Tag: Daniel Kahneman

The Psychology of Risk and Reward

The Psychology of Risk and Reward

An excerpt from The Aspirational Investor: Taming the Markets to Achieve Your Life’s Goals that I think you’d enjoy.

Most of us have a healthy understanding of risk in the short term.

When crossing the street, for example, you would no doubt speed up to avoid an oncoming car that suddenly rounds the corner.

Humans are wired to survive: it’s a basic instinct that takes command almost instantly, enabling our brains to resolve ambiguity quickly so that we can take decisive action in the face of a threat.

The impulse to resolve ambiguity manifests itself in many ways and in many contexts, even those less fraught with danger. Glance at the (above) picture for no more than a couple of seconds. What do you see?

Some observers perceive the profile of a young woman with flowing hair, an elegant dress, and a bonnet. Others see the image of a woman stooped in old age with a wart on her large nose. Still others—in the gifted minority—are able to see both of the images simultaneously.

What is interesting about this illusion is that our brains instantly decide what image we are looking at, based on our first glance. If your initial glance was toward the vertical profile on the left-hand side, you were all but destined to see the image of the elegant young woman: it was just a matter of your brain interpreting every line in the picture according to the mental image that you already formed, even though each line can be interpreted in two different ways. Conversely, if your first glance fell on the central dark horizontal line that emphasizes the mouth and chin, your brain quickly formed an image of the older woman.

Regardless of your interpretation, your brain wasn’t confused. It simply decided what the picture was and filled in the missing pieces. Your brain resolved ambiguity and extracted order from conflicting information.

What does this have to do with decision making? Every bit of information can be interpreted differently according to our perspective. Ashvin Chhabra directs us to investing. I suggest you reframe this in the context of decision making in general.

Every trade has a seller and a buyer: your state of mind is paramount. If you are in a risk-averse mental framework, then you are likely to interpret a further fall in stocks as additional confirmation of your sell bias. If instead your framework is positive, you will interpret the same event as a buying opportunity.

The challenge of investing is compounded by the fact that our brains, which excel at resolving ambiguity in the face of a threat, are less well equipped to navigate the long term intelligently. Since none of us can predict the future, successful investing requires planning and discipline.

Unfortunately, when reason is in apparent conflict with our instincts—about markets or a “hot stock,” for example—it is our instincts that typically prevail. Our “reptilian brain” wins out over our “rational brain,” as it so often does in other facets of our lives. And as we have seen, investors trade too frequently, and often at the wrong time.

One way our brains resolve conflicting information is to seek out safety in numbers. In the animal kingdom, this is called “moving with the herd,” and it serves a very important purpose: helping to ensure survival. Just as a buffalo will try to stay with the herd in order to minimize its individual vulnerability to predators, we tend to feel safer and more confident investing alongside equally bullish investors in a rising market, and we tend to sell when everyone around us is doing the same. Even the so-called smart money falls prey to a herd mentality: one study, aptly titled “Thy Neighbor’s Portfolio,” found that professional mutual fund managers were more likely to buy or sell a particular stock if other managers in the same city were also buying or selling.

This comfort is costly. The surge in buying activity and the resulting bullish sentiment is self-reinforcing, propelling markets to react even faster. That leads to overvaluation and the inevitable crash when sentiment reverses. As we shall see, such booms and busts are characteristic of all financial markets, regardless of size, location, or even the era in which they exist.

Even though the role of instinct and human emotions in driving speculative bubbles has been well documented in popular books, newspapers, and magazines for hundreds of years, these factors were virtually ignored in conventional financial and economic models until the 1970s.

This is especially surprising given that, in 1951, a young PhD student from the University of Chicago, Harry Markowitz, published two very important papers. The first, entitled “Portfolio Selection,” published in the Journal of Finance, led to the creation of what we call modern portfolio theory, together with the widespread adoption of its important ideas such as asset allocation and diversification. It earned Harry Markowitz a Nobel Prize in Economics.

The second paper, entitled “The Utility of Wealth” and published in the prestigious Journal of Political Economy, was about the propensity of people to hold insurance (safety) and to buy lottery tickets at the same time. It delved deeper into the psychological aspects of investing but was largely forgotten for decades.

The field of behavioral finance really came into its own through the pioneering work of two academic psychologists, Amos Tversky and Daniel Kahneman, who challenged conventional wisdom about how people make decisions involving risk. Their work garnered Kahneman the Nobel Prize in Economics in 2002. Behavioral finance and neuroeconomics are relatively new fields of study that seek to identify and understand human behavior and decision making with regard to choices involving trade-offs between risk and reward. Of particular interest are the human biases that prevent individuals from making fully rational financial decisions in the face of uncertainty.

As behavioral economists have documented, our propensity for herd behavior is just the tip of the iceberg. Kahneman and Tversky, for example, showed that people who were asked to choose between a certain loss and a gamble, in which they could either lose more money or break even, would tend to choose the double down (that is, gamble to avoid the prospect of losses), a behavior the authors called “loss aversion.” Building on this work, Hersh Shefrin and Meir Statman, professors at the University of Santa Clara Leavey School of Business, have linked the propensity for loss aversion to investors’ tendency to hold losing investments too long and to sell winners too soon. They called this bias the disposition effect.

The lengthy list of behaviorally driven market effects often converge in an investor’s tale of woe. Overconfidence causes investors to hold concentrated portfolios and to trade excessively, behaviors that can destroy wealth. The illusion of control causes investors to overestimate the probability of success and underestimate risk because of familiarity—for example, causing investors to hold too much employer stock in their 401(k) plans, resulting in under-diversification. Cognitive dissonance causes us to ignore evidence that is contrary to our opinions, leading to myopic investing behavior. And the representativeness bias leads investors to assess risk and return based on superficial characteristics—for example, by assuming that shares of companies that make products you like are good investments.

Several other key behavioral biases come into play in the realm of investing. Framing can cause investors to make a decision based on how the question is worded and the choices presented. Anchoring often leads investors to unconsciously create a reference point, say for securities prices, and then adjust decisions or expectations with respect to that anchor. This bias might impede your ability to sell a losing stock, for example, in the false hope that you can earn your money back. Similarly, the endowment bias might lead you to overvalue a stock that you own and thus hold on to the position too long. And regret aversion may lead you to avoid taking a tough action for fear that it will turn out badly. This can lead to decision paralysis in the wake of a market crash, even though, statistically, it is a good buying opportunity.

Behavioral finance has generated plenty of debate. Some observers have hailed the field as revolutionary; others bemoan the discipline’s seeming lack of a transcendent, unifying theory. This much is clear: behavioral finance treats biases as mistakes that, in academic parlance, prevent investors from thinking “rationally” and cause them to hold “suboptimal” portfolios.

But is that really true? In investing, as in life, the answer is more complex than it appears. Effective decision making requires us to balance our “reptilian brain,” which governs instinctive thinking, with our “rational brain,” which is responsible for strategic thinking. Instinct must integrate with experience.

Put another way, behavioral biases are nothing more than a series of complex trade-offs between risk and reward. When the stock market is taking off, for example, a failure to rebalance by selling winners is considered a mistake. The same goes for a failure to add to a position in a plummeting market. That’s because conventional finance theory assumes markets to be inherently stable, or “mean-reverting,” so most deviations from the historical rate of return are viewed as fluctuations that will revert to the mean, or self-correct, over time.

But what if a precipitous market drop is slicing into your peace of mind, affecting your sleep, your relationships, and your professional life? What if that assumption about markets reverting to the mean doesn’t hold true and you cannot afford to hold on for an extended period of time? In both cases, it might just be “rational” to sell and accept your losses precisely when investment theory says you should be buying. A concentrated bet might also make sense, if you possess the skill or knowledge to exploit an opportunity that others might not see, even if it flies in the face of conventional diversification principles.

Of course, the time to create decision rules for extreme market scenarios and concentrated bets is when you are building your investment strategy, not in the middle of a market crisis or at the moment a high-risk, high-reward opportunity from a former business partner lands on your desk and gives you an adrenaline jolt. A disciplined process for managing risk in relation to a clear set of goals will enable you to use the insights offered by behavioral finance to your advantage, rather than fall prey to the common pitfalls. This is one of the central insights of the Wealth Allocation Framework. But before we can put these insights to practical use, we need to understand the true nature of financial markets.

Focusing Illusions

focusing illusions

My favorite chapter in the book Rapt: Attention and the Focused Life by Winifred Gallagher is called ‘Decisions: Focusing Illusions.’ It’s a really great summary of how focusing on the wrong things affects the weights we use to make decisions. There is a lot of great content packed into this chapter but I’ll attempt to highlight a few points.

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Bounded Rationality

According to the principle of ‘bounded rationality,’ which (Daniel) Kahneman first applied to economic decisions and more recently to choices concerning quality of life, we are reasonable-enough beings but sometimes liable to focus on the wrong things. Our thinking gets befuddled not so much by our emotions as by our ‘cognitive illusions,’ or mistaken intuitions, and other flawed, fragmented mental constructs.

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Loss/Risk Aversion

If you’re pondering a choice that involves risk, you might focus too much on the threat of possible loss, thereby obscuring an even likelier potential benefit. Where this common scenario is concerned, research shows that we aren’t so much risk-averse as loss-averse, in that we’re generally much more sensitive to what we might have to give up than to what we might gain.

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The Focusing Illusion

The key to understanding why you pay more attention to your thoughts about living than to life itself is neatly summed up by what Kahneman proudly calls his ‘fortune cookie maxim’ (a.k.a the focusing illusion): ‘Nothing in life is as important as you think it is while you are thinking about it.’ Why? ‘Because you’re thinking about it!

In one much-cited illustration of the focusing illusion, Kahneman asked some people if they would be happier if they lived in California. Because the climate is often delightful there, most subjects thought so. For the same reason, even Californians assume they’re happier than people who live elsewhere. When Kahneman actually measured their well-being however, Michiganders and others are just as contented as Californians. The reason is that 99 percent of the stuff of life – relationships, work, home, recreation – is the same no matter where you are, and once you settle in a place, no matter how salubrious, you don’t think about it’s climate very much. If you’re prompted to evaluate it, however, the weather immediately looms large, simply because you’re paying attention to it. This illusion inclines you to accentuate the difference between Place A and Place B, making it seem to matter much more than it really does, which is marginal.

To test the fortune cookie rule, you have only to ask yourself how happy you are. The question automatically summons your remembering self, which will focus on any recent change in your life – marriage or divorce, new job or home. You’ll then think about this novel event, which in turn will increase its import and influence your answer. If you’re pleased that you’ve just left the suburbs for the city, say, you’ll decide that life is pretty good. If you regret the move, you’ll be dissatisfied in general. Fifteen years on, however, the change that looms so large now will pale next to a more recent event – a career change, perhaps or becoming a grandparent – which will draw your focus and, simply because you’re thinking about it, bias your evaluation of your general well-being.

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The Effects of Adaptation

Like focusing too much on the opinions of your remembering self, overlooking the effects of adaptation – the process of becoming used to a situation – can obstruct wise decisions about how to live. As Kahneman says, ‘when planning for the future, we don’t consider that we will stop paying attention to a thing.

The tendency to stop focusing on a particular event or experience over time, no matter how wonderful or awful, helps explain why the differences in well-being between groups of people in very different circumstances tend to be surprisingly small – sometimes astoundingly so. The classic examples are paraplegics and lottery winners, who respectively aren’t nearly as miserable or happy as you’d think. ‘That’s where attention comes in,’ says Kahneman. ‘People think that if they win the lottery, they’ll be happy forever. Of course, they will not. For a while, they are happy because of the novelty, and because they think about winning all the time. Then they adapt and stop paying attention to it.’ Similarly, he says, ‘Everyone is surprised by how happy paraplegics can be, but they are not paraplegic full-time. They do other things. They enjoy their meals, their friends, the newspaper. It has to do with the allocation of attention.’

Like couples who’ve just fallen in love, professionals starting a career, or children who go to camp for the first time, paraplegics and lottery winners initially pay a lot of attention to their new situation. Then, like everybody else, they get used to it and shift their focus to the next big thing. Their seemingly blase attitude surprises us, because when we imagine ourselves in their place, we focus on how we’d feel at the moment of becoming paralyzed or wildly rich, when such an event utterly monopolizes one’s focus. We forget that we, too, would get used to wealth, a wheelchair, and most other things under the sun, then turn our attention elsewhere.

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Good Enough

Finally, don’t worry if the choice you made wasn’t the absolute best, as long as it meets your needs. Offering the single most important lesson from his research, Schwartz says, ‘Good enough is almost always good enough. If you have that attitude, many problems about decisions and much paralysis melt away.’

Mental Model: Misconceptions of Chance

We expect the immediate outcome of events to represent the broader outcomes expected from a large number of trials. We believe that chance events will immediately self-correct and that small sample sizes are representative of the populations from which they are drawn. All of these beliefs lead us astray.

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Our understanding of the world around us is imperfect, and when dealing with chance, our brains tend to come up with ways to cope with the unpredictable nature of our world.

“We tend,” writes Peter Bevelin in Seeking Wisdom, “to believe that the probability of an independent event is lowered when it has happened recently or that the probability is increased when it hasn’t happened recently.”

In short, we believe an outcome is due, and that chance will self-correct. The problem with this view is that nature doesn’t have a sense of fairness or memory. We only fool ourselves when we mistakenly believe that independent events offer influence or meaningful predictive power over future events.

Furthermore, we also mistakenly believe that we can control chance events. This applies to risky or uncertain events.

Chance events, coupled with positive reinforcement or negative reinforcement, can be a dangerous thing. Sometimes we become optimistic and think our luck will change, and sometimes we become overly pessimistic or risk-averse.

How do you know if you’re dealing with chance? A good heuristic is to ask yourself if you can lose on purpose. If you can’t, you’re likely far into the chance side of the skill vs. luck continuum. No matter how hard you practice, the probability of chance events won’t change.

“We tend,” writes Nassim Taleb in The Black Swan, “to underestimate the role of luck in life in general (and) overestimate it in games of chance.”

We are only discussing independent events. If events are dependent, where the outcome depends on the outcome of some other event, all bets are off.

Misconceptions of Chance

Daniel Kahneman coined the term misconceptions of chance to describe the phenomenon of people extrapolating large-scale patterns to samples of a much smaller size. Our trouble navigating the sometimes counterintuitive laws of probability, randomness, and statistics leads to misconceptions of chance.

Kahneman found that “people expect that a sequence of events generated by a random process will represent the essential characteristics of that process even when the sequence is short.”

In the paper, Belief in the Law of Small Numbers, Kahneman and Tversky reflect on the results of an experiment, where subjects were instructed to generate a random sequence of hypothetical tosses of a fair coin.

They [the subjects] produce sequences where the proportion of heads in any short segment stays far closer to .50 than the laws of chance would predict. Thus, each segment of the response sequence is highly representative of the “fairness” of the coin.

Unsurprisingly, the same nature of errors occurred when the subjects, instead of being asked to generate sequences themselves, were simply asked to distinguish between random and human-generated sequences. It turns out that when considering tosses of a coin for heads or tails people regard the sequence H-T-H-T-T-H to be more likely than the sequence H-H-H-T-H-T, which does not appear random, and also more likely than the sequence H-H-H-H-T-H. In reality, each one of those sequences has the exact same probability of occurring. This is a misconception of chance.

The aspect that most of us find so hard to grasp about this case is that any pattern of the same length is just as likely to occur in a random sequence. For example, the odds of getting 5 tails in a row are 0.03125 or simply stated 0.5 (the odds of a specific outcome at each trial) to the power of 5 (number of trials).

The same probability rule applies for getting the specific sequences of HHTHT or THTHT – where each sequence is obtained by once again taking 0.5 (the odds of a specific outcome at each trial) to the power of 5 (number of trials), which equals 0.03125.

This probability is true for sequences – but it implies no relation between the odds of a specific outcome at each trial and the representation of the true proportion within these short sequences.

Yet it’s still surprising. This is because people expect that the single event odds will be reflected not only in the proportion of events as a whole but also in the specific short sequences we encounter. But this is not the case. A perfectly alternating sequence is just as extraordinary as a sequence with all tails or all heads.

In comparison, “a locally representative sequence,” Kahneman writes, in Thinking, Fast and Slow, “deviates systematically from chance expectation: it contains too many alternations and too few runs. Another consequence of the belief in local representativeness is the well-known gambler’s fallacy.”

Gambler’s Fallacy

There is a specific variation of the misconceptions of chance that Kahneman calls the Gambler’s fallacy (elsewhere also called the Monte Carlo fallacy).

The gambler’s fallacy implies that when we come across a local imbalance, we expect that the future events will smoothen it out. We will act as if every segment of the random sequence must reflect the true proportion and, if the sequence has deviated from the population proportion, we expect the imbalance to soon be corrected.

Kahneman explains that this is unreasonable – coins, unlike people, have no sense of equality and proportion:

The heart of the gambler’s fallacy is a misconception of the fairness of the laws of chance. The gambler feels that the fairness of the coin entitles him to expect that any deviation in one direction will soon be cancelled by a corresponding deviation in the other. Even the fairest of coins, however, given the limitations of its memory and moral sense, cannot be as fair as the gambler expects it to be.

He illustrates this with an example of the roulette wheel, and our expectations when a reasonably long sequence of repetition occurs.

After observing a long run of red on the roulette wheel, most people erroneously believe that black is now due, presumably because the occurrence of black will result in a more representative sequence than the occurrence of an additional red.

In reality, of course, roulette is a random, non-evolving process, in which the chance of getting a red or a black will never depend on the past sequence. The probabilities restore after each run, yet we still seem to take the past moves into account.

Contrary to our expectations, the universe does not keep an accounting of a random process, so streaks are not necessarily tilted towards the true proportion. Your chance of getting a red after a series of blacks will always be equal to that of getting another red as long as the wheel is fair.

The gambler’s fallacy need not to be committed inside the casino only. Many of us commit it frequently by thinking that a small, random sample will tend to correct itself.

For example, assume that the average IQ at a specific country is known to be 100. And for the purposes of assessing intelligence at a specific district, we draw a random sample of 50 persons. The first person in our sample happens to have an IQ of 150. What would you expect the mean IQ to be for the whole sample?

The correct answer is (100*49 + 150*1)/50 = 101. Yet without knowing the correct answer, it is tempting to say it is still 100 – the same as in the country as a whole.

According to Kahneman and Tversky, such expectation could only be justified by the belief that a random process is self-correcting and that the sample variation is always proportional. They explain:

Idioms such as “errors cancel each other out” reflect the image of an active self-correcting process. Some familiar processes in nature obey such laws: a deviation from a stable equilibrium produces a force that restores the equilibrium.

Indeed, this may be true in thermodynamics, chemistry, and arguably also economics. These, however, are false analogies. It is important to realize that the laws governed by chance are not guided by principles of equilibrium, and the number of random outcomes in a sequence does not have a common balance.

“Chance,” Kahneman writes in Thinking, Fast and Slow, “is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. In fact, deviations are not “corrected” as a chance process unfolds, they are merely diluted.”

The Law of Small Numbers

Misconceptions of chance are not limited to gambling. In fact, most of us fall for them all the time because we intuitively believe (and there is a whole best-seller section at the bookstore to prove) that inferences drawn from small sample sizes are highly representative of the populations from which they are drawn.

By illustrating people’s expectations of random heads and tails sequences, we already established that we have preconceived notions of what randomness looks like. This, coupled with the unfortunate tendency to believe in the self-correcting process in a random sample, generates expectations about sample characteristics and representativeness, which are not necessarily true. The expectation that the patterns and characteristics within a small sample will be representative of the population as a whole is called the law of small numbers.

Consider the sequence:

1, 2, 3, _, _, _

What do you think are the next three digits?

The task almost seems laughable because the pattern is so familiar and obvious – 4,5,6. However, there is an endless variation of different algorithms that would still fit the first three numbers, such as the Fibonacci sequence (5, 8, 13), a repeated sequence (1,2,3), a random sequence (5,8,2) and many others. Truth is, in this case, there simply is not enough information to say what the rules governing this specific sequence are with any reliability.

The same rule applies to sampling problems – sometimes, we feel we have gathered enough data to tell a real pattern from an illusion. Let me illustrate this fallacy with yet another example.

Imagine that you face a tough decision between investing in the development of two different product opportunities. Let’s call them Product A or Product B. You are interested in which product would appeal to the majority of the market, so you decide to conduct customer interviews. Out of the first five pilot interviews, four customers show a preference for Product A. While the sample size is quite small, given the time pressure involved, many of us would already have some confidence in concluding that the majority of customers would prefer Product A.

However, a quick statistical test will tell you that the probability of a result just as extreme is, in fact 3/8, assuming that there is no preference among customers at all. This in simple terms, means that if customers had no preference between Products A and B, you would still expect 3 customer samples out of 8 to have four customers vouching for Product A.

Basically, a study of such size has little to no predictive validity – these results could easily be obtained from a population with no preference for one or the other product. This, of course, does not mean that talking to customers is of no value. Quite the contrary – the more random cases we examine, the more reliable and accurate the results of the true proportion will be. If we want absolute certainty, we must be prepared for a lot of work.

There will always be cases where a guesstimate based on a small sample will be enough because we have other critical information guiding the decision-making process or we simply do not need a high degree of confidence. Yet rather than assuming that the samples we come across are always perfectly representative, we must treat random selection with the suspicion it deserves. Accepting the role imperfect information and randomness play in our lives and being actively aware of what we don’t know already makes us better decision-makers.

Regression Toward the Mean: An Introduction with Examples

Regression to the mean is a common statistical phenomenon that can mislead us when we observe the world. Learning to recognize when regression to the mean is at play can help us avoid misinterpreting data and seeing patterns that don’t exist.

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It is important to minimize instances of bad judgment and address the weak spots in our reasoning. Learning about regression to the mean can help us.

Nobel prize-winning psychologist Daniel Kahneman wrote a book about biases that cloud our reasoning and distort our perception of reality. It turns out there is a whole set of logical errors that we commit because our intuition and brains do not deal well with simple statistics. One of the errors that he examines in Thinking Fast and Slow is the infamous regression toward the mean.

The notion of regression to the mean was first worked out by Sir Francis Galton. The rule goes that, in any series with complex phenomena that are dependent on many variables, where chance is involved, extreme outcomes tend to be followed by more moderate ones.

In Seeking Wisdom, Peter Bevelin offers the example of John, who was dissatisfied with the performance of new employees so he put them into a skill-enhancing program where he measured the employees’ skill:

Their scores are now higher than they were on the first test. John’s conclusion: “The skill-enhancing program caused the improvement in skill.” This isn’t necessarily true. Their higher scores could be the result of regression to the mean. Since these individuals were measured as being on the low end of the scale of skill, they would have shown an improvement even if they hadn’t taken the skill-enhancing program. And there could be many reasons for their earlier performance — stress, fatigue, sickness, distraction, etc. Their true ability perhaps hasn’t changed.

Our performance always varies around some average true performance. Extreme performance tends to get less extreme the next time. Why? Testing measurements can never be exact. All measurements are made up of one true part and one random error part. When the measurements are extreme, they are likely to be partly caused by chance. Chance is likely to contribute less on the second time we measure performance.

If we switch from one way of doing something to another merely because we are unsuccessful, it’s very likely that we do better the next time even if the new way of doing something is equal or worse.

This is one of the reasons it’s dangerous to extrapolate from small sample sizes, as the data might not be representative of the distribution. It’s also why James March argues that the longer someone stays in their job, “the less the probable difference between the observed record of performance and actual ability.” Anything can happen in the short run, especially in any effort that involves a combination of skill and luck. (The ratio of skill to luck also impacts regression to the mean.)

“Regression to the mean is not a natural law. Merely a statistical tendency. And it may take a long time before it happens.”

— Peter Bevelin

Regression to the Mean

The effects of regression to the mean can frequently be observed in sports, where the effect causes plenty of unjustified speculations.

In Thinking Fast and Slow, Kahneman recalls watching men’s ski jump, a discipline where the final score is a combination of two separate jumps. Aware of the regression to the mean, Kahneman was startled to hear the commentator’s predictions about the second jump. He writes:

Norway had a great first jump; he will be tense, hoping to protect his lead and will probably do worse” or “Sweden had a bad first jump and now he knows he has nothing to lose and will be relaxed, which should help him do better.

Kahneman points out that the commentator had noticed the regression to the mean and come up with a story for which there was no causal evidence (see narrative fallacy). This is not to say that his story could not be true. Maybe, if we measured the heart rates before each jump, we would see that they are more relaxed if the first jump was bad. However, that’s not the point. The point is, regression to the mean happens when luck plays a role, as it did in the outcome of the first jump.

The lesson from sports applies to any activity where chance plays a role. We often attach explanations of our influence over a particular process to the progress or lack of it.

In reality, the science of performance is complex, situation dependent and often much of what we think is within our control is truly random.

In the case of ski jumps, a strong wind against the jumper will lead to even the best athlete showing mediocre results. Similarly, a strong wind and ski conditions in favor of a mediocre jumper may lead to a considerable, but a temporary bump in his results. These effects, however, will disappear once the conditions change and the results will regress back to normal.

This can have serious implications for coaching and performance tracking. The rules of regression suggest that when evaluating performance or hiring, we must rely on track records more than outcomes of specific situations. Otherwise, we are prone to be disappointed.

When Kahneman was giving a lecture to Israeli Air Force about the psychology of effective training, one of the officers shared his experience that extending praise to his subordinates led to worse performance, whereas scolding led to an improvement in subsequent efforts. As a consequence, he had grown to be generous with negative feedback and had become rather wary of giving too much praise.

Kahneman immediately spotted that it was regression to the mean at work. He illustrated the misconception by a simple exercise you may want to try yourself. He drew a circle on a blackboard and then asked the officers one by one to throw a piece of chalk at the center of the circle with their backs facing the blackboard. He then repeated the experiment and recorded each officer’s performance in the first and second trial.

Naturally, those that did incredibly well on the first try tended to do worse on their second try and vice versa. The fallacy immediately became clear: the change in performance occurs naturally. That again is not to say that feedback does not matter at all – maybe it does, but the officer had no evidence to conclude it did.

The Imperfect Correlation and Chance

At this point, you might be wondering why the regression to the mean happens and how we can make sure we are aware of it when it occurs.

In order to understand regression to the mean, we must first understand correlation.

The correlation coefficient between two measures which varies between -1 and 1, is a measure of the relative weight of the factors they share. For example, two phenomena with few factors shared, such as bottled water consumption versus suicide rate, should have a correlation coefficient of close to 0. That is to say, if we looked at all countries in the world and plotted suicide rates of a specific year against per capita consumption of bottled water, the plot would show no pattern at all.

no correlation
No Correlation

On the contrary, there are measures which are solely dependent on the same factor. A good example of this is temperature. The only factor determining temperature – velocity of molecules — is shared by all scales, hence each degree in Celsius will have exactly one corresponding value in Fahrenheit. Therefore temperature in Celsius and Fahrenheit will have a correlation coefficient of 1 and the plot will be a straight line.

Perfect Correlation
Perfect Correlation

There are few if any phenomena in human sciences that have a correlation coefficient of 1. There are, however, plenty where the association is weak to moderate and there is some explanatory power between the two phenomena. Consider the correlation between height and weight, which would land somewhere between 0 and 1. While virtually every three-year-old will be lighter and shorter than every grown man, not all grown men or three-year-olds of the same height will weigh the same.

Weak Correlation
Weak to Moderate Correlation

This variation and the corresponding lower degree of correlation implies that, while height is generally speaking a good predictor, there clearly are factors other than the height at play. When the correlation of two measures is less than perfect, we must watch out for the effects of regression to the mean.

Kahneman observed a general rule: Whenever the correlation between two scores is imperfect, there will be regression to the mean.

This at first might seem confusing and not very intuitive, but the degree of regression to the mean is directly related to the degree of correlation of the variables. This effect can be illustrated with a simple example.

Assume you are at a party and ask why it is that highly intelligent women tend to marry men who are less intelligent than they are. Most people, even those with some training in statistics, will quickly jump in with a variety of causal explanations ranging from avoidance of competition to the fears of loneliness that these females face. A topic of such controversy is likely to stir up a great debate.

Now, what if we asked why the correlation between the intelligence scores of spouses is less than perfect? This question is hardly as interesting and there is little to guess – we all know this to be true. The paradox lies in the fact that the two questions happen to be algebraically equivalent. Kahneman explains:

[…] If the correlation between the intelligence of spouses is less than perfect (and if men and women on average do not differ in intelligence), then it is a mathematical inevitability that highly intelligent women will be married to husbands who are on average less intelligent than they are (and vice versa, of course). The observed regression to the mean cannot be more interesting or more explainable than the imperfect correlation.

Assuming that correlation is imperfect, the chances of two partners representing the top 1% in terms of any characteristic is far smaller than one partner representing the top 1% and the other – the bottom 99%.

The Cause, Effect, and Treatment

We should be especially wary of the regression to the mean phenomenon when trying to establish causality between two factors. Whenever correlation is imperfect, the best will always appear to get worse and the worst will appear to get better over time, regardless of any additional treatment. This is something that the general media and sometimes even trained scientists fail to recognize.

Consider the example Kahneman gives:

Depressed children treated with an energy drink improve significantly over a three-month period. I made up this newspaper headline, but the fact it reports is true: if you treated a group of depressed children for some time with an energy drink, they would show a clinically significant improvement. It is also the case that depressed children who spend some time standing on their head or hug a cat for twenty minutes a day will also show improvement.

Whenever coming across such headlines it is very tempting to jump to the conclusion that energy drinks, standing on the head or hugging cats are all perfectly viable cures for depression. These cases, however, once again embody the regression to the mean:

Depressed children are an extreme group, they are more depressed than most other children—and extreme groups regress to the mean over time. The correlation between depression scores on successive occasions of testing is less than perfect, so there will be regression to the mean: depressed children will get somewhat better over time even if they hug no cats and drink no Red Bull.

We often mistakenly attribute a specific policy or treatment as the cause of an effect, when the change in the extreme groups would have happened anyway. This presents a fundamental problem: how can we know if the effects are real or simply due to variability?

Luckily there is a way to tell between a real improvement and regression to the mean. That is the introduction of the so-called control group, which is expected to improve by regression alone. The aim of the research is to determine whether the treated group improve more than regression can explain.

In real life situations with the performance of specific individuals or teams, where the only real benchmark is the past performance and no control group can be introduced, the effects of regression can be difficult if not impossible to disentangle. We can compare against industry average, peers in the cohort group or historical rates of improvement, but none of these are perfect measures.

***

Luckily awareness of the regression to the mean phenomenon itself is already a great first step towards a more careful approach to understanding luck and performance.

If there is anything to be learned from the regression to the mean it is the importance of track records rather than relying on one-time success stories. I hope that the next time you come across an extreme quality in part governed by chance you will realize that the effects are likely to regress over time and will adjust your expectations accordingly.

What to Read Next

Daniel Kahneman Explains The Machinery of Thought


Israeli-American psychologist and Nobel Laureate Daniel Kahneman is the founding father of modern behavioral economics. His work has influenced how we see thinking, decisions, risk, and even happiness.

In Thinking, Fast and Slow, his “intellectual memoir,” he shows us in his own words some of his enormous body of work.

Part of that body includes a description of the “machinery of … thought,” which divides the brain into two agents, called System 1 and System 2, which “respectively produce fast and slow thinking.” For our purposes, these can also be thought of as intuitive and deliberate thought.

The Two Systems of Thinking

Psychologists have been intensely interested for several decades in the two modes of thinking evoked by the picture of the angry woman and by the multiplication problem, and have offered many labels for them. I adopt terms originally proposed by the psychologists Keith Stanovich and Richard West, and will refer to two systems in the mind, System 1 and System 2.

  • System 1 operates automatically and quickly, with little or no effort and no sense of voluntary control.
  • System 2 allocates attention to the effortful mental activities that demand it, including complex computations. The operations of System 2 are often associated with the subjective experience of agency, choice, and concentration.

If asked to pick which thinker we are, we pick system 2. However, as Kahneman points out:

The automatic operations of System 1 generate surprisingly complex patterns of ideas, but only the slower System 2 can construct thoughts in an orderly series of steps . I also describe circumstances in which System 2 takes over, overruling the freewheeling impulses and associations of System 1. You will be invited to think of the two systems as agents with their individual abilities, limitations, and functions.

System One: Quick

These vary by individual and are often “innate skills that we share with other animals.”

We are born prepared to perceive the world around us, recognize objects, orient attention, avoid losses, and fear spiders. Other mental activities become fast and automatic through prolonged practice. System 1 has learned associations between ideas (the capital of France?); it has also learned skills such as reading and understanding nuances of social situations. Some skills, such as finding strong chess moves, are acquired only by specialized experts. Others are widely shared. Detecting the similarity of a personality sketch to an occupational stereotype requires broad knowledge of the language and the culture, which most of us possess. The knowledge is stored in memory and accessed without intention and without effort.

System Two: Deliberate

This is when we do something that does not come naturally and requires some sort of continuous exertion.

In all these situations you must pay attention, and you will perform less well, or not at all, if you are not ready or if your attention is directed inappropriately.

Paying attention is not really the answer as that is mentally expensive and can make people “effectively blind, even to stimuli that normally attract attention.” This is the point of Christopher Chabris and Daniel Simons in their book The Invisible Gorilla. Not only are we blind to what is plainly obvious when someone points it out but we fail to see that we are blind in the first place.

The Division of Labour Between System One and Two

Systems 1 and 2 are both active whenever we are awake. System 1 runs automatically and System 2 is normally in a comfortable low-effort mode, in which only a fraction of its capacity is engaged. System 1 continuously generates suggestions for System 2: impressions, intuitions, intentions, and feelings. If endorsed by System 2, impressions and intuitions turn into beliefs, and impulses turn into voluntary actions. When all goes smoothly, which is most of the time, System 2 adopts the suggestions of System 1 with little or no modification. You generally believe your impressions and act on your desires, and that is fine— usually.

When System 1 runs into difficulty, it calls on System 2 to support more detailed and specific processing that may solve the problem of the moment. System 2 is mobilized when a question arises for which System 1 does not offer an answer, as probably happened to you when you encountered the multiplication problem 17 × 24. You can also feel a surge of conscious attention whenever you are surprised. System 2 is activated when an event is detected that violates the model of the world that System 1 maintains. In that world, lamps do not jump, cats do not bark, and gorillas do not cross basketball courts. The gorilla experiment demonstrates that some attention is needed for the surprising stimulus to be detected. Surprise then activates and orients your attention: you will stare, and you will search your memory for a story that makes sense of the surprising event. System 2 is also credited with the continuous monitoring of your own behavior—the control that keeps you polite when you are angry, and alert when you are driving at night. System 2 is mobilized to increased effort when it detects an error about to be made. Remember a time when you almost blurted out an offensive remark and note how hard you worked to restore control. In summary, most of what you (your System 2) think and do originates in your System 1, but System 2 takes over when things get difficult, and it normally has the last word.

The division of labor between System 1 and System 2 is highly efficient: it minimizes effort and optimizes performance. The arrangement works well most of the time because System 1 is generally very good at what it does: its models of familiar situations are accurate, its short-term predictions are usually accurate as well, and its initial reactions to challenges are swift and generally appropriate. System 1 has biases, however, systematic errors that it is prone to make in specified circumstances. As we shall see, it sometimes answers easier questions than the one it was asked, and it has little understanding of logic and statistics. One further limitation of System 1 is that it cannot be turned off.

[…]

Conflict between an automatic reaction and an intention to control it is common in our lives. We are all familiar with the experience of trying not to stare at the oddly dressed couple at the neighboring table in a restaurant. We also know what it is like to force our attention on a boring book, when we constantly find ourselves returning to the point at which the reading lost its meaning. Where winters are hard, many drivers have memories of their car skidding out of control on the ice and of the struggle to follow well-rehearsed instructions that negate what they would naturally do: “Steer into the skid, and whatever you do, do not touch the brakes!” And every human being has had the experience of not telling someone to go to hell. One of the tasks of System 2 is to overcome the impulses of System 1. In other words, System 2 is in charge of self-control.

[…]

The question that is most often asked about cognitive illusions is whether they can be overcome. The message of these examples is not encouraging. Because System 1 operates automatically and cannot be turned off at will, errors of intuitive thought are often difficult to prevent. Biases cannot always be avoided, because System 2 may have no clue to the error. Even when cues to likely errors are available, errors can be prevented only by the enhanced monitoring and effortful activity of System 2. As a way to live your life, however, continuous vigilance is not necessarily good, and it is certainly impractical. Constantly questioning our own thinking would be impossibly tedious, and System 2 is much too slow and inefficient to serve as a substitute for System 1 in making routine decisions. The best we can do is a compromise: learn to recognize situations in which mistakes are likely and try harder to avoid significant mistakes when the stakes are high. The premise of this book is that it is easier to recognize other people’s mistakes than our own.

Still Curious? Thinking, Fast and Slow is a tour-de-force when it comes to thinking.

A Discussion on the Work of Daniel Kahneman

Edge.org asked the likes of Christopher Chabris, Nicholas Epley, Jason Zweig, William Poundstone, Cass Sunstein, Phil Rosenzweig, Richard Thaler & Sendhil Mullainathan, Nassim Nicholas Taleb, Steven Pinker, and Rory Sutherland among others: “How has Kahneman’s work influenced your own? What step did it make possible?”

Kahneman’s work is summarized in the international best-seller Thinking, Fast and Slow.

Here are some select excerpts that I found interesting.

Christopher Chabris (author of The Invisible Gorilla)

There’s an overarching lesson I have learned from the work of Danny Kahneman, Amos Tversky, and their colleagues who collectively pioneered the modern study of judgment and decision-making: Don’t trust your intuition.

Jennifer Jacquet

After what I see as years of hard work, experiments of admirable design, lucid writing, and quiet leadership, Kahneman, a man who spent the majority of his career in departments of psychology, earned the highest prize in economics. This was a reminder that some of the best insights into economic behavior could be (and had been) gleaned outside of the discipline

Jason Zweig (author of Your Money and Your Brain)

… nothing amazed me more about Danny than his ability to detonate what we had just done.

Anyone who has ever collaborated with him tells a version of this story: You go to sleep feeling that Danny and you had done important and incontestably good work that day. You wake up at a normal human hour, grab breakfast, and open your email. To your consternation, you see a string of emails from Danny, beginning around 2:30 a.m. The subject lines commence in worry, turn darker, and end around 5 a.m. expressing complete doubt about the previous day’s work.

You send an email asking when he can talk; you assume Danny must be asleep after staying up all night trashing the chapter. Your cellphone rings a few seconds later. “I think I figured out the problem,” says Danny, sounding remarkably chipper. “What do you think of this approach instead?”

The next thing you know, he sends a version so utterly transformed that it is unrecognizable: It begins differently, it ends differently, it incorporates anecdotes and evidence you never would have thought of, it draws on research that you’ve never heard of. If the earlier version was close to gold, this one is hewn out of something like diamond: The raw materials have all changed, but the same ideas are somehow illuminated with a sharper shift of brilliance.

The first time this happened, I was thunderstruck. How did he do that? How could anybody do that? When I asked Danny how he could start again as if we had never written an earlier draft, he said the words I’ve never forgotten: “I have no sunk costs.”

William Poundstone (author of Are You Smart Enough To Work At Google?)

As a writer of nonfiction I’m often in the position of trying to connect the dots—to draw grand conclusions from small samples. Do three events make a trend? Do three quoted sources justify a conclusion? Both are maxims of journalism. I try to keep in mind Kahneman and Tversky’s Law of Small Numbers. It warns that small samples aren’t nearly so informative, in our uncertain world, as intuition counsels.

Cass R. Sunstein (Author, Why Nudge?)

These ideas are hardly Kahneman’s most well-known, but they are full of implications, and we have only started to understand them.

1. The outrage heuristic. People’s judgments about punishment are a product of outrage, which operates as a shorthand for more complex inquiries that judges and lawyers often think relevant. When people decide about appropriate punishment, they tend to ask a simple question: How outrageous was the underlying conduct? It follows that people are intuitive retributivists, and also that utilitarian thinking will often seem uncongenial and even outrageous.

2. Scaling without a modulus. Remarkably, it turns out that people often agree on how outrageous certain misconduct is (on a scale of 1 to 8), but also remarkably, their monetary judgments are all over the map. The reason is that people do not have a good sense of how to translate their judgments of outrage onto the monetary scale. As Kahneman shows, some work in psychophysics explains the problem: People are asked to “scale without a modulus,” and that is an exceedingly challenging task. The result is uncertainty and unpredictability. These claims have implications for numerous questions in law and policy, including the award of damages for pain and suffering, administrative penalties, and criminal sentences.

3. Rhetorical asymmetry. In our work on jury awards, we found that deliberating juries typically produce monetary awards against corporate defendants that are higher, and indeed much higher, than the median award of the individual jurors before deliberation began. Kahneman’s hypothesis is that in at least a certain category of cases, those who argue for higher awards have a rhetoric advantage over those who argue for lower awards, leading to a rhetorical asymmetry. The basic idea is that in light of social norms, one side, in certain debates, has an inherent advantage – and group judgments will shift accordingly. A similar rhetorical asymmetry can be found in groups of many kinds, in both private and public sectors, and it helps to explain why groups move.

4. Predictably incoherent judgments. We found that when people make moral or legal judgments in isolation, they produce a pattern of outcomes that they would themselves reject, if only they could see that pattern as a whole. A major reason is that human thinking is category-bound. When people see a case in isolation, they spontaneously compare it to other cases that are mainly drawn from the same category of harms. When people are required to compare cases that involve different kinds of harms, judgments that appear sensible when the problems are considered separately often appear incoherent and arbitrary in the broader context. In my view, Kahneman’s idea of predictable coherence has yet to be adequately appreciated; it bears on both fiscal policy and on regulation.

Phil Rosenzweig

For years, there were (as the old saying has it) two kinds of people: those relatively few of us who were aware of the work of Danny Kahneman and Amos Tversky, and the much more numerous who were not. Happily, the balance is now shifting, and more of the general public has been able to hear directly a voice that is in equal measures wise and modest.

Sendhil Mullainathan (Author of Scarcity: Why Having Too Little Means So Much)

… Kahneman and Tversky’s early work opened this door exactly because it was not what most people think it was. Many think of this work as an attack on rationality (often defined in some narrow technical sense). That misconception still exists among many, and it misses the entire point of their exercise. Attacks on rationality had been around well before Kahneman and Tversky—many people recognized that the simplifying assumptions of economics were grossly over-simplifying. Of course humans do not have infinite cognitive abilities. We are also not as strong as gorillas, as fast as cheetahs, and cannot swim like sea lions. But we do not therefore say that there is something wrong with humans. That we have limited cognitive abilities is both true and no more helpful to doing good social science that to acknowledge our weakness as swimmers. Pointing it out did it open any new doors.

Kahneman and Tversky’s work did not just attack rationality, it offered a constructive alternative: a better description of how humans think. People, they argued, often use simple rules of thumb to make judgments, which incidentally is a pretty smart thing to do. But this is not the insight that left us one step from doing behavioral economics. The breakthrough idea was that these rules of thumb could be catalogued. And once understood they can be used to predict where people will make systematic errors. Those two words are what made behavioral economics possible.

Nassim Taleb (Author of Antifragile)

Here is an insight Danny K. triggered and changed the course of my work. I figured out a nontrivial problem in randomness and its underestimation a decade ago while reading the following sentence in a paper by Kahneman and Miller of 1986:

A spectator at a weight lifting event, for example, will find it easier to imagine the same athlete lifting a different weight than to keep the achievement constant and vary the athlete’s physique.

This idea of varying one side, not the other also applies to mental simulations of future (random) events, when people engage in projections of different counterfactuals. Authors and managers have a tendency to take one variable for fixed, sort-of a numeraire, and perturbate the other, as a default in mental simulations. One side is going to be random, not the other.

It hit me that the mathematical consequence is vastly more severe than it appears. Kahneman and colleagues focused on the bias that variable of choice is not random. But the paper set off in my mind the following realization: now what if we were to go one step beyond and perturbate both? The response would be nonlinear. I had never considered the effect of such nonlinearity earlier nor seen it explicitly made in the literature on risk and counterfactuals. And you never encounter one single random variable in real life; there are many things moving together.

Increasing the number of random variables compounds the number of counterfactuals and causes more extremes—particularly in fat-tailed environments (i.e., Extremistan): imagine perturbating by producing a lot of scenarios and, in one of the scenarios, increasing the weights of the barbell and decreasing the bodyweight of the weightlifter. This compounding would produce an extreme event of sorts. Extreme, or tail events (Black Swans) are therefore more likely to be produced when both variables are random, that is real life. Simple.

Now, in the real world we never face one variable without something else with it. In academic experiments, we do. This sets the serious difference between laboratory (or the casino’s “ludic” setup), and the difference between academia and real life. And such difference is, sort of, tractable.

… Say you are the manager of a fertilizer plant. You try to issue various projections of the sales of your product—like the weights in the weightlifter’s story. But you also need to keep in mind that there is a second variable to perturbate: what happens to the competition—you do not want them to be lucky, invent better products, or cheaper technologies. So not only you need to predict your fate (with errors) but also that of the competition (also with errors). And the variance from these errors add arithmetically when one focuses on differences.

Rory Sutherland

When I met Danny in London in 2009 he diffidently said that the only hope he had for his work was that “it might lead to a better kind of gossip”—where people discuss each other’s motivations and behaviour in slightly more intelligent terms. To someone from an industry where a new flavour-variant of toothpaste is presented as being an earth-changing event, this seemed an incredibly modest aspiration for such important work.

However, if this was his aim, he has surely succeeded. When I meet people, I now use what I call “the Kahneman heuristic”. You simply ask people “Have you read Danny Kahneman’s book?” If the answer is yes, you know (p>0.95) that the conversation will be more interesting, wide-ranging and open-minded than otherwise.

And it then occurred to me that his aim—for better conversations—was perhaps not modest at all. Multiplied a millionfold it may very important indeed. In the social sciences, I think it is fair to say, the good ideas are not always influential and the influential ideas are not always good. Kahneman’s work is now both good and influential.