When Confronted with An Explanation that is Based on Mathematics
 

First off I'm not a mathematics expert especially when compared to many on this site. However, I know that many, many real world situations and phenomona can be modeled mathematically. I'm fairly certain that most people eschew explanations that are based on mathematical models. I'm not sure why this is. I was explaining some basic portfolio theory concepts mentioning mathematical concepts the other day and the reaction I got was a typical one. It went something like, " I don't know about the math you're mentioning but common sense tells me this ..." in a slightly condescending way. I wasn't offended at all but I wonder why people seem to believe that their common sense is a superior way to analyze complex problems. Of course my viewpoint is subjective so maybe others don't agree but that's my take. I suppose the short answer is that mathematics is an abstract, difficult subjet but what I was referring to wasn't sophisticated mathematics at all and in fact I would expect anyone who had a grasp of high school math to understand. I guess what I'm saying is that I've found that even explanations that are based on relatively unsophisticated mathematical concepts are eschewed. I'm not complaining I'm just curious if anyone else shares my viewpoint and has some insight.

Re: When Confronted with An Explanation that is Based on Mathematics
 

I'll start by saying that I agree completely with you. Any explanation that cannot withstand mathematical scrutiny is of dubious value. That said, I think there a couple of things going on here. First, many people are untrained in the scientific method. They simply rely too heavily on anecdotal evidence and gut feeling. They "know what they saw" and to challenge them is considered a personal affront.

One example of this is the "hot hand" in basketball. Statistical analysis has shown that this is a myth. That is a particular player has exactly the same chance of making his next shot whether he has missed his last five shots or made his last five shots. Every discussion I have seen of this topic has resulted in vigorous rebuttal from basketball players. The rebuttal is always based on personal experience and never on the actual statistical analysis.

I do believe intuition has some value. If a mathematical model is not consistent with intuition then the assumptions of the model should be looked at. All mathematical models are based on observations and assumptions.

Paul

Re: When Confronted with An Explanation that is Based on Mathematics
 

I think that many people who are bad at math, or just don't like it or trust it, tend to rely on "common sense". In order to sway people with a mathematical argument you have to dumb it down quite a bit, and that isn't worth doing most of the time.

The best response to your questioner is probably something like: "Why does that work?" or "Could you elaborate on that?". Feel them out to see where exactly they are missing the point, to make it easier to explain to them.

You probably give people too much credit in having a grasp of high-school mathematics.

Re: When Confronted with An Explanation that is Based on Mathematics
 

Many words ended up on the cutting room floor for this response.

Suffice it to say, I hate the fact that most people do not put any thought into their decisions. People like the one you mentioned probably feels threatened by math, for whatever reason, and finds it easier to attack with emotional arguments than to think about the situation in a regimented way.

(In some cases, there are overriding considerations that make the math/logic that is being discussed moot. Usually though in these cases, the person with the big picture will let you know why your analyses are pointless, e.g. "It doesn't matter how much money we could save outsourcing new Navy construction to another country because that compromises national security.")

Re: When Confronted with An Explanation that is Based on Mathematics
 

You can't stick all the time with the math either, because pure math will get you nonsensical results like .9999999 = 1.0, in that old puzzle of:

1/9 = .111111111111111111111111111111111
x9
9/9 = .999999999999999999999999999999999

9/9 = 1.0

1.0 = .999999999999999999999999999999999

But, back to the point, the problem is that people are mathematically illiterate in many respects and explaining things in such a fashion will only get glassy-eyed looks of ignorance.

Such is life.


Barron Vangor Toth
www.BarronVangorToth.com

Re: When Confronted with An Explanation that is Based on Mathematics
 

[ QUOTE ]
One example of this is the "hot hand" in basketball. Statistical analysis has shown that this is a myth. That is a particular player has exactly the same chance of making his next shot whether he has missed his last five shots or made his last five shots. Every discussion I have seen of this topic has resulted in vigorous rebuttal from basketball players. The rebuttal is always based on personal experience and never on the actual statistical analysis.

[/ QUOTE ]

Not really on the subject of mathamatical debating, but I disagree with your belief that the "hot hand", as you call it, is entirely mythical. There is such a thing as a player getting into his rhytem. It probably has to do with muscle memory or something similar. I agree that it's not because he is just "on fire tonight" or some other made up explaination, but science and human anatomy can prove that muscle memory is very real, and could very well affect the performance of a basketball player.

Re: When Confronted with An Explanation that is Based on Mathematics
 

Intuition has its place, and mathematical analyses have their place. Neither is the absolutely correct way to make a decision. Paul's example of the 'hot hand' myth I feel is incorrect; how is mathematical analysis going to take into account all of the factors that go into making a shot? Of course it isn't going to do that, it only looks at the results. Such things have little basis when we're looking at one event. The theory of probability and statistical analysis are based on ceteris paribus (all else being equal). Since we know that isn't the case in the "hot hand" example, our intuitions of human psychology may do a hell of a lot better than statistical analysis.

Human intuition is obviously far more flawed than statistical analysis and people make far more errors when they use intuition incorrectly. But it still has its place.

Re: When Confronted with An Explanation that is Based on Mathematics
 

0.1111111... infinitely repated is equal to 1/9.
0.9999999... infinitely repeated is equal to one.
0.1111111 (not infinitely repeated) is not equal to 1/9. It is a little less than 1/9.

Re: When Confronted with An Explanation that is Based on Mathematics
 

I think a lot of people don't really understand math, beyond very simple arithmetic (and some not even that), always struggled with math, and therefore don't really trust math. For example, it amazes me that many people can't understand why roulette is a -EV game. This is not a good thing for society in general, but it is a good thing if you want to play winning poker, because many people would rather trust their gut feeling that that gutshot is going to hit this time than realise that they are not going to make enough money when it does hit to pay for the times it doesn't hit.

Re: When Confronted with An Explanation that is Based on Mathematics
 

[ QUOTE ]
I guess what I'm saying is that I've found that even explanations that are based on relatively unsophisticated mathematical concepts are eschewed.

[/ QUOTE ] If people are not familiar with things that rely heavily on % or statistics, they probably don't realize that Math is right more often then their hunch. And if they still don't want to accept that, then they are stubborn idiots.

Re: When Confronted with An Explanation that is Based on Mathematics
 

Because we're naturally inclined to learn experientially, and building models is like the opposite way to learn. It's why bad poker players make terrible plays for years, like not value betting the river enough in HE. They remember the times they get raised/checkraised rather than thinking mathematically about what exactly they're risking and how often they have to be right.

Also, explaining modern portfolio theory to someone who is disinclined to want to listen is the most frustrating thing on earth.

Re: When Confronted with An Explanation that is Based on Mathematics
 

[ QUOTE ]
You can't stick all the time with the math either, because pure math will get you nonsensical results like .9999999 = 1.0, in that old puzzle of:

1/9 = .111111111111111111111111111111111
x9
9/9 = .999999999999999999999999999999999

9/9 = 1.0

1.0 = .999999999999999999999999999999999

But, back to the point, the problem is that people are mathematically illiterate in many respects and explaining things in such a fashion will only get glassy-eyed looks of ignorance.

Such is life.


Barron Vangor Toth
www.BarronVangorToth.com

[/ QUOTE ]

0.9999... (repeating forever) does (exactly) equal 1.

It's just another way of expressing the same number.

It's the same way 2/5 = 4/10. Just because they don't look the same, doesn't mean they aren't the same.

I really don't feel like typing out the mathematical proof (mainly because I can't exactly remember it), but they are EXACTLY the same number. "0.9999..." is just a ugly result of the decimal number system.


Edit: If that doesn't convince you, look at it from this perspective.

Two numbers, A and B, are said to be different when tehre exists some X such that, A < X < B.

Said more simple, two numbers are the same if there's a number between them (incidently, in the real number system if there is one number, there's an infinte number).

It should be easy to see that no such number exists in the case of .999... and 1, and therefore they're the same number.

Re: When Confronted with An Explanation that is Based on Mathematics
 

Ockhams Razor is why.

Re: When Confronted with An Explanation that is Based on Mathematics
 

Lots of people dont like thinking and maths requires thinking. Lots of other people are scared of maths.

or maybe he was just deeply uninterested in portfolio theory.

chez

Re: When Confronted with An Explanation that is Based on Mathematics
 

It's not just those that are 'generally' poor at math though.
Some who are, in fact, good in certain areas of math still fail miserably in other areas and continue to trust their own flawed instincts or self-delusional observations.


I know a guy who is quite good at general math. Can multiply a couple of 4-digit numbers in his head (which is something I can't do)....but he swears that roulette is beatable by varying one's bet and by noticing certain 'patterns'. he was convinced that 32 was more likely to fall if the previous spin was 23....and vice-versa. and that if black fell 3x in a row it was better than 50% to fall again on the next spin.
Again, if you asked him "Hey jerry. What's 7629 X 2564?" he would give you the correct answer.


My sister's boyfriend took several math and statistics courses in college....and swears that he has a winning system for craps because he always leaves after he has won $100 or lost $50...whichever happens first.
"see?? that way when I win I am winning more than when I lose."
Again, he got A's in his college courses. But he uses this 'system' because some pit-boss friend of his in LV taught it to him.
I am not quite articulate enough to entirely convince him that the number of times he loses only $50 will happen more than the times he wins $100 to cause net-losses in the long-run.
but I did start to get somewhere by explaining that "on each roll...if you are at a 1% disadvantage...then you remain at a 1% disadvantage no matter how long you play."



More to your original point however....when I dealt BJ (for 8 mths) I very rarely had a player who actually played with the correct basic-strategy (some would come close...but then fail to double their soft-18 or split their 9's or some other kind of play that most non-expert players don't know to do).
Many of these players would stand on their 14-16 vs. 7-10 and say "I don't care what the book says. Hitting that just doesn't work for me."
If someone else told them that the book is correct and it was developed by math people smarter than us who plugged millions of hands into a computer to determine what plays would give the player the best chance then they would argue "But that's just stupid. I don't care what the math says or what 'the book' says. You can just tell that if you hit a 15 against a 7 you are going to lose. If you can't see that then you're just stupid. Why on earth would you play 'by the book' when the book is so obviously wrong?"
I have dealt to higher-income professionals (doctors, lawyers, etc) who subscribed to this logic.


I have often wondered why I am smart enough to know that the MIT math-types are better for BJ strategy even on plays that normally would be counter-intuitive to my own instincts. I have the ability to ignore my instincts and make the play the the 'experts' tell me is correct because I know they are smarter than me.

I agree that it's interesting stuff though.

Re: When Confronted with An Explanation that is Based on Mathematics
 

[ QUOTE ]
[ QUOTE ]
One example of this is the "hot hand" in basketball. Statistical analysis has shown that this is a myth. That is a particular player has exactly the same chance of making his next shot whether he has missed his last five shots or made his last five shots. Every discussion I have seen of this topic has resulted in vigorous rebuttal from basketball players. The rebuttal is always based on personal experience and never on the actual statistical analysis.

[/ QUOTE ]

Not really on the subject of mathamatical debating, but I disagree with your belief that the "hot hand", as you call it, is entirely mythical. There is such a thing as a player getting into his rhytem. It probably has to do with muscle memory or something similar. I agree that it's not because he is just "on fire tonight" or some other made up explaination, but science and human anatomy can prove that muscle memory is very real, and could very well affect the performance of a basketball player.

[/ QUOTE ]

[ QUOTE ]
Intuition has its place, and mathematical analyses have their place. Neither is the absolutely correct way to make a decision. Paul's example of the 'hot hand' myth I feel is incorrect; how is mathematical analysis going to take into account all of the factors that go into making a shot? Of course it isn't going to do that, it only looks at the results. Such things have little basis when we're looking at one event. The theory of probability and statistical analysis are based on ceteris paribus (all else being equal). Since we know that isn't the case in the "hot hand" example, our intuitions of human psychology may do a hell of a lot better than statistical analysis.

[/ QUOTE ]

I knew when I posted this I would get these kinds of responses. Like I predicted people are rebutting based on personal experience and not refuting the statistical analysis. One of the points of the research is that people can believe things very strongly that simply are not true. I had hoped that poker players would understand the nature of streaks and how they can lead a person to conclusions that do not stand up to mathematical scrutiny.

Just to be clear, this is not my theory. When I first heard it I was incredulous myself. However, this has been studied many times over the last twenty years by professors of mathematics and psychology. The findings have been published and scrutinized. Every single time the finding is the same: there is no such thing as a hot hand. It is purely a psychological phenomonon.

A google search reveals dozens of links on the subject. Here are three:

More recent hot hand study
clustering web site with section on hot hands
web site devoted to hot hand research

To Adios (original poster):

You wrote:

[ QUOTE ]
I'm fairly certain that most people eschew explanations that are based on mathematical models. . . . , " I don't know about the math you're mentioning but common sense tells me this ..."

[/ QUOTE ]

It looks like you were right on.

Paul

Re: When Confronted with An Explanation that is Based on Mathematics
 

Did the statistical analysis take into account every factor? That is to say, the time of the game, the reaction of the other players, and so on? Of course not. So you've proven your point, but I hardly think that it's a myth if everyone believes it. That is, while it may be a myth, the psychological implications of belief in such a myth are sure to impact the on-court play.

That said, would you give the last shot to the player who'd been missing his shots all night? Of course not. There's probably something wrong with him. Statistical analysis would say he's no more likely to miss that shot than he is any other shot, but that is clearly incorrect in this case.

Analysis and the scientific method look great the wider our perspective is. When we try to take into account all the factors, analysis and the scientific method break down. They do a hell of a lot better than intuition but they are highly fallible, especially to those capable of making serious errors in judgment.

This is made evident in No Limit Hold 'Em. Sometimes, players are forced to make decisions based on extremely unlikely holdings for the opponent. Statistically, it is incredibly unlikely that a player is holding AA when we are holding say, two queens. But we are forced by his betting to make decisions based on the now incredibly likely possibility that our opponent is beating us.

My point is, statistical analysis can make plenty of errors, especially when misapplied. I feel that the 'hot hand' myth could easily be misapplied by an 'academic' coach who gives the ball to a guy who obviously doesn't have it that night. I'm simply not ready to worship at the altar of the scientific method. Plus poker players like Doyle Brunson make me think that intuition can do a lot better than analysis in a rare few.

Re: When Confronted with An Explanation that is Based on Mathematics
 

[ QUOTE ]
It's not just those that are 'generally' poor at math though.
Some who are, in fact, good in certain areas of math still fail miserably in other areas and continue to trust their own flawed instincts or self-delusional observations.

[/ QUOTE ]

People have heavily relied upon all their life based on fallacies, myths, biases, and karma to the extent that scientific reasoning is still a disbelief to them.

I have a friend like you who can spit complex calculations as easy and as fast as you and I could punch them into a calculator. However, put him in a poker game and he'll say his favorite hand is 6-9 (for obvious reasons) and he'll always raise with it. This, mathematically and statistically, makes absolutely no sense and is for the most part a definite -EV play.

The nature of gambling takes on one where it leads players into heavy supersitition. This is especially true in most Asian cultures where people consider it extremely bad luck if you tap them on the shoulders or stand too close them when they are gambling.

Casino's use this pyschological tactic well to their advantage. Major casinos contruct and design the game floor to visually mesmerize players. Once players start playing with the bright lights, action and sounds they get semi-hypnotized. Some players will find it hard to get up and leave and the design of the large casinos makes it so that walking out that door is hard and a long walk sometimes.

Sure enough, in most house games where the rules and definitions are fixed it is not possible to beat the games in the long run. Having said that, one should never play them apart from entertainment value purposes. So I guess from that standpoint, it's ok to have some fun and "go with the flow/hot hand" situation. However, failing to realize that the previous result is completely independent and exclusive to the next result is detrimental indeed.

Lawrence

Re: When Confronted with An Explanation that is Based on Mathematics
 

One of the biggest mistakes people who are fairly good at analyzing situations make is failing to commpare it to an alternative.

For instance, I could say "Is good to win $100?" But if I say, the alternative is a 1/5 chance at winning $10,000, its very clear. Identifying that there often is an alternative is something most people overlook.

In the lesser of two evils, most people are reluctant to choose a "bad" choice, even if not acting results in a worse choice. That's exactly what hitting on a 16 is. You will usually lose. But you are going to usually lose anyway.

Re: When Confronted with An Explanation that is Based on Mathematics
 

[ QUOTE ]
Edit: If that doesn't convince you, look at it from this perspective.

Two numbers, A and B, are said to be different when tehre exists some X such that, A < X < B.

Said more simple, two numbers are the same if there's a number between them (incidently, in the real number system if there is one number, there's an infinte number).

[/ QUOTE ]

Thank you for saving me half an hour in a dusty attic looking for half forgotten textbooks!

Re: When Confronted with An Explanation that is Based on Mathematics
 

Poor, poor, poor example talking about basketball or sports in general guys. Your argument is great for a NUMBERS game but the mindset of a player as well as outside conditions influence them on a game by game (and second by second) basis so that their '% of making the next shot' is not always static, but unable to be analyzed so closely due to small sample size of that game (say a player takes 30 shots) versus the larger season/career.

You are overlooking the fact that confidence can win sports competitions. It cannot turn a poker hand into a winner or let you roll well in craps.

Revise the argument so that you are not open to such an easy (intuitive! ha) criticism.

Re: When Confronted with An Explanation that is Based on Mathematics
 

LokiV, I agree, and that's what I was saying in my previous post. But right there in your objection you're showing the flaws of statistical analysis in general.

I think Doyle Brunson's argument about the 'rush' is what we're talking about here. I don't have Super/System on me but as I remember, Brunson is vague about whether or not the 'rush' is something real (that big hands tend to follow on one another, which is a clear fallacy), or whether it is simply perceived to be real (a player tends to be more believable if he's been showing down winners all night).

Anyway, people disagree with statistics mainly because they don't live long enough and don't have good enough memories to see that by and large these things are true. In a game like limit poker, that disbelief is deadly.

Re: When Confronted with An Explanation that is Based on Mathematics
 

Confidence in your ability to influence opponent behaviour can make many a dicy hand never having to go to showdown.

But I don't see what your reply had to do with mine. [img]/images/graemlins/smile.gif[/img]

Re: When Confronted with An Explanation that is Based on Mathematics
 

[ QUOTE ]
I think Doyle Brunson's argument about the 'rush' is what we're talking about here. I don't have Super/System on me but as I remember, Brunson is vague about whether or not the 'rush' is something real (that big hands tend to follow on one another, which is a clear fallacy), or whether it is simply perceived to be real (a player tends to be more believable if he's been showing down winners all night).

[/ QUOTE ]

I think Doyle meant that if you get pocket rockets twice in a row you are much more likely than usual to get a quality hand next deal as well.
But with his personal history I'd be a bit superstitious as well. (Praying, cancer, only winning sessions for almost a year etc.)

Re: When Confronted with An Explanation that is Based on Mathematics
 

re the hot hand:
As a musician, I can tell you reams about muscle memory. It's not a theory-it's a fact. That's what practice is creating.
In young children who study music, as they practice they are actually building nerve pathways. This process becomes much slower as we age, but I think it can still happen (given enough repetion) up to a certain age.
I enjoy watching athletes perform, because I relate to what they are doing physically.
I can ALWAYS tell you if a free throw will go in, simply by watching the player prepare and release his shot. I don't have to see the trajectory of the ball--just the player.
You can tell when they are mentally prepared, and when the physical follow-through is accomplished perfectly--just LOOK at them closely.
They are all talented, and when they "do what they do" the right way--they will sink the shot. They have YEARS of muscle memory at those distances, heights, etc. But you can also see any slight lapse of concentration, physical fatigue, edginess, etc. This will prevent them from sinking the shot.

Re: When Confronted with An Explanation that is Based on Mathematics
 

Attempting to connect performance in sports and provable statistical probabilities in poker is comparing apples to oranges. Anyone who has made a serious study of performance in sports will be able to easily point out the differences. For example.......hitting a baseball.

You may be able to accurately predict a batters’ likely performance (in the long run) based upon his statistical history, but, there are many overriding factors where attempting to predict an individual event (a single upcoming at-bat) would be foolish. Take a career .333 hitter......EVERYTHING BEING EQUAL, he is more than likely going to get a hit in tonight’s game if he gets to the plate three times.........UNLESS........

..........he’s got the flu.....pulled a groin muscle......been run over by a truck........etc. etc.

A players’ ability to play to their historical performance level is determined by a multitude of variables. The many thousands of hours that a hitter spends in the batting cage are about a few critical things. Given that the player possesses the raw ability (strength, hand-to-eye coordination, etc); it’s all about what is commonly referred to as “muscle memory”. Practice does NOT make perfect...........PERFECT practice makes perfect!!

So with respect, I have to disagree with Paul2432’s using his ‘hot hand’ analogy. It is a misapplication of math as it disregards the ‘ceteris paribus’ (all else being equal) rule. Disraeli hit it right on the head......”lies, damned lies....and statistics”.

As far a poker.......a number of posters here have posited their thoughts about how many players favor intuition, ‘common sense’ (theirs), or some other belief based thought process over the certainty of statistical probability. The problem that I see with this is that both intuition and common sense are unique to each individual, and are based mainly upon whatever perspective each person has on the subject being discussed. Perspective, of course, is relative; hence the sometimes wide and differing points of view one encounters.......Religion, anybody??!!

I’m not a math guy, but just because I cannot fathom the complexities of some of the mathematical models that have been proven to be correct is no reason for me to dismiss them, as many appear to be perfectly comfortable doing. As another poster said, I choose to believe those math experts that have done the leg work of proof to a point of acceptability amongst their expert peers. If any of the basic math foundation ‘stuff’ that we use today to formulate basic strategy was incorrect, there would be public, active disagreement and debate amongst the math ‘guys’.

Anyway, to get back to adios’ original post.........My guess is that most people dismiss mathematical model explanations because they don’t trust anything that doesn’t make sense in their own personal universe. This does seem to be a common theme in the history of man, does it not?

This is the Psychology Forum, so I assume that we’re looking for psychologically based explanations as to some of this behavior? Well, hell....I’m likely as good (or bad) an outhouse shrink as the next guy, so for my 2 cents worth I’d say it boils down to two things.........

Open mindedness....Are we willing to constantly challenge our own beliefs and understanding of the world around us in order to increase our knowledge and awareness?

Self-honesty.....Are we willing to be as brutally honest with ourselves as necessary in order to accomplish this?

All we can do is try............

Re: When Confronted with An Explanation that is Based on Mathematics
 

Three obvious explanations:

People who are not good or knwledgeable at math will not accept mathematical models, even simple ones because:

1. There is a tremendous implication regarding themselves, if in fact, it often requires math beyond their ken to explain things. Thus their is a stong psychological defense mechanism to deny it.

2. Those times thay have been shown how math explains things they don't understand it and thus disbelieve that it works as well as it does (when done right).

3. Most mathmeticians who try to model things do a lousy job.

Normative versus Descriptive models of mind processes
 

You want to buy a new car.

And since you are a diligent fellow, you purchase all the trade magazines, google the internet, etc, to identify the best value for your budget range. After a week's thorough research, and scanning over oodles of statistics, opinion polls, experts' polls, etc etc, you have narrowed it down to the best car for you, the Croco 8000 (for example), which combines the best safety, speed, etc, for the price costs that you can afford. Alright! You settle on the Croco 8000 and decide to buy it first thing Saturday morning.

The same evening you are invited to a cocktail party and, you mingle, the issue of your new car comes up. A man you met at the party, and had a long and very enjoyable talk about favourite movie actresses, tells you that the Croco 8000 is an unreliable car. Why, only last week his first cousin had a near fatal accident because the steering wheel locked when making a turn! And the price is a ridiculous theft; it should retail much, much lower.

You are shaken in your conviction. Next morning, you strike off the Croco 8000 from your list and start looking anew.

...What happened here, if you step back and think about it a little, is that you have chosen one man's anecdotal (and possibly not very reliable) testimony against the combined wisdom of experts and the buying public. This, however, is not an atypical scenario *. This is how a lot (if not most) people take decisions!

Although "mathematics" (i.e. probability theory, algebra, game theory, etc) often provides us with the correct choice, we humans do not always (or usually) follow its advice -- for many reasons.

And the people who behave this way (i.e. "irrationally") are NOT just people with mediocre intelligence. David Sklansky speculated elsewhere that around 5% of the people have the ability to get a PhD in Physics, implying that approximately that percent of people have what is commonly termed "the smarts". But a whole bunch of choice experiments conducted with psychologists, economists or statisticians as subjects, have shown that they are no different at all from "common people" in terms of heuristics! (And, sometimes, the self-correction factor of the experiment's subjects is insignificant even after the subjects have been properly trained for the kind of choice they will be presented with.)

Now, is that really "the smarts"? [img]/images/graemlins/cool.gif[/img]

A work is waiting to be written about people's choices in gambling games, and particularly poker, and about the potential for driving (controlling) those choices. Perhaps when I go to jail.


<font color="white"> .</font>


* : The example is lifted from Thaler.

Re: When Confronted with An Explanation that is Based on Mathematics
 

People are just dumb.

Re: When Confronted with An Explanation that is Based on Mathematics
 

Some thoughts on sports and hot-shooter theory:


Hitting a baseball is different than making a basket.

In baseball, you are facing a couple of different pitchers everyday. In this 1-on-1 matchup there are some pitchers who are going to give certain batters fits...and it doesn't have to just be definable like 'left-handed curve-ball specialists'. Some pitchers styles or even psychological approaches (example: "he thinks I'll waste a pitch away with an 0-2 count....and rarely expects me to fire a heater on the inside corner in this situation") can give some batters fits even if the rest of the league is lighting them up for 7 runs a game.

In hoops, you're always shooting at the same hoop. Same height, generally the same types of shots, etc. So it is easier to compare the success rate of a 'hot-shooter' with the streaks one would normally expect to happen for a 50% shooter in a computer simulated game.
Of course, defensive schemes change and players get more intelligent and adjust as well so perhaps it really ISN'T that much different than baseball.
Lebron James is a much better player this year because he is improving his shot-selection. When the opposition tries to double-team him he is getting MUCH better at turning down a bad shooting opportunity and finding an open teammate. This, in turn will give him more good shooting opportunities on later possessions as teams are forced to guard the other scorers.
So....in basketball...it's not JUST about "take the shot. make the shot." It's a bit more complex than that.

I could be a 60% shooter in a series of games against junior-high kids...but if you put me on the floor against a bunch of D-1 players I would be lucky if I could make many shots at all even with an offense specifically designed to make me the premier scorer on the team.

However, I think even I could score a few points in the NBA if I had Michael Jordan or Lebron James or John Stockton trying to dish me the ball.

See?? Change the teammates or change the opposition or just a change in the defense within the course of the game effects the shooting percentages.


Additionally, there are some players who don't do terribly well when there is pressure and others who tend to rise to the occasion MORE when the pressure is greater.

Perhaps this is all within the mathematical norm....but I do believe that some players have a lesser chance of getting a base-hit or making an important basket when the game is on the line simply because of the psychological differences in the situation.

Re: When Confronted with An Explanation that is Based on Mathematics
 

[ QUOTE ]
I do believe intuition has some value.


[/ QUOTE ]

I'm not repelled by mathematics, but I'll ask a counter question. Why is it that mathematically skilled poker players only grudgingly admit the value of intuition and common sense when it comes to poker success. The biggest, most successful poker players in the world are not mathematical geniuses. I read an intereseting article or interview recently with Barry Greenstein, who is a math whiz and a world class player, and he said that math really doesn't hold a candle to people skills in the biggest games. I don't know what Chip Reese has said on the matter, but I doubt he's a math Einstein. Doyle Brunson? Phil Ivey? I'll bet every one of these people makes most of their money off of general poker skill, people skills, hustle, intuation, etc. far more than math. My theory is that math is probably a very interesting field that doesn't appeal to a lot of people. If you do have skills in that area, it's probably a natural tendency to want to overstate it's application to poker because, well, you find it interesting and spend a lot of your time on it.

Re: When Confronted with An Explanation that is Based on Mathematics
 

Math is good at answering questions. It is not so good at knowing what the right question is in the first place.

As Sklansky said, a lot of models just aren't that good. Properly setting up a model is just as much art as science.

In poker the information is incomplete, so you have to constantly make assumptions. Once the assumptions are made you can do the math, but if the assumptions are wrong, you may make the wrong decision.

Paul

Re: When Confronted with An Explanation that is Based on Mathematics
 

[ QUOTE ]
Some thoughts on sports and hot-shooter theory:


Hitting a baseball is different than making a basket.

In baseball, you are facing a couple of different pitchers everyday. In this 1-on-1 matchup there are some pitchers who are going to give certain batters fits...and it doesn't have to just be definable like 'left-handed curve-ball specialists'. Some pitchers styles or even psychological approaches (example: "he thinks I'll waste a pitch away with an 0-2 count....and rarely expects me to fire a heater on the inside corner in this situation") can give some batters fits even if the rest of the league is lighting them up for 7 runs a game.

In hoops, you're always shooting at the same hoop. Same height, generally the same types of shots, etc. So it is easier to compare the success rate of a 'hot-shooter' with the streaks one would normally expect to happen for a 50% shooter in a computer simulated game.
Of course, defensive schemes change and players get more intelligent and adjust as well so perhaps it really ISN'T that much different than baseball.
Lebron James is a much better player this year because he is improving his shot-selection. When the opposition tries to double-team him he is getting MUCH better at turning down a bad shooting opportunity and finding an open teammate. This, in turn will give him more good shooting opportunities on later possessions as teams are forced to guard the other scorers.
So....in basketball...it's not JUST about "take the shot. make the shot." It's a bit more complex than that.

I could be a 60% shooter in a series of games against junior-high kids...but if you put me on the floor against a bunch of D-1 players I would be lucky if I could make many shots at all even with an offense specifically designed to make me the premier scorer on the team.

However, I think even I could score a few points in the NBA if I had Michael Jordan or Lebron James or John Stockton trying to dish me the ball.

See?? Change the teammates or change the opposition or just a change in the defense within the course of the game effects the shooting percentages.


Additionally, there are some players who don't do terribly well when there is pressure and others who tend to rise to the occasion MORE when the pressure is greater.

Perhaps this is all within the mathematical norm....but I do believe that some players have a lesser chance of getting a base-hit or making an important basket when the game is on the line simply because of the psychological differences in the situation.

[/ QUOTE ]

Bob,

Bear with me, as I'm still trying to figure out whether we're in agreement or disagreement!!

LOL [img]/images/graemlins/confused.gif[/img]

Re: When Confronted with An Explanation that is Based on Mathematics
 

I agree with you for the most part with slightly minor differences.

If EVERYTHING else were pretty much equal then I would tend to believe the idea of the 'hot-hand' is just psychological and mostly non-existent.

In bowling, archery and darts the situation for each round is pretty much the same. Although in bowling there are 'better lanes' and 'worse lanes' I guess.

But I submit that the chances of someone rolling a perfect game (12 strikes in a row) is going to be EXACTLY the same as the frequency with which he rolls strikes and the odds of hitting 12 straight.
In other words, if a guy is rolling a perfect game and an announcer said 'This guy is REALLY hot and clearly has the confidence going' or whatever I would tend to believe that idea is mostly hog-wash.
If 70% of his rolls are strikes over his last 200 games then there is a VERY strong likelihood that he will roll 8 or 9 strikes consecutively at some point.



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..........he’s got the flu.....pulled a groin muscle......been run over by a truck........etc. etc.

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This idea does have some merit also. Even though I tend to think that individual match-ups and defenses, etc are more important.

Reminds me of a story of a ball-player I knew who had gotten red-hot...then suddenly had one of the worst batting performances I had ever seen, going 0-for-5 with 5 strikeouts.

Here's what happened. The team was playing the 1st game of a road-trip in a city noted for it's partying.
The manager told him that he had been doing so well that he was giving him ADVANCE notice that he was getting the day off for the next game. so go out and have a good time and don't worry about it because you won't be playing anyway.


So, he went out and partied...and showed-up blitzed....and then the guy who was supposed to play in his place twisted his knee during batting-practice.

Without any other players available he HAD to play again.
So he went 0-for-5 witht the 5 K's.

He informed me that he was seeing 3 balls a good deal of the time and was just trying to swing at the middle-one.

I told him that he evidently should have tried swinging at one on either side....because the middle one was clearly the wrong choice.

Re: When Confronted with An Explanation that is Based on Mathematics
 

"That is a particular player has exactly the same chance of making his next shot whether he has missed his last five shots or made his last five shots."

But doesn't the mental state of a person affect this? Are you saying concertration has no influence on skill?

That's kind of like saying that a player who will definately hit a longterm 20%ROI in $100 sngs has the same likelyhood of placing 1st as usual even if he isn't playing his A-game.

I'm not arguing against mathematics here, just that maybe you need more info to reach a conclusion?

Surely averages are not constant if the the influences change? For your basketball scenario, what about motivation, physical change (the flu, injury, age etc)?

I guess my arguement is that nothing is 100% if the situation is subject to change. e.g. you can't state that a player will always have x% changing (motivation, concerntration, skill, age, health etc etc etc).

To state something as mathematical fact, the factors would have to be constant. eg 2+2 is always 4 since 2 is always worth 2.

Re: When Confronted with An Explanation that is Based on Mathematics
 

Well, this is just a flaw in our representation system. When we choose base 10 to represent numbers, we get anomalies such as 9.999... as just another way to write 10.0. If you choose a different base, you will find different anomalies like this too.

Re: When Confronted with An Explanation that is Based on Mathematics
 

[ QUOTE ]
"That is a particular player has exactly the same chance of making his next shot whether he has missed his last five shots or made his last five shots."

But doesn't the mental state of a person affect this? Are you saying concertration has no influence on skill?

That's kind of like saying that a player who will definately hit a longterm 20%ROI in $100 sngs has the same likelyhood of placing 1st as usual even if he isn't playing his A-game.

I'm not arguing against mathematics here, just that maybe you need more info to reach a conclusion?

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What you are saying is a hypothesis, based on your intuition. The point of the "hot hand" studies mentioned earlier is an attempt to test the hypothesis. It may or may not be true, but you can't just assume it's true cause it would seem to be.

If you didn't read the link, the study I read was an analysis of shots made and missed during the NBA All-Star Game 3-point Shootout. The study included many reasons why the 3-point contest was a good place to get data (it was a difficult shot in a highly competitive situation...the trials occur only a few seconds apart, and there is no external factors like the opponents defending you harder after a set of successful shots).

The net result was that shooters were no more "streaky" than a computer simulation would indicate, and also that after an announcer declaring that a shooter was "HOT!" that he was no more likely to make the next shot than his average would indicate.

Re: When Confronted with An Explanation that is Based on Mathematics
 

I didn't read that particular link, some other link on here was about the Philadelphia 76ers in the early 80s. I think that study 'proving' there is no such thing as a "hot hand" is dubious precisely because it is removed from game conditions. Sure the players are competing, but not in the natural element where one would hope to find the hot hand.

Mathematical modeling makes sense, but again, over the long term is where it makes the most sense. I always thought the Red Sox would never beat the Yankees until they abandoned their mathematical approach to the game. The "Moneyball" strategy is based on getting walks and hitting home runs, and over the long term it is surely better than having players who do not get on base as often and do not hit many home runs. But in the ALCS this year, it was Dave Roberts who stole the key base that allowed the Red Sox to tie and eventually win Game 4. Stolen bases are, according to that philosophy, usually too risky for the reward, so most teams that use this philosophy don't have guys who can steal bases.

Over the short term, correct intuition can win out over mathematics. The problem with math is that it is best used when analyzing one or a few variables. Some things simply don't lend themselves to that.

Re: When Confronted with An Explanation that is Based on Mathematics
 

[ QUOTE ]
The net result was that shooters were no more "streaky" than a computer simulation would indicate, and also that after an announcer declaring that a shooter was "HOT!" that he was no more likely to make the next shot than his average would indicate.

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Well that's a bit different then. Alot of time's when someone is 'hot' or 'cold' or something it's just variance. I thought you guys were talking about the probability of making the shot remaining the same every time he plays.

Variance is influenced by skill as well though. When your've got your A game on, you'll hit more (for whatever you do) so hot and cold streaks exist (in form and out of form), you just can't identify them by judging the results.

Re: When Confronted with An Explanation that is Based on Mathematics
 

Now if the player was interviewed afterwards and said he had 100% concerntration, that he's never felt better etc etc then you could conclude he was hot. That's assuming his statement wasn't influenced by his performance.