[abmack]

I study economics at Harvard University and am also an avid golfer/student of golf course architecture. I prepared this paper, "A Model of Score Minimization and Rational Strategic Behavior in Golf" for a seminar in behavioral economics. I have long contended that there is a lot of room for economic models to be applied to golf. This is the first paper I have written on the subject and I hope to build on it in order to develop a larger body of work.

Abstract:
Previous research on golf focuses on data analysis but no theory exists to explain the findings. This paper represents the first step of a larger research project whose goal is to build formal models which can be used to study the strategic decisions made by golfers. As a starting point on which future papers can build, it seems important to have a model rational choice and perfect information which assumes that the representative golfer’s utility comes only from shooting as low a score as possible. Thus, for each shot that he hits, he will choose, from a number of possible strategies, the one which, ex ante, will produce the lowest expected score. First, I define golf club distances and golf shot error probability using a series of simple equations. Next, I use these in order to examine the choices that the score-minimizing agent will make in different scenarios and under different assumptions. Among other things, my model predicts that the rational golfer will always choose additional yardage over additional accuracy for his tee shots.

Introduction (except):
The goal of this research project is to develop a theoretical framework and the necessary models in order to examine how and why golf course architecture causes amateur golfers  to make irrational strategic decisions, tee-to-green, in the course of a recreational round of golf. In this paper, I define strategic behavior to be irrational if it is inconsistent with a strategy that minimizes expected score.
I would appreciate any constructive feedback on this paper. It can be downloaded here:

http://scholar.harvard.edu/mack/publications/model-score-minimization-and-rational-strategic-behavior-golf

Thank you to Bill Brightly for pointing out the DEFINITION OF 'RATIONAL BEHAVIOR':
A decision-making process that is based on making choices that result in the most optimal level of benefit or utility for the individual. Most conventional economic theories are created and used under the assumption that all individuals taking part in an action/activity are behaving rationally.

[Benjamin Litman]

Andrew: I look forward to reading this with interest. In the meantime, say hello to the good folks over at Fresh Pond.

[Eric Strulowitz]

I study economics at Harvard University and am also an avid golfer/student of golf course architecture. I prepared this paper "A Model of Score Minimization and Rational Strategic Behavior in Golf" for a seminar in behavioral economics. I have long contended that there is a lot of room for economic models to be applied to golf. This is the first paper I have written on the subject and I hope to build on it in order to develop a larger body of work.

Abstract:
This paper represents the first step of a larger research project which aims to study strategic decisions in golf. Given that the goal of the game is to achieve the minimum possible score on a hole or over a round, I argue that the most rational approach to playing golf involves an agent minimizing his expected score on a hole given a choice of strategies. Next, I develop mathematical models of golf club distances and golf shot error probability. I use these in order to examine the choices that the score-minimizing agent will make in different scenarios and under different assumptions. Among other things, my model predicts that the rational golfer will always choose additional yardage over additional accuracy for his tee shots.

Introduction (except):
The goal of this research project is to develop a theoretical framework and the necessary models in order to examine how and why golf course architecture causes amateur golfers  to make irrational strategic decisions, tee-to-green, in the course of a recreational round of golf. In this paper, I define strategic behavior to be irrational if it is inconsistent with a strategy that minimizes expected score.
I would appreciate any constructive feedback on this paper. It can be downloaded here:

https://docs.google.com/file/d/0Bxs9aXAlBkmTRVd5Y2swODFxc1E/edit?usp=docslist_api

Is this some kind of joke?

Address the ball, hit the dang thing,  walk to it and hit the next shot.   Enjoy the scenery, enjoy the company of your friends, and thank the good Lord you have been given the gift of health to play this great game.  That simple!  No mathematical models or theoretical frameworks needed.

If this is the way" intellectuals"  from big name schools look at the world, no wonder the world is in the shape it is.

[abmack]

Eric,

What about tournament play?

During casual rounds, don't you think about course management?

While you may not like this type of approach, I think that as I build on this research, I will be able to identify/quantify what combinations of risks  distinguish great holes.

and yes, this is how economists think about the world.

[David Davis]

Andrew,

I think it's interesting to try to and create a model for something like this. What would be a great addition to this research would be of course the practical applications of your model with for example video analysis backing them up. Applying the model on a few different levels of players in order to effectively teach them to improve their course management skills - thus proving the validity of your model.

Now I didn't read everything in great detail do to lack of time so if you discussed exactly this point which I didn't see off hand, then my apologies. Those were the first thoughts that jumped into my mind.

I do think a complex model like this will be far to difficult for anyone but the most serious of players to utilize effectively.

[JC Jones]

I study economics at Harvard University and am also an avid golfer/student of golf course architecture. I prepared this paper "A Model of Score Minimization and Rational Strategic Behavior in Golf" for a seminar in behavioral economics. I have long contended that there is a lot of room for economic models to be applied to golf. This is the first paper I have written on the subject and I hope to build on it in order to develop a larger body of work.

Abstract:
This paper represents the first step of a larger research project which aims to study strategic decisions in golf. Given that the goal of the game is to achieve the minimum possible score on a hole or over a round, I argue that the most rational approach to playing golf involves an agent minimizing his expected score on a hole given a choice of strategies. Next, I develop mathematical models of golf club distances and golf shot error probability. I use these in order to examine the choices that the score-minimizing agent will make in different scenarios and under different assumptions. Among other things, my model predicts that the rational golfer will always choose additional yardage over additional accuracy for his tee shots.

Introduction (except):
The goal of this research project is to develop a theoretical framework and the necessary models in order to examine how and why golf course architecture causes amateur golfers  to make irrational strategic decisions, tee-to-green, in the course of a recreational round of golf. In this paper, I define strategic behavior to be irrational if it is inconsistent with a strategy that minimizes expected score.
I would appreciate any constructive feedback on this paper. It can be downloaded here:

https://docs.google.com/file/d/0Bxs9aXAlBkmTRVd5Y2swODFxc1E/edit?usp=docslist_api

Is this some kind of joke?

Address the ball, hit the dang thing,  walk to it and hit the next shot.   Enjoy the scenery, enjoy the company of your friends, and thank the good Lord you have been given the gift of health to play this great game.  That simple!  No mathematical models or theoretical frameworks needed.

If this is the way" intellectuals"  from big name schools look at the world, no wonder the world is in the shape it is.

 

[John Kavanaugh]

Infant economics. I would have to question if you play golf more than casually or have studied the professional game at all. Please for your own sake, and for any other serious golfer who may stumble on this trite, contact Phil Mickelson and ask for his input. This would be his cup of tee.

[BCrosby]

Andrew -

I look forward to reading your essay. Interesting topic.

If you care about scoring, golf architecture ought to matter to you. The intersection of the two has been the theme (in one form or another) of many threads over the years here at GCA. Tom Doak, Pat Mucci and others have had lots to say on the topic. You might try to dig up some of those old threads by way of the crack GCA search function.

Your essay may cover this, but the issues you take on were a frequent topic of some of the best writing about golf architecture during the Golden Age, albeit they approached it in a much more narrative way. It is something they cared deeply about.

I am always surprised that there there are active participants on a site about golf architecture who seem to have missed some of those basic aspects of the history of the discipline they purport to find so interesting. That's forgivable, however. Less forgivable is when they go the extra mile to belittle attempts by a student to discuss topics important to the discipline in a new, different way.

After reading your piece, I will get back with comments/questions if that is ok.

Thanks for posting. Ignore the trolls.

Bob

[John Kavanaugh]

Bob,

Read it yourself before you call people trolls. The math could have been beautiful instead of this over simplistic connect the dots observation. When Robin Williams is referenced at the very start you have to question the seriousness of the paper.

[Kyle Harris]

I am not sure how you are going to bridge the gap between strategic intent of the golfer's play, and the strategic result of the golfer's play. I understand you'll have some variable for shot error, but I don't quite understand why you would assume the golfer would pick additional distance over additional accuracy off the tee every time, especially on the holes within reach of a tee shot.

Suppose a golfer intends to use Strategy A for one hole, but due to a missed shot he ends up in position to use Strategy R. From Strategy R's position he then employs an equally effective strategy for holing the ball as Strategy A. The way I understand things, you model would either miss this outcome completely or determine it to be completely equal.

"Two bad shots and one really good shot still makes three"

-Walter Hagen(?)

I also don't understand how you will measure and account for golfer preference. For example, I much prefer when a bailout area is either short or long of the target, and have no trouble playing over trouble knowing that I have ample space behind. Your model does not seem to account for golfer preference in this manner. One golfer could be as effective as twenty other golfers consistently playing a different strategy. Would your model "go with the majority" despite the conflicting variable of golfer abilities/tactics?

[Carl Johnson]

Is this some kind of joke?

Obviously!  Nice parody.

[Jeff_Brauer]

I read it. Will have to read again before making serious comment.

That said, snarky comments are easy enough....what will you be tackling next? An easier subject like "Understanding women?"

Seriously, my first take away is that the decision process is so far from linear (and as you posit, logical) that many more factors would have to plug into any equation.

I have picked the brains of many tour pros, and found the level of logical thinking (that they can explain verbally anyway) varies. I expect the level would vary more on lesser levels of play.

Also to be considered is how they feel on any given day.  Talking with Lanny Wadkins many years ago, asking how he would pay a hole, his response was "If I was feelling good, I would rope a draw down the speed slot and go for another fifty yards. If not so good, I would probably hit a conservative cut to the middle of the fairway."

How do you account for gut feel in any statistical analysis?  Game situation (down two with two to play, etc.)

Honest Question, because I do like the approach. I don't see 32 pages as being much more than a summary or a sub topic if you really got into it.  However, I will read it again, because I liked where it was going, even with those questions in mymind.

[John Kavanaugh]

Even when Sergio needed birdie on the last hole of the playoff yesterday he didn't hit driver.

[Mark Pavy]

Andrew,

Perhaps you could explain how this paper is relevant to your economic degree?

[abmack]

Infant economics. I would have to question if you play golf more than casually or have studied the professional game at all. Please for your own sake, and for any other serious golfer who may stumble on this trite, contact Phil Mickelson and ask for his input. This would be his cup of tee.

Bob,
Read it yourself before you call people trolls. The math could have been beautiful instead of this over simplistic connect the dots observation. When Robin Williams is referenced at the very start you have to question the seriousness of the paper.

John,

I've played all my life and I'm a 6 handicap.

Though I address some of you concerns in the content, I'll repeat... This paper is not meant to describe actual golf behavior but rather that of "homo economicus" a fully "rational" golfer, who, I believe, would be focused entirely on minimizing his expected score. In future work, I plan to develop preference/utility functions to describe strategic behavior so as to capture actual golf behavior. The paper which I have posted is not a final treatise on golf. Instead, it is the first step towards developing a theoretical framework of how golfers make decisions.

Please keep in mind the following:
(a)   I submitted this paper for a seminar and I am looking for feedback... there is a lot that I have to improve on.
(b)   You are correct that my math is not particularly sophisticated. Extensions will use an approach called "dynamic programming".
(c)   Economists/students of economics have senses of humor, too. The majority of my readers are non-golfers
      and Robin Williams's description of the game is funny and not entirely disconnected from the truth.

[Bill Brightly]

I have not read it but I hear Mark Broadie's "Every Shot Counts" is very good. Seems to me he did a lot of the statistical analysis that you are interested in. Perhaps that is worth reading as background information.

[Bill_McBride]

"Economists...have senses of humor too."   Oh yeah, then why do they call it "the dismal science?"

Actually I learned an economist joke while studying economics at UC Santa Barbara.  "It would be great to have a one armed economist."   Why?  "Because he could never say, 'But on the other hand.'"

Behavioral economics is actually a great way to study strategic decisions, not strategy, on the golf course, but there are at least a million, probably many millions, of variables, from handicap to weather to conditions of competition etc etc forever. 

Congratulations on finding an interesting thesis concept.  Have fun.  If that's possible for economists.   

[Michael Felton]

One thing to watch out for is that situation matters a great deal in what is the optimal strategy. For example, there are situations where a double bogey and a bogey and a par have the same net impact on the player. Only a birdie results in a different impact. A player who is a shot out of the lead playing the final hole who is 5 clear of 3rd place is going to play a hole wildly differently from a different player in a different tournament who is leading by 2. Neither player may want to minimise his expected score. The first guy wants to maximise his chances of making birdie to the detriment of all else, while the second player wants to minimise his chances of making double.

Further, players on the web.com tour have to win to make serious progress. Players on the PGA Tour do well if they just finish in the money every week. Thus, the web.com players have a much more "let it all hang out" attitude and if they miss three cuts and win a tournament because that's the way the cards fell, then great. PGA Tour players play a much more conservative game as a general rule I think. Obviously there are exceptions to that and the top end PGA tour folks play differently again.

It's an interesting idea and I would be curious to see what you come up with. I would second Bill Brightly's suggestion to read Mark Broadie's book. It has a lot of data that should help you determine what is the optimal strategy in any given situation for a given skill level.

[Steve Lang]

Even when Sergio needed birdie on the last hole of the playoff yesterday he didn't hit driver.

I believe there was a famous Hogan quote to the same effect; when asked why he didn't hit driver, his reply: " I didn't have to" ...

[Jason Topp]

Andrew - how does this approach vary from the strokes gained method used by Mark Brodie? 

Also - this shot link data could be very valuable for your research.  I am not certain how one gets access but I do believe academic institutions have access.  http://www.pgatour.com/stats/academicdata/institutions.html

[Patrick_Mucci]

Eric,

What about tournament play?

During casual rounds, don't you think about course management?

AB,

A problem you face is the inability to identify and differentiate a good decision from a bad outcome.

I've made thousands upon thousands of good decisions that resulted in bad outcomes.

I've also made bad decisions that produced exceptionally good results.

While you may not like this type of approach, I think that as I build on this research, I will be able to identify/quantify what combinations of risks  distinguish great holes.

The body doesn't always obey the mind.
Put another way, "The best laid plans of......"

Often, the architect misleads or deceives the golfer, causing them to make bad decisions.

Then, there are those golfers who make nothing but bad decisions.

Why should that golfer determine the architectural value of a hole ?



and yes, this is how economists think about the world.

[Joe Zucker]

One of the largest handicaps of economics (and any study where experiments are not possible) is the inability to effectively control for all variables like many have noted, but that doesn't mean we can't learn something.  A rational golfer will attempt to minimize his expected score from any given point, but this strategy may or may not yield the best score on one particular playing.  But it is the best on average.

Great courses do the best job of getting the golfer to make irrational decisions.  They are tempting and lure us into hitting shots that are not the best percentage play.  Sometimes being risky pays off if you get lucky, other times the percentage play (Zach Johnson laying up on every par 5 when he won at Augusta), unfortunately the we don't have the counter-factual easily available.

I would love to run an experiment on a course by playing a 460 hole as a par 4 one day then a par 5 the next and watch how the strategy and scores change.  That might be as close as you could get to a valid experiment on a course.

[Garland Bayley]

After reading the first sentence or two, I would suggest you don't refer to golfer decisions as irrational. Ill-advised, perhaps, but not irrational.

Sometimes you just want to hit the shot for the thrill of it, not because it is rational, or irrational.

[Garland Bayley]

Why does a player have to carry 14 clubs for varying distance? Many pros will tell you that you need to be able to hit the same club accurately to different distances. Perhaps two of the clubs are a long and a short putter. Perhaps two are an 8 iron, and a 15 wood, same distance, different flight.

[Garland Bayley]

"I establish expected score minimization as the foundational standard

model of rational behavior."

There you go with rational behavior again, when you are really speaking of score optimization.

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