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The Danish Air Force, as luck would have it, had just the aircraft. As luck would have it, right in front of me were lawyers from the same firm representing the plaintiffs. It's all luck about Nanny's eyes; and maybe you are only throwing away a chance you'll never have again. We really ought to be dancing—but I'll try my luck once more on No. Greif's luck had saved him, and what was life to him was death to Rex.

In addition to the idioms beginning with luck. The popularity of this beloved game took off in the mids and has been an essential part of the canon of classic board games ever since. RELATED WORDS win , stroke , serendipity , happiness , prosperity , wealth , profit , kismet , health , smile , karma , blessing , advantage , weal , break , fluke , luckiness , godsend , opportunity , success. Nearby words lucite , lucius , lucius i , lucius ii , lucius iii , luck , luck into , luck of the devil , luck of the draw , luck out , luckie. Idioms down on one's luck , in unfortunate circumstances; unlucky: She hated to see her old friend so down on her luck.

In baseball, too, the best hitters only come to the plate a little more frequently than one in nine times. Soccer and American football also have a similar number of players active at any time, but the quarterback takes almost all of the snaps for a football team. So if the action filters through a skill player, it has an effect on the dynamics. The second aspect is sample size. As you learn early on in statistics class, small samples have larger variances than larger samples of the same system.

For instance, the variance in the ratio of girls to boys born at a hospital that delivers only a few babies a day will be much higher than the variance in a hospital that delivers hundreds a day. As larger sample sizes tend to weed out the influence of luck, they indicate skill more accurately. In sports, I looked at the number of possessions in a college basketball game versus a college lacrosse game.

Although lacrosse games are longer, the number of possessions in a basketball game is approximately double that of a lacrosse game. So that means that the more skillful team will win more of the time. Go back to baseball. A team can get lots of players on base through hits and walks, but have no players cross the plate, based on when the outs occur. In theory, one team could have 27 hits and score zero runs and another team can have one hit and win the game Basketball is the game that has the most skill. Football and baseball are not far from one another, but baseball teams play more than 10 times the games that football teams do.

Constitutive Luck

Baseball, in other words, is close to random — even after games the best teams only win about 60 percent of their games. Hockey, too, has an enormous amount of randomness. One interesting thought is that the National Basketball Association and National Hockey League have had lockouts in successive seasons. Both leagues play a regular schedule of 82 games. If the NHL season proceeds with a fraction of the normal number of games, the outcomes will be very random.

The Four Faces of Luck

Perhaps the very best teams will have some edge, but you can almost be assured that there will be some surprises. Arbesman: You devote some attention to the phenomenon of reversion to the mean. Most of us think we understand it, but are often wrong. What are ways we go wrong with this concept and why does this happen so often? Mauboussin: Your observation is spot on: When hearing about reversion to the mean, most people nod their heads knowingly. But if you observe people, you see case after case where they fail to account for reversion to the mean in their behavior.

It turns out that investors earn dollar-weighted returns that are less than the average return of mutual funds. At first blush it seems hard to see how investors can do worse than the funds they invest in.

Voltaire’s Luck | Lapham’s Quarterly

The insight is that investors tend to buy after the market has gone up — ignoring reversion to the mean — and sell after the market has gone down — again, ignoring reversion to the mean. The practice of buying high and selling low is what drives the dollar-weighted returns to be less than the average returns. This pattern is so well documented that academics call it the " dumb money effect.

Saying it differently, any time luck contributes to outcomes, you will have reversion to the mean. This is a statistical point that our minds grapple with. Reversion to the mean creates some illusions that trip us up. One is the illusion of causality.

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A famous example is the stature of fathers and sons. Tall fathers have tall sons, but the sons have heights that are closer to the average of all sons than their fathers do. Likewise, short fathers have short sons, but again the sons have stature closer to average than that of their fathers.

Few people are surprised when they hear this.

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So tall sons have tall fathers, but the height of the fathers is closer to the average height of all fathers. I guess the main point is that there is nothing so special about reversion to the mean, but our minds are quick to create a story that reflects some causality. Now say she comes home with an excellent grade, reflecting good skill and very good luck. What would be your natural reaction? But what is likely to happen on the next test?

Well, on average her luck will be neutral and she will have a lower score. Now your mind is going to naturally associate your positive feedback with a negative result. The same happens with negative feedback. Should your daughter come home with a poor grade reflecting bad luck, you might chide her and punish her by limiting her time on the computer.

Her next test will likely produce a better grade, irrespective of your sermon and punishment.

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The main thing to remember is that reversion to the mean happens solely as the result of randomness, and that attaching causes to random outcomes does not make sense. Examples include aging in athletics and competition in business. But the point is that randomness alone can drive the process. Arbesman: In your book you focus primarily on business, sports, and investing, but clearly skill and luck appear more widely in the world. In what other areas is a proper understanding of these two features important and often lacking?

Mauboussin: One area where this has a great deal of relevance is medicine. But he also showed that 80 percent of the results from observational studies are either wrong or exaggerated. The problem is that people hear about, and follow the advice of, these observational studies. Indeed, Ioannidis is so skeptical of the merit of observational studies that he, himself a physician, ignores them. One example I discuss in the book is a study that showed that women who eat breakfast cereal are more likely to give birth to a boy than a girl. This is the kind of story that the media laps up.

Statisticians later combed the data and concluded that the result is likely a product of chance. Arbesman: What are some of the ways that sampling including undersampling, biased sampling, and more can lead us quite astray when understanding skill and luck? Undersampling failure in business is a classic example. Companies select one or the other and the results show that companies that select the high-risk strategy either succeed wildly or fail. In other words, the high-risk strategy has a large variance in outcomes and the low-risk strategy has smaller variance.

Say a new company comes along and wants to determine which strategy is best. On examination, the high-risk strategy would look great because the companies that chose it and survived had great success while those that chose it and failed are dead, and hence are no longer in the sample. In contrast, since all of the companies that selected the low-risk strategy are still be around, their average performance looks worse. This is the classic case of undersampling failure. The question is: What were the results of all of the companies that selected each strategy? But this problem plagues a lot of business research.

The question is not: Were all successful companies hedgehogs? The question is: Were all hedgehogs successful? The second question undoubtedly yields a different answer than the first. One example, which I learned from Howard Wainer , relates to school size.

The Good Luck Fairy

Researchers studying primary and secondary education were interested in figuring out how to raise test scores for students. So they did something seemingly very logical — they looked at which schools have the highest test scores.

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  8. They found that the schools with the highest scores were small, which makes some intuitive sense because of smaller class sizes, etc. But this falls into a sampling trap. The next question to ask is: which schools have the lowest test scores? The answer: small schools. This is exactly what you would expect from a statistical viewpoint since small samples have large variances. So small schools have the highest and lowest test scores, and large schools have scores closer to the average.

    Since the researchers only looked a high scores, they missed the point. This is more than a case for a statistics class. Education reformers proceeded to spend billions of dollars reducing the sizes of schools. One large school in Seattle, for example, was broken into five smaller schools. It turns out that shrinking schools can actually be a problem because it leads to less specialization—for example, fewer advanced placement courses. Wainer calls the relationship between sample size and variance the " most dangerous equation " because it has tripped up some many researchers and decision makers over the years.

    Arbesman: Your discussion of the paradox of skill—that more skillful the population, the more luck plays a role—reminded me a bit of the Red Queen effect , where in evolution, organisms are constantly competing against other highly adapted organisms. Do you think there is any relationship? Mauboussin: Absolutely.

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    I think the critical distinction is between absolute and relative performance.