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.
Next Post in Series: Unpredictability: Hot Hands vs. Gambler’s Fallacies
