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Wednesday, April 7th, 2010 | ISSN 1556-5696

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Historical Ghost Investigations Part I: Kimo / Therapy

Scientific Paranormal Investigation (cover)

Coming soon … Radford’s new book

Ghost investigations often feature in television shows and other media. Typically, these amount to people wandering around at night with EMF detectors, talking into the darkness and jumping at shadows and noises.

But how does one do a scientific paranormal investigation? On this first half of a two-part MonsterTalk, the hosts review two past ghost investigations (Ben Radford’s “Kimo Theater Ghost” and Dr. Karen Stollznow’s “Waverly Hills Sanatorium” investigations) and discuss some of the techniques that can help solve such cases. What steps are common to this type of research? Learn more this week on MonsterTalk.


In this week’s eSkeptic, Andrew Bernardin discusses the tendency to find meaning in random patterns. In particular, he discusses sports talk notions such as the “hot hand” and being “in the zone.” Bernardin endeavors to deconstruct the zone and plunge the hot hand in a bucket of ice water. This article appeared in Skeptic magazine, volume 11, number 2.

Dr. Andrew Bernardin is a writer, lecturer, and adjunct professor of psychology at Daytona Beach Community College. He enjoys basketball and tennis and other sports that involve both skill and chance. He lives in Florida with his mixed-doubles partner (a.k.a. his wife).


illustration by saim79 found at http://www.sxc.hu/photo/1006624

The Tea Leaves of Sports Talk
Finding Meaning in Random Sequences

by Dr. Andrew Bernardin

ALTHOUGH I ENJOY PLAYING BASKETBALL, I cannot claim to have ever experienced a “hot hand.” Luke-warm, maybe. Nor have I ever found myself “in the zone.” Even if equipped with a G.P.S. and a topological map, I don’t know if I could even locate the zone. Perhaps because of this, I will endeavor to deconstruct the zone and plunge the hot hand in a bucket of ice water.

The non-phenomenon of basketball’s hot hand has been addressed elsewhere (see Michael Shermer’s review of the book, Intuition: Its Powers and Perils, in Vol. 10, No. 1 of Skeptic magazine). In brief, the findings indicate that a player who has hit a number of shots, and is thus considered hot, is no more likely to hit the next shot than his or her overall shooting percentage would predict.

So there’s no hot hand. Is this a big deal? I think so. The type of superstitious thinking behind the hot hand operates far beyond the basketball court. And although it may provide entertainment, when unchecked it can lead us seriously astray.

Half a decade ago, tennis champion Goran Ivanisevic played at Wimbledon. That year he went on a winning streak. He advanced further and further toward the finals. Goran was one of the top players in the world, so this wasn’t all that surprising. Nonetheless, Goran didn’t want to jinx himself. So, game after game, he wore the same hat, which he did not bother to launder. Maybe he was aware of research showing that detergent can wash away benevolent spirits, positive vibrations, and quantum luck tunnels. Why Goran believed his hat was more instrumental to his good play than, say, his underwear, I don’t know. With each match the hat got dirtier and sweatier and, no doubt, smellier. Was Goran’s hat responsible for his advancing in the tournament? I’m sure Adidas, Nike, or whichever company had their logo on it, wished this were so.

With the help of his hat, Goran made it to the finals. Also making it to the finals was the world rated number one Goliath of Wimbledons, Pete Sampras. Goran continued to play well in the finals, but his hat was apparently insufficiently powerful to overcome Sampras’ dominating service game.

Superstitious behavior, whether on a tennis court, basketball court, football field, or golf course, is relatively easy to recognize. Everyone can plainly see, for example, a baseball player making a sign of the cross before getting into the batter’s box (in the name of the father, the son, and Babe Ruth, help me send the ball into the leftfield bleachers). Another form of sports superstition, finding meaning in random sequences, has a broader following than the quirky rituals and good luck charms of individual players. It permeates the talk of broadcasters, athletes, and fans; it infiltrates the minds of those drawn to games of all types.

Superstitious behavior has been called irrational. Which it is. Yet while many people consider irrationality to be the consequence of faulty logic, much of it can be attributed to a straightforward problem of information misuse and/or neglect. When we are being rational, we properly weigh information to come to some conclusion or decision. Irrationality can thus be seen as the result of one or a number of the following: too little information, biased selection of information, poor quality information, and the improper weighing of information.

Backspin-doctoring Sports

One day in early 2003, I became aware of my own tendency to think irrationally in the domain of sports. I had played basketball and performed poorly. Many more of my shots found the outside of the rim than the inside of the net. I lingered on the court, trying to diagnose what had gone wrong. Why was my shooting “off?” Was I giving the ball enough backspin? I put up a shot with more backspin, and swish. Ah-hah. I took three more shots and hit all three. So that was it. I wasn’t putting enough backspin on the ball. This was the hopeful conclusion I came to after hitting four shots in four attempts. I headed to the shower enthused, imagining that my play would be forever improved.

Fortunately, I am a skeptic. That is why in the following weeks I began to test my conclusion. Over a number of sessions I took 800 free throws (shots from the penalty line): 400 without concentrating on anything other than trying to get the ball through the hoop, and another 400 while concentrating on giving the ball backspin. I chose 400 because I considered that number sufficiently large to rule out the influence of what some would call luck but what I think of as a non-representative sequence or “turn of events.” Because I am not a mathematician, and perhaps because my brain lacks an adequate level of serotonin, I wanted to err, if I did, on the side of too many trials of what I consider to be a pleasingly repetitive behavior.

The results: I hit 278 of the 400 “regular” shots, or 69.5%. Of the “backspin” shots, I hit 267 of 400, or 66.8%. Evidently, adding more backspin to my shooting was not going to transform my game.

What had caused me to come to the faulty conclusion that additional backspin was the difference between poor shooting and good? Too little information. There is not enough data contained in only four trials to develop any sound conclusions. And herein lies the key to superstition in sports: humans have the habit of bringing a quick-draw, deterministic mindset to probabilistic phenomena.

With a deterministic event, there is a strict relation between cause and effect. If I hold a coin in my hand and drop it, the coin will fall to the ground. Each and every time I drop the coin it falls to the ground. Because the relation is deterministic, I can accurately predict the outcome. A probabilistic event, on the other hand, entails a relation between cause(s) and effect that is not one to one. There is, instead, a probability that a particular outcome will follow. In the case of the coin, the effect of it landing heads up cannot be strictly determined. I can only give the probability that it will land heads up: 50%. Try as I might, I cannot determine the outcome of the drop. As importantly — and central to the point — I also cannot, in hindsight, ascribe causal reasoning as to why the outcome was one way or the other. The coin didn’t land tails-up because it wanted to, or because I’m unlucky, or because I was leaning on my left foot. The coin simply landed tails-up and that’s all I can say about it. As a human I may be wired to find a simple reason for everything, but when it comes to probabilistic events, I must keep that tendency in check. If I don’t, I will end up talking gibberish.

Because there isn’t a one-to-one correspondence between cause and effect with probabilistic events, it becomes necessary to gather a lot of information. For instance, imagine you are visiting a foreign planet and you want to know whether a balloon filled with oxygen gas will rise or sink in the windless atmosphere. In this case, you would only have to release the balloon a few times to determine the answer. After a limited number of trials you could predict what would happen. And you could offer a simple explanation as to why it did happen — something about the difference between the weight of the oxygen molecules in the balloon and those in the surrounding atmosphere. In this scenario, the balloon falling or rising would be a deterministic event. You could accurately predict what would happen. You could also offer a straightforward explanation for what had happened.

Suppose you have established that the balloon sinks. Whether or not it will pop upon hitting the uniformly jagged surface of the planet is another question. The answer to this question may belong in the realm of probability. If you dropped the balloon twice and it didn’t pop, you might be foolish to predict that the third time it also wouldn’t pop. If a dropped balloon popped sometimes, but not others, then you could not determine the outcome of any subsequent drop. You would have to drop the balloon many, many times to establish the probability of what would happen. And once it happened, you could only explain any particular outcome by referring to the probabilities that you established.

The above doesn’t mean you are unable to learn or know anything about the balloon and its tendency to pop. You may discover, for example, that imparting a spin to the balloon increases the likelihood it will pop. However, to figure out what the probability is you couldn’t rely on a few trials. Any conclusions drawn from a limited number of trials, from too little information, would be meaningless. So you make a great number of trials and discover that imparting a spin to the balloon increases its probability of popping by, say, 10%.

On your next trial, you spin the balloon as you release it, and it pops upon hitting the ground. Can you then conclude that the spin caused it to pop? No. It may have popped regardless of the spin. There’s no way for you to know whether the spin played a role in that particular pop or not.

The Precisely Imprecise Nature of Sports

Sports are exciting because we cannot precisely predict the outcome. If the team to win the Super Bowl could be forecast by adding the weight of the players for each side and comparing them, what fun would that be? Las Vegas, for one, would lose interest.

Sporting events are probabilistic because human behavior is more like the flight of shotgun pellets than laser-guided missiles. Our elbows are not made of titanium. There is always a degree of imprecision — and thus randomness — in how we perform. Even the great Tiger Woods, under ideal conditions, is not going to shoot under par every time he plays golf. His play is imprecise. And when Tiger is imprecise, he is not precisely imprecise. The alternatives to a perfect drive or putt are many and cannot be predicted. Our imprecision generates random outcomes. And, whisperings of golf commentators aside, there is no meaning in the random.

If you situated Tiger Woods 200 yards from the green and told him to hit the ball within 20 feet of the pin, you could not predict whether he would succeed on one shot or the next. After hitting 100 balls, the result would most likely resemble a shotgun blast — white pellets marring a green target, some of the marks inside the designated bulls-eye, some outside. If Tiger hit 60% of his shots within the bulls-eye, what could you say about those 100 shots? Well, from that distance Tiger hit 60% of his shots within 20 feet of the pin.

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Now imagine witnessing those 100 shots individually, as each one was made. What could you conclude about a single shot having hit or missed the target? Could you say that Tiger was distracted if he missed, or that he was “feeling it” if he hit? No. The same goes for short strings of hits and misses. Ten hits in a row does not mean that Tiger is on fire. Likewise, if Tiger misses his next 10 out of 15, we cannot rationally speak about some drop in performance.

All-Star George’s Hoop Dreams

The game of basketball is particularly well suited to this discussion because the better players hit roughly 50% of their shots. What is the probability that a player is going to score on any given shot? Toss a coin. What is the reason a player hit or missed a specific shot? Unless the shot was deflected by an opponent, we cannot speak rationally about the cause of a single, probabilistic event.

One night, while reading in bed, I wondered what would happen if I pretended a tossed coin was a basketball player. What would “his” performance look like? Would “he” get as hot and cold as the pros? I fetched a quarter and dubbed it “All Star George.” Because marquee players put up roughly 20 shots per game, I drew a 20 x 5 grid. George would shoot 10 shots in the first half, and 10 in the second, for a 5 game series, resulting in a total of 100 shots. While sitting up in bed — not what you would call controlled laboratory conditions — I began flipping the coin, making “m” (miss) and “h” (hit) marks on the paper.

In the first half of the first game, the sequence looked like this: m-h-m-m-m-h-h-h-m-m. At halftime, George had hit 40% of his shots. As you can see, though George is a 50% shooter, his hits and misses do not predictably alternate. We know that. At least one part of our brain knows that.

For the second half the results were surprising: h-h-h-h-h-h-h-h-m-h. My quarter, George, had “caught fire,” making 90% of his shots. What had inspired George to do this? Combining stats for both halves, in the first game All Star George hit 13 of 20, or 65%. My quarter was obviously trying to impress me.

During the second game, George hit 50% of his first half shots. Would he again catch fire in the second half? The ensuing sequence again surprised me: m-m-m-m-m-m-h-m-h-h. George went on another streak, but this time it was of misses. He hit only 3 of 10, although he did “pick it up” toward the end of the game. George’s shooting percentage for the second game was 40%. Maybe his legs hadn’t recovered from the great effort he put into the second half of the first game.

In the middle of the third game I had to bring in another player. George the 1st had rolled under the bed. It was at this time in my flip, catch, slap, scribble routine that my wife looked over the top of the book she was trying to read. She told me that if I didn’t wrap it up soon, she would cancel my research funding.

Although I knew the probability of George hitting heads was 50%, I could not predict what would happen on each individual flip. Nor could I predict what George’s shooting percentage would be for half of a game. When I completed the 5 games, I found that in only 4 of the 10 halves (10 shot sequences) did George hit the expected 50%. For the first halves of all 5 games, George hit 22 of 50 shots, which is 44%. For the second halves of the 5 games, George hit 28 shots of 50, or 56%. Could I have concluded from these 100 shots that George tended to “step it up” in the second half of each game? No. Numbers clipped from limited sequences are no more meaningful than the pattern left by tea leaves in the bottom of a cup. Once again, for probabilistic events we need a lot of information.

If you’re quick with math you will have noticed that over the 5-game series George went a perfect 50 for 100 — just what one would expect. What are the chances of that? I imagine it’s at the peak of a bell curve of probability, but not the only statistically likely outcome.

The Nicks v. the Twenty-Fivers

I had conducted my quarter-flipping test during the NBA playoffs, which followed on the heels of the NCAA tournament games called March Madness. While watching the basketball contests, I had been hearing statements such as: he’s really raised the level of his game (after a string of hits), they’re looking for someone to get a hot hand (I kid you not), they’re completely out of sync (after a string of misses), that basket will really build his confidence (same thing happened for George, I think), he’s making some good shot selections (string of hits), he’s rushing his shot (he missed), I couldn’t find my rhythm (he missed a lot), and he hasn’t stepped it up (after a player went 1 for 6, rather than his average 2.9 for 6).

Many of the NCAA games were so close I wondered if the winner could be said to have been determined by the toss of a coin … by luck (a sequence terminating at a fortuitous point?). Though sports commentators may jabber about the winning team having “brought their A game,” in such a close contest, and with all other things being equal — for instance, one team not having lost their best player to injury — could the commentators come to any rational conclusion about the outcome?

For my next coin-tossing project, I decided to re-enact a game. I would pit one coin against another, alternating tosses like trips up and down a basketball court. I called one team the “Nicks” and used a nickel to represent them. The other I called the “Twenty-Fivers.” Each coin would be tossed 100 times during the game. For each hit, or “heads,” the team would be awarded 2 points. Due to the probability of a coin coming up heads, I figured the final score would be, oh, near-100 to near-100. But would either coin take a dramatic lead during the contest?

As in basketball, I broke the game into two halves with two periods each half (to avoid confusion, I’ll forgo the customary term “quarters”). It began with a coin toss. I must admit I was excited to see who would win. Because I have the sad habit of rooting for the underdog in almost any contest — and am thus frequently disappointed by the outcome — I secretly rooted for the smaller Nicks.

Ten shots into the game, the Nicks were up 14 to 10, having hit 7 of 10. Twelve shots later they were up 16 to 10. At 20 shots they were up by 4, having hit 2 more shots than the Twenty- Fivers. The Nicks increased their lead by the end of the period to 28 to 22. For that period, my Nicks had shot 56%, the opposition, 44%.

During the first half of the second period, each coin went on a mini-run, with the Nick’s lead increasing, then falling back to 6 points. Then, during the end of the second period, my team went flat, hitting only 2 of 8. Meanwhile, the Twenty-Fivers went an impressive 7 for 8 and took the lead. The score: 50 to 56. In the second period the Nicks had shot a somewhat wimpy 44%, while the Twenty-Fivers razzle-dazzled their way to a red-hot 68% shooting.

I gave my Nicks a pep talk during half-time. I know, a good scientist tries to eliminate all bias, but I couldn’t help myself. “You can do it!” I coached my coin. I was both amused and dismayed by my sincere excitement over a competition involving the tossing of two coins, but this was high drama.

Third period. Although neither team scored above average, and both went 0 for 6 at some point, my Nicks did particularly poorly. For the period — a 25-flip sequence — they shot a dismal 36%. Hadn’t they listened to me? Meanwhile, the Twenty-Fivers shot a respectable 48% and increased their lead to double digits. The score after three periods of play: 68 to 80. Could my Nicks rally in the fourth period?

During the final period of play, both teams shot “lights out.” My Nicks put together two impressive strings, hitting 7 for 7 — they were in the zone — then later going 5 for 5. Unfortunately, the Nick’s 68% shooting in the final period wasn’t enough. The Twenty-Fivers shot 64%, winning the game 112 to 102. Apparently the Twenty- Fivers “wanted it more.”

The quarter I tossed landed heads-up 56 times out of 100, 6% greater than expected. Is this unusual? The result, certainly, is somewhat farther out of the fat of the bell curve than a perfect 50% would be. Maybe I could repeat the project 100 times and not get the same result. And that is what makes sports so exciting. Beyond the real human drama, such as raw ability, strategy, injuries, rivalries, etc., sporting events entail a virtual mosh-pit of probabilities.

Science Interrupted

This is not to say that the outcome of sporting events is completely random, the result of a coin toss. Were a pee-wee football team to play the Tampa Bay Buccaneers, the 2003 NFL Super Bowl champions would win. Probably. And that probability is very, very high. That said, if the two teams played a game every day for a million years, one day the pee-wees might win one. Just as if you were to prop a monkey at a keyboard, sooner or later, through random typing, he might string out the entire Origin of Species. It may take a billion trillion years, but it could happen. Trying to grasp the meaning, or lack thereof, of probabilities can be like forcing a square peg into a round hole — we aren’t accustomed to thinking that way.

Despite the fact that we can rationally say so little about the causes of an individual hit or miss, or even short strings of hits or misses, whether they be in golf, basketball, tennis, baseball or even croquet, human beings tend to jump to conclusions. We like to find meaning for things, and so we do, whether or not this is rational behavior.

In the first game of the 2003 NBA finals, the New Jersey Nets hit their first three shots. They had just come off a one-week layoff, having waited for the Spurs to finish out their series with the Los Angeles Lakers. The television commentators, always in need of something to talk about, had speculated as to whether the time off would help the Nets or hurt them. After going three for three, one of the talking-heads declared that there was “no rust on them.” Had the Nets missed their first three, I’m sure I would have heard how they were rusty. Funny, my tossed coins never got rusty, though they did go on streaks.

In a sense, superstitious thought is science interrupted. A relationship is sought and found, but there is a serious lack of follow-through. The conclusions are premature; they are based upon too little information.

During the closing seconds of game two of the NBA finals, the Spur’s Steven Jackson missed a potentially game-winning three-point shot. He had hit his previous two. One of the commentators, an ex-player who really should understand the game better, proposed that Jackson missed the relatively wide-open shot because a Nets player was rushing at him and “when someone is coming at you like that, it can throw your shot off.” There had to be a distinct reason why the shot missed.

Maybe, just maybe, Jackson missed that shot because he is a 40% shooter from that distance (give or take 10%). Under the best of circumstances, such as on an empty court while fully concentrating, Jackson will miss shots, for no particular reason. Why? Because a human athlete is imprecise, and this imprecision produces random outcomes. Nothing meaningful can be said about randomness.

During that same game, the star player for New Jersey, Jason Kidd, hit his last 6 free throws to “win the game” for the Nets. (Why the final points in a game, and not the initial points or middle points, are responsible for a win is another issue.) The still-sweating Kidd was interviewed. “How did you do it?” he was asked. Jason replied, “I knew we had to win this one and there wasn’t going to be a second chance.”

So Kidd put his will power into over-drive? Why wouldn’t he always give 110%? The answer: because fortuitous sequences eventually come to an end. For a 70% free-throw shooter to hit 6 in a row is not a Herculean feat, as much as fans and announcers would like to view it as such.

In game five, Jason Kidd hit his first 4 shots. One commentator concluded that Kidd had definitely brought his “A” game. The other concurred: Kidd was “hot.” Apparently it is possible to cool off instantly while simultaneously falling into one’s “D” game. Kidd hit only 1 of his next 9 shots. Both sports commentators had jumped to a premature conclusion.

Why do irrational beliefs such as the hot hand persist? Perhaps, in part, because the need persists. It is difficult to project human motives and meaning onto raw numbers such as 50%. But with a sequence such as miss-hit-miss-missmiss- hit-miss-hit-hit-hit, a dramatic story can be told about hot hands and cold chokes. Each event has its story, every turn, a reason.


Announcing SkeptiCal, the first Northern California
Science & Skepticism conference

Saturday, April 24, 2010, 9 am – 6 pm
David Brower Center, downtown Berkeley

CO-SPONSORED BY BAY AREA SKEPTICS and the Sacramento-Area Skeptics, the conference will feature lectures, breakout sessions, and exhibits. Speakers include: Brian Dunning, Professor Ian Faloona, Chris Jay Hoofnagle, Brian Malow, Dr. David Morrison, Wallace Sampson, MD, Dr. Kiki (Kirsten Sanford, PhD), Dr. Eugenie C. Scott, Dr. Seth Shostak, and Dr. Karen Stollznow. (Exact speakers and topics may change.) READ more about the speakers and their lecture topics.

Admission is limited and we expect to sell out, so you are encouraged to register soon. Tickets are $40, or $55 with a t-shirt and can be purchased online.

LEARN MORE & REGISTER


Why Darwin Matters (cover)

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NEW ON SKEPTICBLOG.ORG
Would I Ever Pray for a Miracle?

Michael Shermer discusses the statistics of so-called “miracles” on his recent appearance on ABC 20/20 and tells us whether he would ever pray for a miracle.

READ the post

NEW ON MICHAELSHERMER.COM
Surviving Death on Larry King Live

Have you ever died and come back to life? Me neither. No one has. But plenty of people say that they have, and their experiences were the subject of an episode of Larry King Live last December on which I appeared as the token skeptic among a tableful of believers…

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LECTURE REMINDER: Physicist Dr. David GOODSTEIN

On Fact and Fraud (detail of cover)

On Fact & Fraud:
Cautionary Tales from
the Front Lines of Science

Sunday, April 11, 2010 at 2 pm

In his lecture based on his new book, On Fact and Fraud, Caltech physicist David Goodstein looks at actual cases in which fraud was committed or alleged, explaining what constitutes scientific misconduct and what doesn’t, and outlines some ethical foundations needed to discern and avoid fraud wherever it may arise. READ more…

41 Comments »

41 Comments

  1. Disappointed says:

    I continue to be disappointed by the shallowness of the articles I have seen here. This is another example. In his experiment on “backspin” the author does not measure how much backspin he actually put on the ball. All he shows is that his perception of backspin does not correlate with success.

    This kind of error is used to create propaganda (advertising) just as much as “patterns”. For example, pharmaceutical companies do “placebo-controlled double-blind studies”. But the researchers do not measure if the subjects are blinded or not, much like the author did not measure his “backspin”. In fact, when subjects are asked what they think they are taking, they often know if they are on placebo or active agent. So the “blind” is not effective, but the results are published as if it is.

    The author also assumes that because a system gives results which appear random, that it is probabilistic. This is a false assumption as deterministic systems can exhibit such behavior. If we assume a system is probabilistic then we are likely to stop looking for deterministic influences. This is essentially what is done by people in the middle ages who said that diseases were “God’s will” . Fortunately not everyone threw up their hands and accepted such a fate.

    I do agree with the author that many “patterns” are correlations and not causal. I use this with my migraine patients who are looking for migraine “triggers”. I do not think that telling people who are finding such patterns that they should stop looking is a useful answer. It is better to teach people how to really test their hypotheses, which the author does not do in this article.

    As an aside, MS Excel is a quick and dirty tool for running simulations of randomness.

    • Paul says:

      I agree that the foul shot experiment was flawed. The author took 400 shots thinking about nothing except getting the ball through the hoop, and 400 shots thinking about nothing except backspin. But this proves nothing. Athletes eventually realize that thinking hinders performance. In most athletic situations your mind must be blank and your body must be loose. Once you start thinking you tighten up. So you when you practice putting backspin on the ball you think about it. Then once it is time to perform you forget because it is muscle memory. But if you are thinking during the performance your performance will be sloppy. When the author was thinking about nothing except getting the ball through the hoop that was closer to thinking about nothing, and closer to proper sports performance. I’d place a blind bet, based on this article, that I could take the author down in a one on one game of hoops.

  2. Henry says:

    I am a non-believer, but I have prayed, and I feel that although it is obviously superstitious behavior, I also feel it was useful. An example: I am a teacher at a community college. Once or twice a year, perhaps, I would get dragged into something and suddenly find myself due in a three-hour class in five minutes. Feeling unprepared, I would say to myself, “god help me get this done.” Small g. Never did I expect any outside intervention or supernatural assistance. As I explained to some religious fiends in an informal conversation about the power of prayer, I explained it this way. Jesus said, “The kingdom of God is within you.” I believe that. I believed that I had the inner resources to teach my class well, and my prayer was simple a meditative form of preparing myself. I think rituals are valuable because they are a form of mental preparation. When I played golf, I had a ritual I went through before every drive–alignment, stance, grip, firm left side. I also had a 2 handicap. Superstition” No. Mental preparation, focus? Yes. If I was driving well for the first few holes, I was more relaxed and confident for the rest of the round.

    As an avid baseball fan, I believe that attitude means a great deal. There are times when you can see the wheels come off a team or a player, and you know what’s going to result. Example: Sunday my wife and I were at a baseball game, and the home pitcher was beginning to look rattled. He walked the first batter in one inning. The next hitter was a power hitter. I said to my wife, “He’s going to clock it.” On the next pitch the batter hit it into the upper deck in right field. Superstitious? Supernatural? No. There are tea leaves, and they can be read.

  3. Anders says:

    “the home pitcher was beginning to look rattled. He walked the first batter in one inning. The next hitter was a power hitter. I said to my wife, “He’s going to clock it.” On the next pitch the batter hit it into the upper deck in right field. Superstitious? Supernatural? No. There are tea leaves, and they can be read.”

    You making a successfull “prediction” like that doesn’t prove anything. Did you even read the article? This is basically just what it’s adressing. Because the event is probabilistic, being right just once doesn’t say anything. You have to have a lot more data to say anything abouth wther or not you’re capable of predicting (better than chanse) a probabilistic event.

    • Henry says:

      My “prediction” was just one example. If you think that attitude, atmosphere and confidence don’t have anything to do with sports, you don’t know anything about sports. And rituals, superstitions, and practices that athletes follow are part of it, and they matter.

      • Mark says:

        Henry, Henry, Henry….you poor thing.

      • Andy O says:

        I’ve heard this sort of thing a lot – after presenting something that is unlikely, the claimant says, “but it happens all the time.” The fun thing to do is ask what the odds are – a number, not just an opinion. They invariably have NO IDEA how to actually calculate odds.

  4. Loughlin Tatem says:

    One of the best decisions I have made has been to subscribe to skeptic magazine and I am thinking very seriously of attending some of these lectures and discussion sessions.
    By the way, how does one go about quantifying back spins on a ball that one has thrown, and is there really any need for that type of knowledge if one has done sufficient appropriate testing? Isn’t there a time when one has sufficient evidence to rationally make sound judgment about how things work?After asserting the back spin proportions do I move on to decide which of my fingers was last to release the ball and let it fly?

  5. Ready Done says:

    Muscle memory has alot to do with it.

    • Michael says:

      While I understand and accept the premise of the author’s article, I am disappointed that the argument did not address Ready Done’s point. Flipping a coin doesn’t involve any skill; shooting a basketball and hitting a golf ball are improvable skills with which, I believe, trained practitioners can “catch fire” at times.

  6. stefanos arapogloy says:

    I partly disagree with the mathematic and probabilistic approach Dr. Andrew Bernardin does. How can a streak of coin results be compared with a streak of made shots by players ingame? Having a lot of basketball experience myself i can fully understand how the “hot hand” phenomeno can really happen.

    Shots made by athletes can be affected by many factors, such as stamina, body condition, training, psycology, talent etc. The randomness of a shot is relative, and that can be easily understood if we imagine Shaquille O’Neil having a 3pt shooting match up with Kobe Bryant. A streak of made shots can be easier expected from Kobe due to the factors mentioned above. Psycology has an enormous impact on basketball players ( i only refer to this sport due to my knowledge ). Situations like a steak of made shots, a crucial game time or a large crowd watching the game can affect player’s psycology, and therefore, player’s strengh,speed,decisions,stamina,precision etc. This could lead to a streak of made shots, which happened for reasons different from maths and stats, and could explain correctly the expression “hot hand”

    (this is my first post and my english is very poor because im greek plz dont be too hard on me :S )

  7. Disappointed says:

    The issue is whether a string of successes is due to hidden variables which can be influenced or probability.

    In a non-linear system with feedback between variables when not all variables and relationships are known it is extremely difficult to answer this question.

    What tends to happen is that the person answering the question merely speaks from their own prejudice and uses logic as a justification.

    My disappointment lies in my observation that the “skeptics” cannot seem to be aware of their own biases nor skeptical of their own conclusions

  8. kennwrite says:

    I find Dr. Bernardin’s article interesting. However, for those who took his discussion too seriously, then I would suggest that they sit with some hard-core sports fans and attempt to argue pure logic in an emotionally filled room.

    All sports fans suspend logic when it comes to determining outcomes, and allow themselves belief in the non-linear.

    I was going to take issue with the good doctor’s aside note that a monkey could type out the Origin of Species given a million billion years, but … what the heck, given the larger-than-life suspension of reality that every sports fan and many sports participants possess when it comes to competition, I guess it’s just not important to split hairs.

    k

  9. Bonsai says:

    I, too, was disappointed by the “hot hand” article by Dr. Bernadin. The hot runs experienced from time to time by virtually all athletes is so well known and accepted that I am surprised to find an article questioning it in a publication that prides itself on rationality and logical thought.

    Ready Done is correct that muscle memory accounts for the ability to perform all kinds of spectacular feats, not the least of which is a kid’s ability to learn to ride a bike. However, what is relevant here is what triggers such a run, and, equally valid, what triggers the abysmal performance when the run is over.

    I am satisfied that such runs (good and bad) occur when several conditions come together. Some of which may be: a state of mind that allows one to concentrate on the task without outside distractions; the necessary embedded muscle memory (built over thousands of repeats); an initial success (producing the desire to do exactly the same again); followed by a relaxed feeling that one has ‘got it together.’ In essence, you allow muscle memory free and unfettered access to the job at hand.

    Consider a garden path just 12 inches wide, (perhaps with a ‘keep off the grass sign’) across a fine lawn . . . . no problem for anybody. But now replace the path with a 12 inch wide path over a 3000 foot chasm and see how relaxed and confident you are. Emotion and state of mind are all-important.

    More interesting however is the naïve acceptance of the randomness of repeated coin tosses made under virtually identical (and relaxed) conditions. Presumably, the coin was tossed maybe 12 inches high, caught with one hand and transferred to the back of the other hand. Under these conditions I would not expect anywhere near a random result.

    Many years ago during my soccer refereeing days I was disturbed by the habit of some refs. to insist the player call the coin before the ref. tossed the coin a modest height, catching it in one hand and transferring it to the back of the other hand. It seemed possible to ‘fix’ the toss. Not that choice of end or initial possession is a big deal in soccer, but the principle of it bothered me, and I decided to test it. I tossed the coin in the above manner and tried to get a ‘heads,’ sometimes it worked. Then, after some practice I got pretty good at the toss and was able to achieve about a 75% chance of heads every time. Now Dr. Bernardin was not trying to fix the toss, but his highly repeatable technique probably resulted in a non-random result . . . . rendering not just his premise faulty, but his test method also.

  10. Alan says:

    Interesting article. However, I wonder if the author’s self-professed lack of basketball skill didn’t limit his judgment somewhat about “hot hands” in basketball.

    In my experience as a basketball player, I think there is definitely some truth to the “hot hand”. As a player, you know it when it happens. You’re in the zone, and you know the ball is going in. You just do. It has nothing to do with statistics, or what happened before. You’re in a certain mental state where your body is detached from your brain, and you can feel your body going through the motions, and you subconsciously just know whether the shot is “Good” or “not’. When you’re hot, you know it. You have the confidence as well as other factors working perfectly in harmony for you, which synergistically improve your shooting performance.

    • James Taylor says:

      I would be skeptical of the “hot hand” too were it not for the fact that I’ve experienced and witnessed it. I’ve watched and actively played basketball for over fifty years. It exists. It’s a confluence of skill, attitude, physical condition, environment, and any number of psychological factors. I support the effort to debunk such unscientific phenomena but it’s funny– all the “hot hand” debunkers I’ve read in the past never really played the game.

  11. Tom says:

    Hot hands don’t exist? What about Joe Dimaggio’s 56 game hitting streak in 1941? Was that skill or luck?

  12. Ian Leslie says:

    Hasn’t this piece been written a hundred times in the last few years? What’s more interesting is a very recent piece of stat research (on baseball I think) indicating that games aren’t “independent events” and that the hot hand isn’t therefore a complete illusion. Listen to “Are We Coins?” on WNYC Radio Lab for more.

  13. Stephen Kennamer says:

    If you have never been in the zone or had a hot hand, you are better off not writing about the phenomenon as if (a) you know what it means and (b) you can disprove it by flipping coins. Just because a player shooting fouls will, over time, find his hits and misses averaging out to his lifetime percentage–like a coin that approaches 50% heads the more it is flipped–does not mean that the player is exactly LIKE a coin. Schermer might as well say that health and sickness are like your car starting or not starting–batteries work for a while and then they don’t, so there is no such thing as catching a cold by sitting around in damp clothing.

    Schermer’s immediate detour into silly superstitions about clothing shows the depth of his incomprehension. It’s a non-sequitur, but apparently he thinks it isn’t. We all understand that I won’t play better because I didn’t change my underwear (although my BELIEF that I will may bolster my confidence, which may be a contributing factor to being in the zone). But I may play better if I am peaking as an athlete, being on a particular day well trained, well rested, and easy in my mind.

    At one point, Schermer is so incoherent as to write the following: “Ten hits in a row does not mean that Tiger is on fire. Likewise, if Tiger misses his next 10 out of 15, we cannot rationally speak about some drop in performance.” Clearly, there HAS been a drop in performance–that is a rational statement in all galaxies, based on objective data. I hope what Schermer meant to say is that we cannot rationally speak about “a cold hand.” But in making his mundane point, Schemer shows a tin ear for sports commentary. “On fire” and “cold hand” are ordinary metaphors that merely translate objective data about successful and unsuccessful shots. Schermer might as well get his shorts bunched up over people saying it is a “hot day” or a “cold day” based on a laughably small segment of the range of temperatures from absolute zero to the heat at the center of a star.

    There is a famous video of Michael Jordan making his sixth three-point basket of a playoff game, still in the first half; and then, as he goes back down the floor, he shrugs, as if to say, “I just can’t miss, I don’t understand it myself.” Here’s the point: he doesn’t have a superstitious belief about being in the zone that can be confirmed or disconfirmed by my flipping some coins; he IS in the zone.

    Every athlete of any ability has experienced being in the zone: the running feels easy and the time is spectacular; the pitcher is able to hit the catcher’s mitt with every pitch. Next time out, the pitcher feels good, warms up well, and walks the first four batters he faces. There is only a tiny fragment of an intelligible point in this woefully written and poorly argued article: explanations for the phenomenon after the fact are all just guesses. But to argue that it does not exist is to make a fetish of skepticism.

  14. Stephen Kennamer says:

    Sorry for getting the name of the author wrong throughout my comment. Had a cold hand typing.

  15. USA says:

    “hot hand”, “in the zone” = figurative language.

    They are not predictors, they are descriptors.

  16. Ken Voet says:

    Decently written, but i have to disagree. The assumption of the article is that each “shot” is independent of the proceeding one. The multiple examples with the coin flip essential compared two different things. Is it unreasonable to assume that since there is so much variability in the human athlete that each shot might NOT be independent. In other words, the previous shot may influence the next shot. As you said, you experimented with your shot after your misses. If after every shot, an athlete can analyze there form, does it not make since that the probability of each shot changes? If so, then why could a player not become “hot” if they’ve increased there probability.

  17. Ted says:

    The question of whether a player really gets “in the zone” or not can be answered, I think, by doing a statistical analysis of the “streakiness” of players. Are some players more “streaky” than others–i.e., do they tend to go on runs where they hit shots (get hits) in succession more than other players who have comparable field goal percentages (batting averages)? If everything were random, then streakiness would also be random, but my intuition tells me that some players are more streaky than others. I imagine someone has analyzed this before; is there any data on this?

  18. Harry Beckwith says:

    I read Thomas Gilovich’s book years ago, with special interest, and readily endorsed his view about the Hot Hand.

    And yet there is this strange personal story.

    I started in 38 games in my high school career. I was a 74% free throw shooter and a 38% field goal shooter, and averaged 6.5 points per game.

    In the 14th game, in the second quarter of a game–just eight minutes–I made five consecutive 19 foot shots from precisely the same spot–left of the top of the key. Five for five on what today would be a three pointer.

    17 games later, in the second quarter of a game–just eight minutes–I made five consecutive 19 foots from precisely that same spot–left of the top of the key–from where I made the identical shots 17 games before. And perhaps worth mentioning: both were away games, and both times the baskets were at the south end of the visiting team’s court, and on the far side of our team’s bench.

    These two games were among just six games in which I scored in double figures in an entire game–and I scored in doubled figure in a single quarter in these two outlier games.

    Adding to the strange parallels: In each game I scored two points in the third quarter and none in the first or fourth. 0-10-2-0 both times.

    My odds of making any one of those shots, by the way, would not have been 38%. Given the distance of each shot, the odds of making any one shot was not better than 30%. And it doesn’t help one’s odds when the other team, sensing you might be in a zone, becomes more zealous in stopping you from getting the ball, much less shooting it, and especially from the spot from where you seem to have the hot hand.

    Mathematically, my performance can be shown to be possible, of course. For it to happen twice over that space of games, in that period of time, from a player who rarely in his career made five shots in an entire game, certainly possible, yet so improbable that it seems to beg some good explanation.

    Did it feel different at the time? It certainly seemed that way. Unconscious, as they say, and if there is a hot hand, that might be key. You don’t think; the ball enters and leaves your hand and you’ve no memory of what happened in between. The ball goes in once again, and you head back on defense.

    Is there a hot hand? Maybe not. The odds of winning the Power Ball are at least as ridiculous as what I did, but the missing element there is that you cannot argue that shooting a ball is truly random. Your mind enters the equation–which is why putting from three feet is not random either. If you start to think about the consequence too much, you start missing more often than the rule of randomness would dictate. Why would the reverse, in this case in basketball, not be true: That a sudden sense of invincibility, or sheer luck, might not increase your chances of making a shot?

    • Andy O says:

      You can’t look at it as “Five for five.” You have to include a longer run than that. Presumably you missed the 0th and 6th, and in that sequence of 7, you were 5 for 7. Point is, you can’t afterwords pick the specific five shots. Hindsight isn’t allowed when doing the statistics. You really need to make that PREdiction, not the POSTdiction.

      I think the question of hot streaks is not one of ‘did the athlete luck out or use some sort of concentration’, but one of ‘is there some outside influence doing it, such as the will of god.’

  19. Stuart Munro says:

    Some of the assumptions about partial positive reinforcement are not necessarily good. In dealing with situations where we don’t know all the relevant inputs, there are two things going on, the attempt to predict the next outcome, and the attempt to recognize a pattern. A notionally random situation that delivers a probably skewed outcome, equivalent to 7 heads in a row on a coin toss, is more likely than not non-random. This is the thing Taleb is so excited about.

    The lucky hat may help too. Most sporting behaviour relies heavily on subconciously controlled actions, which seem to be influenced by irrational factors,such as mood or confidence. By ascribing the ‘lucky’ character to a variable they can control, a player attempts to reinforce the subconcious elements of success. In some instances they might do better to tape and analyse their physical performance, but as a stop gap, the lucky item is a parsimonious and low-cost attempt to control the pschological elements of a sport – a rational use of an irrational device.

  20. NYTwin81 says:

    I agree with the commenters who are skeptical (as it were) of Dr. Bernardin’s article.

    Although Dr. Bernardin is right that, sometimes, it’s a mere statistical quirk when a basketball player who makes (say) four three pointers in a row, and we are merely imposing a pattern ex post when we say the player is hot (after all, maybe the player has just gotten lucky), it’s equally incorrect to say, ex post, that all such “hot” streaks are merely the incidental product of probability (after all, skill and practice may play a role, a la Michael Jordan).

    Dr. Bernardin’s experiment assumes that a team will have a 50/50 shooting percentage, which, I think, corrupts the experiment.

    Let’s consider baseball batting averages instead, where there are obvious and indisputable variations. Would Dr. Bernardin really maintain that a player who has a lifetime average of .305 is no more likely to have a ten game hitting streak than a player who has a lifetime average of .220? That’s obviously not true. The reason is, someone who hits .305 has better mechanics, has a better eye, is more confident at the plate, etc., and that contributes to the likelihood of a streak. So that when that batter gets hot, there’s a reason–it’s not blind chance.

    Dr. Bernardin’s analysis of Steven Jackson’s missed shot also doesn’t make a lot of sense. Sure, Jackson might have missed the shot anyway, since he doesn’t make every three-point shot he takes even when he’s wide-open. But might a defender in his face have contributed to the miss? Of course. That’s like saying “Well, that batter struck out because he only gets a hit 30% of the time” when a pitcher is placing his pitches perfectly, mixing speeds, and throwing a vicious slider.

    Probabilities are involved in sports, but probability isolated from all factual context (i.e., skill, practice, mechanics, state of mind, etc.) does not control.

  21. NYTwin81 says:

    Whoops, a slight correction to the following passage (see asterisks):

    But might a defender in his face have contributed to the miss? Of course. *To say otherwise would be* like saying “Well, that batter struck out because he only gets a hit 30% of the time” when a pitcher is placing his pitches perfectly, mixing speeds, and throwing a vicious slider.

  22. Jon says:

    I continued to be shocked at how committed to the belief of skepticism most skeptics adhere.

    This article is ridiculous in its proof that no hot hand exists. Yes, we all understand that if you flip a coin and it lands heads three times in a row it is still 50/50 that it will land. And yes, there are certainly many times when a player will just hit a bunch in a row out of luck.

    But, yet, it’s very easy to believe that a player gets into a rhythm where he starts to hit an above average number of shots. If you actually want to debunk a hot hand myth how about running some numbers, rather than just using a coin as a stand in… which does not represent a basketball player at all.

    It would be a very simple experiment. Find games where someone has hit, say, 4 out of 5 of his shots… From there you could measure how his average is after that.

    I hate to be one of those haters on comments, but skeptics, and skeptic magazine, continue to be an embarrassment to the world of reason.

  23. NYTwin81 says:

    One more comment from me: It occurs to me that Dr. Bernardin could argue that the result in the .220/.305 batting average example is consistent with his theory, because the player that has hit .305 is more likely to get more hits in a subsequent season, so he’s more likely to have his hits randomly assort into a ten game hitting streak.

    The better argument is what others have already said: when a player is “locked in,” it’s a palpable thing. In batting, it means a player is seeing the ball better, feeling relaxed, etc. And while it’s still statistically possible that he’ll go 0-for-the-game in any given game, it’s less likely to happen than his overall season average, ex post, would indicate–because of the player’s skill, not chance.

    Others have referred to Joe DiMaggio’s 56 game hitting streak. That’s particularly instructive, because the odds of even someone who hit .356 (as he did in 1941) hitting safely in 56 games are vanishingly small. Also keep in mind that DiMaggio had a 61 game hitting streak on the San Francisco Seals, his minor league ballclub. If players can’t get hot, and it’s all about randomness, the odds of Joe DiMaggio hitting safely in 56+ games twice in his professional career are *absurdly* small. But if skill, and being “in the zone,” play a role, it’s much less far-fetched.

  24. Jon says:

    I’m afraid that most of this article and the research that preceded it doesn’t quite address the question. Of course, everyone has some kind of local average that they tend towards during some period of time. The average is composed of streaks as well as consistent shooting. The difficulty lies in knowing when to start counting the “next shot.” There are currently no statistics kept on when a player is in the zone and when not. If you don’t know which “next shots” to count and which not, you’re measuring nothing of salience to the question.

    A further difficulty lies in the fact that getting hot occurs during a game (not while practicing freethrows in your driveway). This means the opposing players react. They try to make the hot player cool down. This is an important part of the game, because when the opposing team reacts, while it may close down the hot player it opens up opportunities for the other players. This is also why no NBA player will ever care if you find hot shooting to be statistically random.

    The author has imported a notion of “average” into the real world here which is out of place. No one knows what a players average is, except in the most superficial and after-the-fact sort of way: we know what happened. Part of the game is battling with other players to do the things which will establish their averages. The results are statistically regular, but still dependent on context — including how often players tend to get hot and under what conditions.

    A better thought experiment for this article would have been to imagine what would happen if half the games in the NBA were played against mice. I imagine that then we would see some streaks. Ironically, however, what the statistician might see as streaks would actually be the true shooting ability of the players, absent game effects. But this might actually be what a hot streak is: a period of time in which true shooting ability is relatively unimpeded owing to fortuitous circumstances: confidence, good pick setting, tired defenders… etc. This kind of thing can go on and on, and complicating everything is the belief of players in hot hands, which leads many of them to shoot excessively in an effort to bring on the hot hand, thus lending to their shooting averages a sort of post-modern quality.

    BTW: some skepticism should be reserved for mathematics and the practical limits of specific applications.

    • jeff says:

      But you can get “hot” shooting free throws in your driveway. If you’ve trained your muscle memory enough through repeated practice, then you can go on incredible streaks shooting free throws. I was nothing more than a decent 2-guard on a bad high school team and I could make 30, 40 free throws in a row if I was in the right rhythm.

      It seems to me that your overall percentage is obviously going to include cold spells and streaks, but as others have pointed out, these are not just random distributions. When you’re in the zone you can feel it, and you know the shot’s going in when it leaves your fingertips. Just as when you’re not feeling right, when you’re “cold,” the ball fells awkward leaving your hand, and sometimes you’ll make shots that feel like air balls (although, more likely than not, it’ll just be an air ball).

  25. Sam says:

    “Nor have I ever found myself “in the zone.” Even if equipped with a G.P.S. and a topological map, I don’t know if I could even locate the zone. Perhaps because of this, I will endeavor to deconstruct the zone”

    So because the author has never been in the zone, it doesn’t exist? A lazy start, which leads to a lazy article. On top of the countless amounts of anecdotal quotes from athletes, there is plenty of legitimate research on “the zone” (also called “flow” or “peak performance”). I’m disappointed that the author did not try to look up any of the studies done on flow by researchers in the field of sport psychology. Many qualitative investigations have taken place on what “the zone” feels like and how people were able to enter that zone. Other research is looking at ways to increase the likelihood of being able to enter it. Finally, the author could have talked to someone who runs on a regular basis. Frequently, they end up “in the zone” with what’s called the “runner’s high.” “The zone” most certainly exists.

  26. Timothy Black says:

    It seems very strange to me that an article making a mathematical claim neither contained nor elicited any comments containing any actual math. Only a few commenters raised the relevant question about the hot hand: “streakiness” (or, equivalently, statistical independence).

    Just as probability distributions tell us how often to expect an event (e.g., 1/2), they can tell us how often to expect a *sequence* of events. If coin tosses (or made shots) are independent of each other (and “identically distributed,” i.e., drawn from the same distribution), then no sequence is any more likely than any other. This can be checked by examining the data.

    Example: What is the probability of Jones hitting more than 80% of (to keep it simple) his first ten shots? Well, how many ways can he do this? Answer: 10 choose 8 + 10 choose 9 + 10 choose10 = 56. How many different ways can he shoot those first ten shots? Answer: 10 choose 1 + 10 choose 2 + … + 10 choose 10 = 1023. If the events are IID, then, his chance of shooting 80+% is 56/1023 ~= 5%.

    If (say) NBA players tend to make 80+% of their first ten shots more than 5% of the time, then they are “streaky”—i.e., the shots are *not* independent of each other, and the hot hand exists.

  27. Rich Rostrom says:

    It is certainly true that humans tend to perceive patterns where none exist. Sometimes a “streak” is just an artifact of chance.

    But to believe that all such variances are such artifacts is to assume that ability does not vary. Or circumstances. A basketball player might be “hot” because his team has found a weakness in the other team’s defensive arrangement, which enables him to make easier shots. Or he might be “cold” because he has a nagging injury which interferes with his shooting.

    Does Dr. Bernardin believe this never happens?

  28. Stan says:

    It’s amazing that such a conclusively debunked notion as the “hot hand” still continues to be defended by some of the commenters here. A Cornell professor disproved the notion more than twenty years ago. The argument that the writer of this article “never played the game” is, of course, not an argument at all. If the “hot hand” exists, then at least one rigorous definition of a “hot hand” will give a better prediction of the player’s likelihood of success on the next shot, or his next five shots, than simply applying his overall shooting average will do. And it has been conclusively demonstrated that no such predictive power exists.

    Probably the purest form of the experiment would have to do with free throws. The conditions from one shot to the next are virtually identical. “Muscle memory” would have its strongest effect in this case. However, the Cornell professor (I wish I could remember his name, but he wrote a book called “How We Know What Isn’t So”) showed the following: If a 70% free-throw shooter, in a two-shot free-throw situation, makes the first of his two free throws, then what’s the probability that he’ll make the second? You guessed it: 70%. And if he MISSES the first of two, what do you think is the probability that he’ll hit the second? You guessed it again: 70%.

    The belief in the “hot hand” by athletes and sports fans doesn’t demonstrate the truth of the “hot hand” theory. It demonstrates the human capacity for self-delusion.

  29. Matt says:

    Article completely misses the point. The Zone is all about heightened levels of confidence that most of us have experienced in one aspect of life or another. It’s as real as the undeniable advantage of having confidence. It has nothing to do with superstition.

  30. Sal Monella says:

    I am the world’s worst poker player, but on two occasions I spotted a game (once from a moving car) and immediately joined, in the sudden and sure conviction that I was going to clean the other players out.
    I did.
    Where does this come from? Haven’t a clue.
    For you basketball players: I once saw a deteriorated mentally ill homeless guy carefully peel off most of his rags, place them in a neat pile at his feet, and make three perfect free-throws in a row from outside that big semi-circle. Maybe he was in more zones than one.

  31. Nicholas says:

    Stan, speaking for the Party of Pure Number, said:

    “If the ‘hot hand’ exists, then at least one rigorous definition of a ‘hot hand’ will give a better prediction of the player’s likelihood of success on the next shot, or his next five shots, than simply applying his overall shooting average will do. And it has been conclusively demonstrated that no such predictive power exists.”

    Actually, the item that probably does not exist is “his overall shooting average.” I doubt you’ll be able to come up with a rigorous definition of a shooting average that can be applied to “the next shot, or his next five shots” in the way you suggest, and so your demonstration is invalid.

    May I point out that if a player just hit X shots in a row, his “shooting average” went up? The average is a description after the fact, measured at the end of a season or of a set of shots, and based only on shots actually attempted (whether or not these were during hot streaks).

    I submit you cannot say with certainty what a player’s shooting average IS in any given fraction of the season, or in advance of a shot.

    You cannot apply last year’s average. This year’s will vary. You cannot apply career average; it goes up and down in a career. As the wise idiots say, “that’s why they play the games.”

    You might, like Baseball Prospectus, try to apply some logical average for a given year in a career based on the careers of all similar players in the past, but such models still stand a high chance of turning out wrong for any given ongoing season (odds of success comparable to a coin flip or a free throw!).

    What’s too reductive here is the notion that you can model players with coins or other random number generators. Coins don’t have muscle memory, can’t practice and get better, do not overpractice, cannot be told what play to run, cannot be coached or coaxed or rushed or intimidated, do not worry about their mother’s health, and do not sustain injuries. Coins do not get tired, vary in their blood sugar, have itches, find their mind is suddenly full of thoughts of sex or the tax man, decide to call time out or — this is very, very important — decide not to shoot. Coins don’t decide when to flip themselves.

    It takes a very advanced mathematician to think that these aren’t all among the factors that possibly decide whether a shot is made, and that their cumulative effect cannot account for streaks hot and cold.

    I also don’t see rigorous modeling here of what defines a “shot.” This too is an after-the-fact construct that ignores too many variables to count. It’s good enough for betting strategies and fantasy teams but doesn’t address the question of psychology in time (of which “streaks” are a subcategory).

    A proper model of “shot” would account for the decision to shoot/hold/pass in any given fraction of a second, the timing, whether there’s pressure from the shot clock, the position of all other players on the court, distance from basket, release point and angle, fatigue, unmeasurable physical factors (what’s he digesting just then?) and please brainstorm some more.

    Sufficiently complex events involving many variables only have the appearance of being reductively probabilistic because of the very low number of outcomes that interest the spectator (or the reader of results) after the fact. A shot is made or missed, a game is won or lost, and what really went into and determined a shot’s outcome seems completely irrelevant.

    Every game is a story that develops and is affected by emotional swings and a combat of willed decisions, as well as bounces and wind speeds and the presumed ideal of player averages.

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Reality Check: How Science Deniers Threaten Our Future (paperback cover)

How Science Deniers Threaten Our Future

The battles over evolution, climate change, childhood vaccinations, and the causes of AIDS, alternative medicine, oil shortages, population growth, and the place of science in our country—all are reaching a fevered pitch. Many people and institutions have exerted enormous efforts to misrepresent or flatly deny demonstrable scientific reality to protect their nonscientific ideology, their power, or their bottom line…

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Top 10 Myths About Evolution

Top 10 Myths About Evolution (and how we know it really happened)

If humans came from apes, why aren’t apes evolving into humans? Find out in this pamphlet!

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Top 10 Things You Should Know About Alternative Medicine

Top 10 Things You Should Know About Alternative Medicine

Topics include: chiropractic, the placebo effect, homeopathy, acupuncture, and the questionable benefits of organic food, detoxification, and ‘natural’ remedies.

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Learn to be a Psychic in 10 Easy Lessons

Learn to do Psychic “Cold Reading” in 10
Easy Lessons

Psychic readings and fortunetelling are an ancient art — a combination of acting and psychological manipulation.

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