Golf Club Atlas
GolfClubAtlas.com => Golf Course Architecture Discussion Group => Topic started by: abmack on May 11, 2015, 03:06:56 PM
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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 (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.
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Andrew: I look forward to reading this with interest. In the meantime, say hello to the good folks over at Fresh Pond.
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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 (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.
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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.
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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.
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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 (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.
::) ::)
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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.
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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
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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.
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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?
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Is this some kind of joke?
Obviously! Nice parody.
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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.
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Even when Sergio needed birdie on the last hole of the playoff yesterday he didn't hit driver.
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Andrew,
Perhaps you could explain how this paper is relevant to your economic degree?
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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.
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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.
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"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. ;D
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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.
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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" ...
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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
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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.
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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.
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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.
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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.
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"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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"the strict goal of the game
playing the course in as few strokes as possible."
Kinda goes against the definition of game. If playing for entertainment, using the fewest strokes is hardly entertaining, as it is primarily frustrating. Only an "irrational" player would entertain himself with such a frustrating enterprise.
If playing for competition the goal is to win, or come as near to winning as possible. I think you are going to have to come up with a psychological model instead of an economical model for that goal.
;D
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8) for your consideration
Footnote 1: Amateur golf only.. versus rational behavior is questionable; a competitive behavior am as base case and a Saturday am player are different cases
Tee-to-green shots don’t seem to address hazards around the green, especially with the variance of shot making involved, both x & y directions at play; the same distance shot can give widely different results depending on angles and slopes from good or bad drive locations. I would think lateral variability would be greater issue than distance with most am players
Need the variability of tee and approach shots’ dispersion addressed, e.g., a 3 degree directional error means a lot more at 250 yards than 85, which is simply lumped into “accuracy’ better with shorter clubs and on fairway or on rough next shot.
Homo econimicus plays every Saturday… Few things in nature or human activity are linear, need to use natural log or exponential distributions to address variability that may lead to other cases experienced over time than a golfer with perfect control.
I didn’t directly follow by your nomenclature and equations that the probabilities of linked serial events, i.e., drive and approach shots are really getting multiplied together to give an overall probability of a given score.
State a null hypothesis and at least define some t-testing of probabilities of difference in mean scores at nominal confidence levels like p.84, p.95, or p.99
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"In order to minimize
his score, the player chooses which club to hit given his distance to the target."
If he is playing strategically wouldn't his choice also include hit high, hit low, hit left to right, hit right to left, etc.
Can you even address strategic play, without more choices than "distance to the target"?
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Andrew, I read your paper.
Maybe it is the engineer in me, but I am perplexed by many choices and assumptions you make.
You make a simplification on club distance by assuming that every club can be manipulated to hit +/-5 yards, but wedges are infinitely adjustable downward. This is obviously not a correct assumption. Every club is infinitely adjustable downward, not just wedges. People choose to hit a lower club instead because the success rate is higher with full shots.
I am not sure really that assumption is even required, you can just say that there are 10 yards difference between each club and your aim is to hit the target within 10 yards (since your paper does not care about putting anyway) and make an assumption that anything below minimum wedge distance is same as the minimum wedge distance.
I also don't understand the choice of discussing elevation and wind direction's effect on shot distance but never discussing that in your body. You should just make an assumption that the course is perfectly flat and there is no wind. You are making a lot of assumptions to simplify your work, you might as well go all the way and eliminate some variables.
You can simplify further by making the error as a function of the shot distance (dispersion increases with the length), not per club. This would simplify your equations and make it more realistic.
I am also confused by your declaration that the choice of hitting a long shot and laying up ultimately does not matter since the probability of hitting the green is the same. Just because the probability of hitting rough + probability of hitting green = 1 does not mean that layup + long iron (from fairway) = long drive + short iron (from rough). And this seems to be the whole point of your paper, and I am just having a hard time agreeing with this.
This is not something that is just theoretical. A real life data is available today from PGA's Shot Link. You can verify your claim easily by checking the data to see if your hypothesis is reasonable.
I personally think it would be better to figure out, based on PGA Shot Link data, whether or not most pro's make correct strategic decision from most situations.
Let me know if I am making some erroneous reading of your paper.
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New title.
"Rationalizing Bomb and Gouge in Tour Golf"
;D
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An obviously astute, Harvard-educated young man comes on here and opens his work to critique from the treehouse. Treehouse--mostly--responds not by engaging intellectually with the academic content of the paper, but by tearing down the premise of the paper itself. Color me surprised. ::)
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Andrew, you seem to have put a lot of work into this so well done.
The only comment I can pass on is a comment from Jack Nicklaus, maybe the most rational/analytical golfer of all time, who said something like "If I reckon I can pull off a shot 8 times out of 10 I'll take it on. If my chances are less than 8/10, I'll find another option."
Although whilst 8/10 may be a valid anticipated success ratio at JN's personal skill level, for others a lower ratio will apply, even down to 1/10! But then again not all players are as rational/analytical as JN!
atb
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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.
David,
Thank you for your comment, this research is purely academic for the time being. I'm not really making any suggestions as to how golfers should behave. Frankly, I do not think that many golfers would want to play golf the way I suggest... How boring! My goal is to use this framework and future extensions to quantitatively identify/fail to identify whether great golf holes present strategy choices which have common relative risks... among other things. As I said in the paper developing these framework models is a necessary first step in order to examine these kinds of questions.
Andrew
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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.
Jeff,
What makes you think that pros behave completely rationally, by this I mean that their behavior is not score-minimizing... As John has pointed out, they do not (see Phil Mickelson).
I think the process of advancing the ball from the tee to the green is linear. There are more subtleties but I do not see a problem with summing up expected shot outcomes.
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Andrew,
Perhaps you could explain how this paper is relevant to your economic degree?
Congratulations on finding an interesting thesis concept. Have fun. If that's possible for economists.
There are a lot of economists who study golf, though often as a side interest, eg. Mark Brodie. The scope of questions which fall under the umbrella of economics is rapidly expanding. Especially for behavioral economics.
See:
Pope, D.G. and M.E. Schweitzer. 2011. "Is Tiger Woods Risk Averse? Persistent Bias in the Face of Experience, Competition, and High Stakes," American Economic Review, 101(1): 129-157.
Free Download:
http://whartonsportsbiz.org/documents/research/IsTigerWoodsLossAverse.pdf (http://whartonsportsbiz.org/documents/research/IsTigerWoodsLossAverse.pdf)
I have already written a thesis which was an empirical investigation of an entirely different subject.
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I mentioned Phil not for his style of play but more for his legendary deep thought.
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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.
Patrick,
1. If you read my paper more carefully, you'll see that I do distinguish between good strategy and bad outcomes. I assume that regardless
of the strategy that a player chooses, there is a probability of a bad outcome. These outcomes are associated with lower probabilities of
hitting a good second shot.
2. I agree with you that architects often mislead or deceive the player, causing them to make bad decisions. How they do this is something I seek to identify and quantify, eventually.
Andrew
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I have just read through the paper and it is an interesting approach to formalizing something we discuss a lot on this site. Even if a rigorous mathematical approach does not yield a complete answer to this question, the fact that Andrew attempted this is worthwhile. Very little innovation or progress comes without failure, so it is great to see a new approach even if it has some shortcomings.
Secondly, a few have noted that the assumptions may not be realistic, but that doesn't bother me since my training is in economics too. As a Harvard educated economist, I'm assuming you have read Friedman's article on methodology (Methodology of Positive Economics, I think) and we know that assumptions are good if they help the model deliver accurate results even if the assumptions are not totally accurate. I think the criticism is good and assumptions should be improved where possible, but it is a known short coming and probably not immediately solvable.
Finally, the part of the paper most lacking to me is the discussion at the end. How can the findings of the paper practically inform a player? You mentioned that most golf you see is "irrational" from a score perspective and I agree with that, but how can this be improved? I know you paper is looking at amateur golf, but discussing the role of strategy for a bomb and gouge player vs. a short strategic tour player could be interesting. Basically, I would try to add more context to how golf is actually played. A lot of the comments here seem to hint that golf is more art than math, which is probably true, so including more of the artistic and feel aspect of the game into the discussion section while blending it with your interesting mathematical approach would yield a more complete picture.
Regardless of where this research goes, approaching the game from an unorthodox position is good food for thought.
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I have just read through the paper and it is an interesting approach to formalizing something we discuss a lot on this site. Even if a rigorous mathematical approach does not yield a complete answer to this question, the fact that Andrew attempted this is worthwhile. Very little innovation or progress comes without failure, so it is great to see a new approach even if it has some shortcomings.
Secondly, a few have noted that the assumptions may not be realistic, but that doesn't bother me since my training is in economics too. As a Harvard educated economist, I'm assuming you have read Friedman's article on methodology (Methodology of Positive Economics, I think) and we know that assumptions are good if they help the model deliver accurate results even if the assumptions are not totally accurate. I think the criticism is good and assumptions should be improved where possible, but it is a known short coming and probably not immediately solvable.
Finally, the part of the paper most lacking to me is the discussion at the end. How can the findings of the paper practically inform a player? You mentioned that most golf you see is "irrational" from a score perspective and I agree with that, but how can this be improved? I know you paper is looking at amateur golf, but discussing the role of strategy for a bomb and gouge player vs. a short strategic tour player could be interesting. Basically, I would try to add more context to how golf is actually played. A lot of the comments here seem to hint that golf is more art than math, which is probably true, so including more of the artistic and feel aspect of the game into the discussion section while blending it with your interesting mathematical approach would yield a more complete picture.
Regardless of where this research goes, approaching the game from an unorthodox position is good food for thought.
Joe,
Thank you for excellent and insightful comments. I posted my paper on GCA hoping for exactly this kind of feedback. Very soon, I will post a response to these and other criticisms. Mainly defending my assumptions. I will also lay out how I intend to improve upon this paper. I hope you will let me know what you think when I finish and post.
Much appreciated,
Andrew
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Andrew --
It is no fault of yours that I couldn't make myself finish your paper. I got my fill of academic papers 40 years ago -- and am not enough of a mathematician to make any useful critiques of your thinking.
But you asked for feedback, and I (an editor) have this one minuscule (correctly spelled!) thing to tell you:
Periods and commas go INSIDE quotation marks.
Thanks.
Dan
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Andrew --
It is no fault of yours that I couldn't make myself finish your paper. I got my fill of academic papers 40 years ago -- and am not enough of a mathematician to make any useful critiques of your thinking.
But you asked for feedback, and I (an editor) have this one minuscule (correctly spelled!) thing to tell you:
Periods and commas go INSIDE quotation marks.
Thanks.
Dan
The discretionary rule in The King's English is the way to go.
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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.
I certainly will not hold my breath as this "research" unfolds.
I have taken many courses in Economics, and what a joke they were. Trying to quantify everything with endless graphs and equations. Trying to make what is often irrational and random, rational and predictable. Amazing to me that there are people in education and in government who have never managed a business, never had to hire or fire or manage the complexities of a work force, having to deal with endless regs, a ridiculous tax system, and staying one step above the competition. And these are the people making the decisions for us and using our economy and real lives as a playground to test their silly and conflicting theories. The biggest joke is trying to make this all scientific. Just like you are trying to introduce science and equations to how golf decisions are made. It does not work anywhere but the glass menagerie of higher education. The truth of the matter is, that when it comes to economic forecasting, choosing alternatives , picking a portfolio , or whatever, studies have shown elementary school kids to outperform these so-called experts with the charts, graphs, and formulas.
This research study is certainly benign, have at it, whatever gives you pleasure in this short precious life is great. So , I wish you the best of luck with this and do applaud your apparent passion. That comment you made about this being how economists view the world, that is very scary, more scary than the scariest of horror movies. Like most studies in the social "Sciences" it tries to make the unquantifiable quantifiable. As someone that has managed hundreds of people over the years, and run small businesses, and worked as an employee for large employerss, just when all is running seemingly smooth, you get a curve ball thrown. The more you think you got it all figured out, the more you learn how little you do know. You have got to rely on instinct, and be flexible, and know which resources to call in, you don't have the luxury in the real world of ust falling back on a graph, equation, or economic model . We could certainly say the samething for golf, that is the attraction, the endless curve balls. The real economy is one curve ball after the next, and you survive based on how you cope with these curve balls, Graphs, equations, and economic models won't do a bit of good, except in some classroom or thesis paper. There are too many variables, too many unknowns, the assumptions are subject to endless debate, and most of all, human behavior can be irrational and unpredictable, humans beings and the economy do not work like economist's graphs and equations do, that is just a lot of smokescreen that gives the intellectual community a sense of superiority, and keeps a lot of people in the glass towers employed. And while the glass tower dwellers are drawing their next graph, or preparing their next economic model, the rest of us have to deal with the real world and in spite off all the stupidity and obstacles thrown at us, trying to make it work. We make it work not because of all the self absorbed, pseudo intellectual economic thinkers out there, we do it in spite of them.
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Geeze, Eric. Lighten up! The guy is a student and tried to incorporate golf and golf course architecture into a class assignment...
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8)
"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."
isn't this statement from the department of redundancy department? doesn't it need to be clarified or reworked to separate purpose and objectives... after all, there are rational and irrational strategies which are equally effective.
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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.
I certainly will not hold my breath as this "research" unfolds.
I have taken many courses in Economics, and what a joke they were. Trying to quantify everything with endless graphs and equations. Trying to make what is often irrational and random, rational and predictable. Amazing to me that there are people in education and in government who have never managed a business, never had to hire or fire or manage the complexities of a work force, having to deal with endless regs, a ridiculous tax system, and staying one step above the competition. And these are the people making the decisions for us and using our economy and real lives as a playground to test their silly and conflicting theories. The biggest joke is trying to make this all scientific. Just like you are trying to introduce science and equations to how golf decisions are made. It does not work anywhere but the glass menagerie of higher education. The truth of the matter is, that when it comes to economic forecasting, choosing alternatives , picking a portfolio , or whatever, studies have shown elementary school kids to outperform these so-called experts with the charts, graphs, and formulas.
This research study is certainly benign, have at it, whatever gives you pleasure in this short precious life is great. So , I wish you the best of luck with this and do applaud your apparent passion. That comment you made about this being how economists view the world, that is very scary, more scary than the scariest of horror movies. Like most studies in the social "Sciences" it tries to make the unquantifiable quantifiable. As someone that has managed hundreds of people over the years, and run small businesses, and worked as an employee for large employerss, just when all is running seemingly smooth, you get a curve ball thrown. The more you think you got it all figured out, the more you learn how little you do know. You have got to rely on instinct, and be flexible, and know which resources to call in, you don't have the luxury in the real world of ust falling back on a graph, equation, or economic model . We could certainly say the samething for golf, that is the attraction, the endless curve balls. The real economy is one curve ball after the next, and you survive based on how you cope with these curve balls, Graphs, equations, and economic models won't do a bit of good, except in some classroom or thesis paper. There are too many variables, too many unknowns, the assumptions are subject to endless debate, and most of all, human behavior can be irrational and unpredictable, humans beings and the economy do not work like economist's graphs and equations do, that is just a lot of smokescreen that gives the intellectual community a sense of superiority, and keeps a lot of people in the glass towers employed. And while the glass tower dwellers are drawing their next graph, or preparing their next economic model, the rest of us have to deal with the real world and in spite off all the stupidity and obstacles thrown at us, trying to make it work. We make it work not because of all the self absorbed, pseudo intellectual economic thinkers out there, we do it in spite of them.
Eric,
This is not a forum for me to defend economics so I won't. You may find it surprisingly but I agree with a lot of what you say. The burdens of the endless regulations and disfunctional tax system certainly have been instituted by people who are disconnected from reality. I would consider who is responsible for this system... I think it's the politicians.
Nevertheless, your objection to the field is duly noted.
-
8)
"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."
isn't this statement from the department of redundancy department? doesn't it need to be clarified or reworked to separate purpose and objectives... after all, there are rational and irrational strategies which are equally effective.
I think he is simply using classic economic terms, and "rational behavior" has a precise meaning:
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.
-
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.
I certainly will not hold my breath as this "research" unfolds.
I have taken many courses in Economics, and what a joke they were. Trying to quantify everything with endless graphs and equations. Trying to make what is often irrational and random, rational and predictable. Amazing to me that there are people in education and in government who have never managed a business, never had to hire or fire or manage the complexities of a work force, having to deal with endless regs, a ridiculous tax system, and staying one step above the competition. And these are the people making the decisions for us and using our economy and real lives as a playground to test their silly and conflicting theories. The biggest joke is trying to make this all scientific. Just like you are trying to introduce science and equations to how golf decisions are made. It does not work anywhere but the glass menagerie of higher education. The truth of the matter is, that when it comes to economic forecasting, choosing alternatives , picking a portfolio , or whatever, studies have shown elementary school kids to outperform these so-called experts with the charts, graphs, and formulas.
This research study is certainly benign, have at it, whatever gives you pleasure in this short precious life is great. So , I wish you the best of luck with this and do applaud your apparent passion. That comment you made about this being how economists view the world, that is very scary, more scary than the scariest of horror movies. Like most studies in the social "Sciences" it tries to make the unquantifiable quantifiable. As someone that has managed hundreds of people over the years, and run small businesses, and worked as an employee for large employerss, just when all is running seemingly smooth, you get a curve ball thrown. The more you think you got it all figured out, the more you learn how little you do know. You have got to rely on instinct, and be flexible, and know which resources to call in, you don't have the luxury in the real world of ust falling back on a graph, equation, or economic model . We could certainly say the samething for golf, that is the attraction, the endless curve balls. The real economy is one curve ball after the next, and you survive based on how you cope with these curve balls, Graphs, equations, and economic models won't do a bit of good, except in some classroom or thesis paper. There are too many variables, too many unknowns, the assumptions are subject to endless debate, and most of all, human behavior can be irrational and unpredictable, humans beings and the economy do not work like economist's graphs and equations do, that is just a lot of smokescreen that gives the intellectual community a sense of superiority, and keeps a lot of people in the glass towers employed. And while the glass tower dwellers are drawing their next graph, or preparing their next economic model, the rest of us have to deal with the real world and in spite off all the stupidity and obstacles thrown at us, trying to make it work. We make it work not because of all the self absorbed, pseudo intellectual economic thinkers out there, we do it in spite of them.
You're a weird dude to come at a kid like this and use his intellectual endeavor as your opportunity to sound off against whatever the hell it is you're sounding off against.
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Andrew,
have not read it yet but there may be situations where not maximizing score is rational. I.e. gamesmanship in a Match.
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The Freakonomics guys are writing a book that sounds very similar to your paper. They've run a couple of data mining days at different courses, but I suspect their results may be seriously flawed as Jud was a participant in one.
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;D Garbage in, garbage out....
-
8)
"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."
isn't this statement from the department of redundancy department? doesn't it need to be clarified or reworked to separate purpose and objectives... after all, there are rational and irrational strategies which are equally effective.
I think he is simply using classic economic terms, and "rational behavior" has a precise meaning:
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.
Bill,
This is spot on. When I talk about behavior as being rational, this is what I mean.
Sorry, I've spent too much time in an economics department. I stupidly assumed that this was understood.
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abmack,
With 64 posts, you are WAY too new to understand that "rational behavior" will be a foreign term to most of the the posters on gca.com. :)
I was an economics major MANY years ago. Amazingly, I remember all the terms. Don't let the treehouse get to you! Enjoy your research, get your degree, and just don't become an economist. :) You'll be fine.
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8) and "utility" function appears to be loaded language also that needs to be defined... gas, electric, water, sewer???
sorry i couldn't resist... ::)
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8) and "utility" function appears to be loaded language also that needs to be defined... gas, electric, water???
Of course!
DEFINITION OF 'UTILITY'
1. An economic term referring to the total satisfaction received from consuming a good or service.
A consumer's utility is hard to measure. However, assume that consumers will strive to maximize their utility.
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Hi Andrew,
I'm following along with the thread, and have read about half of the research paper so far.
I was an engineer by training, and like others here, I see the core problem of minimizing score in terms of physics and statistics, and the decision making process as a non-discrete function. Sometimes you aim at the hole, and sometimes you aim two or four or fifteen yards away from the hole, and the number of factors that determine the aiming decision are many. If I think of anything else, I'll chime in. I'll finish reading first.
John