When Confronted with An Explanation that is Based on Mathematics

[Benman]

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I do believe intuition has some value.


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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.

[Paul2432]

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

[Myrtle]

[ 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.

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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]

[MicroBob]

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.

[Mr_J]

"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.

[Malcom Reynolds]

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.

[Toonces]

[ 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.

[Triumph36]

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.

[Mr_J]

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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.

[Mr_J]

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.