approach it much like a man trying to sneak past his boss early Friday afternoon.

Mark

[Phil McDade]

Mark:

I think there are also some interesting risk-reward stats with some of the par 3s, which might indicate some interesting and tempting pin positions that are near risky areas to miss. Holes 6, 12, and 16 have a pretty even mix of birdies to bogeys (6 -- 32 birdes, 46 bogeys; 12 -- 36 and 26; 16 -- 34 and 31). Of course, 12 and 16, yielding more birdies than the front-nine par 3s, also yield far more doubles and others, presumably due to water-bound tee shots. The front-nine par 3s have little variance -- all but a few scores are birdies, pars or bogies. Hole 4 just seems like a very tough hole -- more than a 5-to-1 ratio re. birdies to bogeys.

[Mark Bourgeois]

4 I think has always been a brute and I read somewhere is supposed to be a real veterans hole owing to the wind patterns.

See Romero on 16? Good example of your point.

Mark

[Phil McDade]

I've always liked that pin position on 16 that they have today. You almost never see anyone who ends up down by the pond get their putts to reach the hole -- that must really be uphill! It's a great pin position because it looks like a truly exact shot provides a relatively easy run at birdie, but left or right brings on trouble, or little chance of a birdie.

[Jim Nugent]

I've always liked that pin position on 16 that they have today. You almost never see anyone who ends up down by the pond get their putts to reach the hole -- that must really be uphill! It's a great pin position because it looks like a truly exact shot provides a relatively easy run at birdie, but left or right brings on trouble, or little chance of a birdie.

Wonder two things about that pin:

1.  How big is the landing area, to get the ball within 10 feet of the hole?

2.  What is the average score there, compared to other pin positions at #16? 

[Mark Bourgeois]

Jim

Re: 2.  What is the average score there, compared to other pin positions at #16?

The distribution of scoring by round this year is as follows:
Round 1
Aces = 1%
Birdies = 16%
Pars = 65%
Bogeys = 15%
Doubles = 2%

Round 2
Aces = 0%
Birdies = 17%
Pars = 63%
Bogeys = 14%
Doubles = 5%

Round 3
Aces = 0%
Birdies = 9%
Pars = 71%
Bogeys = 11%
Doubles = 9%

It looks like more played for par.  But for those who didn't, the risk-reward calibration in rounds 1 and 2 was birdie vs. bogey but the Round 3 pin changed the distribution and for the better: the birdies balanced not the bogeys but the double-bogeys.  We saw why with Romero and Mickelson. 

Great risk-reward.  People talk about 2-or-20 / make-or-break type par 3s, here it is at the highest level of the game. Cool, huh?

Mark

[Doug Siebert]

Why are you guys comparing eagles to doubles on the par 5s?  To get a double bogey on 13 or 15 requires more than one error, so doubles aren't due to a failed attempt at the green that ends up in the water.  If you do that you have a pitch to attempt to get an up and down par, or a bogey if your pitch is less than accurate.  You have to screw up that pitch and put it in the water a second time, three putt, or miss the green and fail to get up and down to receive a double bogey.

I think the realistically the spread is eagles to bogies, those doubles and triples are the result of multiple errors on the par 5s, and creating multiple errors is a problem in the players' heads, not a single risk/reward decision.

[jeffwarne]

Doug,
exactly.
the only legitimate analysis of risk reward would be to see how many went for it in two, were successful, and how it affected their score.

If everybody went for it, as they did at 13 in the  90's, it's not risk reward, it's penal architecture.

The doubles come when the guy laid up and chunked his wedge.

[Mark Bourgeois]

Doug and Jeff

Good points.  Answer on eagles / doubles is: just to make a simple representation of the distribution of outcomes. Please see point #2 in reply #30.  I was going to run more numbers but then watched the third round on TiVo and lost interest. Don't need a weatherman to know which way the wind blows -- this whole exercise is moot, isn't it?

But anyway, seeing how many went for two vs didn't and outcomes would be best, yes.  But the overall distribution of scores should provide a representation, too. 

A par 5 with "risk-rewardness" should show more eagles, bogeys and double bogeys, one with less would show a greater number of birdies and pars (at least in the Masters context -- US Open's another story).  I think you still need to count doubles, as an aggressive tee shot is part of the strategy of going for it.  Players who fail on that count either suffer an immediate penalty, as Els did on 13 a few years back by hitting in the creek on 13, or a delayed penalty, as Tiger did in trying that huge cut last year on 15 (although I think he salvaged bogey). If you're planning on laying up you'll play conservatively off the tee.

Here's the comparison of the 13th to the 15th:
Round 1
Birdie + par = 90%, 90%
Eagle+bogey+double = 10%, 10%

Round 2
Birdie + par = 73%, 88%
Eagle+bogey+double = 27%, 11%

Round 3
Birdie + par = 78%, 91%
Eagle+bogey+double = 22%, 9%

Round 4
Birdie + par = 80%, 87%
Eagle+bogey+double = 18%, 13%

Cumulative
Birdie + par = 81%, 89%
Eagle+bogey+double = 19%, 10%

As an aside on the folly of using averages to assess a hole, the 15th played easier than the 13th going by scoring averages (and relative to par the 15th was ranked 18th) -- but the 13th gave up 94% more bogeys and 22% more double-bogeys.

Mark

[Mark Bourgeois]

King Billy:

Keep pitching those bomb-balls in until the town of Hoozio lies bearen flat.

Wm. Butler Cabin Yeats

[jeffwarne]

Doug,
exactly.
the only legitimate analysis of risk reward would be to see how many went for it in two, were successful, and how it affected their score.

If everybody went for it, as they did at 13 in the  90's, it's not risk reward, it's penal architecture.

The doubles come when the guy laid up and chunked his wedge.

So have the roars of the last few days (stay tuned for Sunday) vindicated the "changes" at Augusta that wee so bashed here the last 2 years?
I.e.  did it turn out that once Augusta got some good(normal) April weather the course plays just as exciting as ever and even highlights the play of a few cagey veterans

[TEPaul]

By the way, have any of you guys seen this program on The Golf Channel called "Top Ten?" Who in the world is that hostess Lauren Thompson and who is dressing her---Victoria's Secret?

If some of those rich and lascivious tour pros get a look at her she better run like Hell.