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Unpredictability: Hot Hands vs. Gambler’s Fallacies

We knew before starting this blog that few others are interested in making persuasive psychology practical.  It’s frustrating, but it forces us to research carefully and it ensures our ideas are new and potentially useful, not exhaustively re-hashed impractical nonsense or indecipherable jargon-laced dissertations.  The dearth of information about every-day, real-world, common-man influence strategies is a blessing and curse; we’re doing what few have done before, but few are there to help us do it.

Last week, though, we got help.

In our post Exploring Unpredictable Social Strategies, we made a bold claim: we said that the best way to control your subordinates is to reward them randomly when they do something you like, and that no other method would produce the same results.  We based our claim on solid evidence that random ratio reward schedules induce compliance by trapping reward-seekers in a common probabilistic error called the gambler’s fallacy.  After that, we introduced you to the hot hands fallacy, and advised you to be open with your subordinates about the process, lest they commit this error – the wrong error.  The advice was an even bigger leap than our previous claim because we didn’t have – and didn’t expect to find – a study comparing the relative effects of each kind of fallacy.  The concept was just too new.  So we were surprised last week when we found one with this subtitle: “The hot hand versus the gambler’s fallacy.”  Rarely does a search turn up results like that; we eagerly read it.

The study turned out to be better than we could have hoped.  Not only did it address the same question we were asking ourselves, it did so by experimenting with the same random process (coin-tossing) we’d been using as an example, and its findings suggest we were right: random ratio reward schedules work best if everyone knows that the process, not you, determines who wins and who loses.

The Study

Canadian researchers Christopher J. R. Roney and Lana M. Trick wanted to identify the cognitive mechanics behind the gambler’s and hot hands fallacies.  Because the fallacies predict different outcomes and assume different processes, each one should only occur in mutually exclusive situations.  When outcomes are genuinely random, everyone should be committing the gambler’s fallacy.  When outcomes are plausibly skills-based or are possibly rigged, everyone should be committing the hot hands fallacy.  But have you ever heard someone claim they’re “on a roll” after they win twice or three times in a row?  Of course you have.  Have you ever seen a gambler who’s unable to quit while he or she is ahead?  Hopefully not, but perhaps.  Do you know someone who picks their own “lucky” lottery numbers every week?  More than likely.  In all these examples, the person is committing the hot hands fallacy even though the game is random.  Why?

Roney and Trick hypothesized that the cognitive mechanics involved in each of these fallacies activate or deactivate whenever someone’s beliefs about a process’s outcomes change.  If a person believes he or she or some other human being is somehow skillfully controlling outcomes previously believed to be merely random, then the person should switch from using the gambler’s fallacy to using the hot hands fallacy.  For coin-tossing, it would look like this: changing a person’s focus from the random nature of the coin to the real or imagined skills of the coin-tosser should induce a switch in fallacies.

Testing this theory was incredibly simple.  The experiments involved 124 undergrads (the subjects) watching one of two women flip a coin. In the experimental conditions, one woman would flip seven times, and lie about what came up such that the results were always either HTHTTTT or THTHHHH (alternation followed by repetition).  The subjects would bet on the next outcome each time and record their confidence in the bet.  Before the eighth flip, though, the woman would say one of two lines: “Wow, I’m really throwing a lot of [heads or tails],” or, “Wow, this coin is really coming up with lot of [heads or tails].”  (In the control condition, these lines were not said.)  Then, the woman either kept flipping or handed the coin off to the second woman (who, ostensibly, was there to record the “results.”)  You can see that depending on which of the two phrases was said in between the seventh and eight flips that the researchers intended to re-focus the subject’s attention, changing it ever so slightly toward the woman’s “skill” (the first phrase), or even more intently on the coin (the second phrase).  The researchers also predicted that when the coin changed hands, the gambler’s fallacy would remain in effect regardless of which phrase preceded the eighth flip.

They were mostly right.  As expected, nearly all of the control subjects committed the gambler’s fallacy and predicted the streaks to end on the eighth flip. And, as expected, when the coin changed hands, the gambler’s fallacy was predominant in all cases.  But just a small majority of the subjects who’d heard the first phrase committed the hot hands fallacy and guessed that the repetition would continue.  Something similar happened to the subjects who’d heard the second phrase: about half of them committed the hot hands fallacy, probably because the wording of the second phrase led them to believe the coin itself was biased or “charmed.”

The most revealing data, however, are the confidence scores of the bets placed by the subjects.  Overall, those who committed the hot hands fallacy in the first experimental condition were much more confident in their bets on the outcome of the eighth flip than those who stuck with the gambler’s fallacy.  The highest confidence in bets on reversals, of course, occurred in the control condition.

So, what does this mean for our reward system?  Well, if you keep your method secret from those you want to control, you might lose about half of your rewardees to the hot hands fallacy; once you hit a streak, half of them will expect it to continue, and those who don’t won’t hesitate to change their minds if it does continue.  In other words, they’ll stop trying.  Keep it transparent, though, and they will stay busy doing what you want them to.

Damage Control

Let’s say you’re the supervisor of a group of employees (assembly-line workers, for instance.)  You want your workers to be more efficient because your superiors are worried about their bottom-line.  You remember from business school that incentives are a good way to achieve this goal, but your workers are already well-paid and enjoy several generous benefit packages, so you’re at a loss for how to incentivize them more.  That night, after work, you read on Practical Persuasion that a random-ratio reward system based on a coin-toss is the best way to induce compliance.  The next morning, you call your team together and tell them that each day of the month, whoever is 95 percent productive or better could get $100 cash.  You don’t tell them that the result is determined randomly because you’re afraid they won’t play along.

For two weeks, your employees operate at break-neck speed. Efficiency is consistently in the 80s and 90s, even on Fridays.  A third of your employees are 90 percent productive or higher.  As you expected, about half of those get bonuses.  The money you saved the company on labor and utilities more than makes up for the extra cash.  The bosses sing your praises.

The next two weeks, though, are different.  Productivity flat-lines, and then drops back to previous levels.  You remind your workers that the productivity game is still on, but they don’t seem to care.  Only half of the original productivity all-stars from before make the cut this time.  The bosses suddenly can’t remember your name.

After two more weeks of low productivity, HR organizes a company-wide teamwork seminar that wastes even more time and money. You also have to meet for two hours with the 21-year-old economics major who the bosses hired on as a “business strategies consultant” (he gets paid twice as much as you do, by the way).  You’re pissed. You go home, get drunk, and resolve to expose those two bastards at Practical Persuasion for the frauds they really are.

We hope this doesn’t really happen to anyone.  If it does, don’t hit “send” on that angry email just yet.  We now know that when people aren’t aware that a game is random, they assume it’s rigged after seeing several successively repeating outcomes. Also, a bit more than half of them will be almost certain that it is so.  To get them back, try this: explain how your system works…and then secretly scrap it.  Purposefully alternate your responses for a while.  Many people often mistake these alternations for randomness, so intentionally switching back-and-forth like this should get most of the skeptics back on board.  Be sure to submit to the coin (or whatever random process you’re using) once you’re secure.

Sources

Roney, C. J. R., & Trick, L. M. (2009). Sympathetic magic and perceptions of randomness: The hot hand versus the gambler’s fallacy. Thinking and Reasoning, 15(2), 197 – 210.

The Hot Hands Fallacy

Back in April – in our Exploring Unpredictable Social Strategies post – we told you that the best way to control your subordinates (if you have any) was to reward them randomly when they do something you like.  We explained:

“Each time your rewardees perform a desirable action, flip a coin. If heads, reward it; if tails, ignore it. When the coin generates a long ‘ignore’ streak, your respondent should perform the action over and over again with ever-increasing rapidity and urgency, expecting to be rewarded more and more each time he or she isn’t. This is the gambler’s fallacy at work.”

If you don’t remember, the gambler’s fallacy is a flaw in probabilistic reasoning that causes most people to mistrust long streaks in randomly generated events.  The fallacy gets its name from a common mistake gambler’s make when betting on roulette and slots.  When a roulette wheel has a black streak, players will bet increasingly larger sums of money on red because they think the black streak is more likely to end the longer it continues.  When a slot machine fails to pay out, players will crank the lever faster and faster, depositing money with each pull, because they believe their losing streak will end soon.  In both cases, they’re wrong; random events are always unpredictable.  They’re always as likely to win as they are to continue losing.

If you have the power to give out or withhold rewards, then you should do so using behavioral psychology’s equivalent of the slot machine: the random ratio reward schedule.  This is as easy as requiring your rewardees to “win” a coin toss each time they do something you like before receiving their reward.  Just like the gamblers, they will continue to work harder for your approval if they can’t predict when they will be rewarded.  However, we also supposed that this simple system may not work under certain conditions.  In this post, we’ll show you what those conditions could be.

But first, another fallacy.

The Hot Hands Fallacy

When Amos Tversky’s name appears at the top of a study, there’s a strong chance something you believe will be challenged.  If you like basketball, then the 1985 study he co-authored with Thomas Gilovich (Cornell University) and Robert Vallone (Stanford University) will debunk a common belief you may hold about the game: that some players go on hot or cold scoring “streaks.”  To Tversky, one of the most famous contemporary psychologists (second only to his close friend and colleague Daniel Kahneman; both specialize in cognitive psychology), this sounded like a fallacy.  After all, he and Kahneman documented the existence of the gambler’s fallacy over a decade earlier; he of all people would know flawed reasoning when he saw it.  So he, Gilovich, and Vallone took data from the 1980-81 Philadelphia 76ers’ home games and looked for evidence of streak scoring.

They found none.  Contrary to what 91% of surveyed basketball fans at Cornell and Stanford believed, no player was more likely to score on his second field goal attempt if he had scored on his first attempt, nor was he more likely to score on his third attempt if he had on his first two, and so on.

In case extraneous variables (defensive pressure and shot selection) were contaminating their findings, the authors analyzed free throw data from the Boston Celtics’ 1980-1981 and 1981-1982 seasons.  Did any player’s first free throw attempt affect his second free throw attempt?

No.

Next, the authors set up a controlled shooting test with 26 Cornell players (14 men, 12 women) to eliminate extraneous variables.  Each player shot from a distance at which his or her shooting percentage was 50 percent.  An arc was drawn on the court after this distance was determined, and each player shot once from different points along the arc.  To incentivize accuracy and assess players’ predictions, the players placed high or low bets on each successive shot and were paid a few cents when they scored and were docked a few cents if they missed.

Did statistical streaks appear for players in this part of the study?

No.

Did the players accurately predict their hits and misses?

No; they predicted streaks, though, whenever they made or missed shots successively.

Finally, the authors surveyed the student fans at Cornell and Stanford again to see how well they could interpret basketball data.  Each student was shown six sequences of X’s and O’s (intended to represent hits and misses, respectively) and were asked to indicate which sequences were streaks and which were random.  How did they do?

Terribly.  Only about 30 percent correctly identified the random sequences as random.  About 60 percent believed the random sequences were actually streaks.  And about 70 percent believed that alternating sequences (in other words, streaks of successive hits followed immediately by misses; for example, XOXO) were actually random.  The authors guessed that the reason the students did so poorly on this last test is because they expected repeating outcomes to continue repeating.  In the alternating sequence, the shots did not repeat, and the students saw it as random.  In the random sequences, hits and misses occasionally do repeat, and the students saw them as streaks.  Taken together, these mistakes – seeing streaks in random data where they don’t exist and misinterpreting alternating streaks as random – are called the Hot Hands Fallacy.

The Other Side of the Coin

If you’ve made it this far, you should now be asking yourself why these people did the exact opposite of what gamblers do.  And if you’re really astute, you’ll notice that the Cornell players in the controlled shooting test were gambling on their own attempts, betting that their ‘hot streaks’ and ‘cold streaks’ would continue, not end.

Why aren’t they committing the gambler’s fallacy?

Unfortunately, we don’t know for sure, mainly because no one has tried to find out.  The original Gilovich/Vallone/Tversky study we just examined (known as “GVT” in psychology circles) kicked off a 20-year-long sports argument.  Researches replicated GVT’s basketball studies, taking into account more and more minute variables into their analyses.  Other researchers went into baseball, tennis, golf, mini-golf, darts, bowling, and horseshoes.  We found hardly a study looking for what we were looking for; the mental processes that cause people to commit the fallacy – mental processes that could be exploited.

And then we found Alter and Oppenheimer, 2006.  It’s not a study; it’s a review of the all the work done by cognitive psychologists on the hot hands fallacy since GVT.  Based on their reviews, the authors make this claim:

“…when people assume that a process is random, they expect a more rapid alternation between outcomes than stochastic [randomly determined] modelling would suggest (Falk & Konold, 1997)…Whereas people expect coin tosses to be random, they are willing to entertain the possibility that streaky performance in a human-driven domain like basketball implies a degree of skill…once people decide that a basketball player has violated the assumptions of randomness, his skill is attributed to a ‘hot hand.’” (Alter & Oppenheimer, 2006).

Is this true? If yes, then we must update the advice we gave you back in April.  Yes, continue rewarding your underlings randomly using the coin-toss approach (or any other random method of your choosing).  But make sure they know what’s going on.  If they know they’re being rewarded randomly, they will commit the gambler’s fallacy as planned.  But if they are blind to the process, they’ll give you trouble; each time you repeatedly reward them (heads followed by heads followed by heads, etc.), they will expect you to continue this reward “streak” and will work less hard or more slowly.  The same applies if you repeatedly ignore them (tails followed by tails followed by tails, etc.); they’ll just assume you’re done being generous.  Don’t fall into these traps; inform them that it’s random, and you’ll keep them busy and compliant.

Or so we think.  We still have work to do on this because Alter’s and Oppenheimer’s theory needs hard evidence.  But for now, just to be safe, we’ll take it at face-value.  Make sure your minions know that the coin, not you, is calling the shots.

Sources

Gilovich, T., et al. (1985). The Hot Hand in Basketball: On the Misperception of Random Sequences. Cognitive Psychology, 17, 295-314.
Alter, A.L., and Oppenheimer, D.M. (2006). From a fixation on sports to an exploration of mechanism: The past, present, and future of hot hand research. Thinking and Reasoning, 12(4), 431-444.

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