Although the exercise was presumably a lighthearted effort at attracting attention, the results raise a serious question: How can a group of amateurs do a better job of picking stocks than the majority of dedicated professionals? You would never expect amateurs to outperform professional dentists, accountants, or athletes over the course of a year. In this case, the answer lies in the fact that investing is an activity that depends to a great deal on luck, especially over a short period of time. In this chapter, I'll develop a simple model that will allow us to take a more in-depth look at the relative contributions of luck and skill. I'll also provide a framework for thinking about extreme outcomes and show how to anticipate the rate of reversion to the mean. A deeper discussion of the continuum between luck and skill can help us to avoid some of the mistakes described in chapters 1 and 2 and to make better decisions.
Sample Size, Not Time
Visualizing the continuum between luck and skill can help us to see where an activity lies between the two extremes, with pure luck on one side and pure skill on the other. In most cases, characterizing what's going on at the extremes is not too hard. As an example, you can't predict the outcome of a specific fair coin toss or payoff from a slot machine. They are entirely dependent on chance. On the other hand, the fastest swimmer will almost always win the race. The outcome is determined by skill, with luck playing only a vanishingly small role (for example, the fastest swimmer could contract food poisoning in the middle of a match and lose). But the extremes on the continuum capture only a small percentage of what really goes on in the world. Most of the action is in the middle, and having a sense of where an activity lies will provide you with an important context for making decisions.
As you move from right to left on the continuum, luck exerts a larger influence. It doesn't mean that skill doesn't exist in those activities. It does. It means that we need a large number of observations to make sure that skill can overcome the influence of luck. So Deanna Brooks would have to pick a lot more stocks and outperform the pros for a lot longer before we'd be ready to say that she is skillful at picking stocks. (The more likely outcome is that her performance would revert to the mean and look a lot more like the average of all investments.) In some endeavors, such as selling books and movies, luck plays a large role, and yet best-selling books and blockbuster movies don't revert to the mean over time. We'll return to that subject later to discuss why that happens. But for now we'll stick to areas where luck does even out the results over time.
When skill dominates, a small sample is sufficient to understand what's going on. When Roger Federer was in his prime, you could watch him play a few games of tennis and know that he was going to win against all but one or two of the top players. You didn't have to watch a thousand games. In activities that are strongly influenced by luck, a small sample is useless and even dangerous. You'll need a large sample to draw any reasonable conclusion about what's going to happen next. This link between luck and the size of the sample makes complete sense, and there is a simple model that demonstrates this important lesson. Figure 3-1 shows a matrix with the continuum on the bottom and the size of the sample on the side. In order to make a sound judgment, you must choose the size of your sample with care.
We're naturally inclined to believe that a small sample is representative of a larger sample. In other words, we expect to see what we've already seen. This fallacy can run in two directions. In one direction, we observe a small sample and believe, falsely, that we know what all of the possibilities look like. This is the classic problem of induction, drawing general conclusions from specific observations. We saw, for instance, that small schools produced students with the highest test scores. But that didn't mean that the size of the school had any influence on those scores. In fact, small schools also had students with the lowest scores.
FIGURE 3-1
Sample size and the luck-skill continuum
Source: Analysis by author.
In many situations we have only our observations and simply don't know what's possible.2 To put it in statistical terms, we don't know what the whole distribution looks like. The greater the influence luck has on an activity, the greater our risk of using induction to draw false conclusions. To put this another way, think of an investor who trades successfully for a hundred days using a particular strategy. He will be tempted to believe that he has a fail-safe way to make money. But when the conditions of the market change, his profits will turn to losses. A small number of observations fails to reveal all of the characteristics of the market.
We can err in the opposite direction as well, unconsciously assuming that there is some sort of cosmic justice, or a scorekeeper in the sky who will make things even out in the end. This is known as the gambler's fallacy. Say you're watching a coin being tossed. Heads comes up three times in a row. What do you think the next toss will show? Most people will say tails. It feels as if tails is overdue. But it's not. There is a 50-50 chance of both heads and tails on every toss, and one flip has no influence on any other. But if you toss the coin a million times, you will, in fact, see about half a million heads and half a million tails. Conversely, in the universe of the possible, you might see heads come up a hundred times in a row if you toss the coin long enough.
It turns out that many things in nature do even out, which is why we have evolved to think that all things balance out. Several days of rain are likely to be followed by fair weather. But in cases near the side of the continuum where outcomes are independent of one another, or close to being so, the gambler's fallacy is alive and well. This influence casts its net well beyond naive gamblers and ensnares trained scientists, too.3
When you're attempting to select the correct size of a sample to analyze, it's natural to assume that the more you allow time to pass, the larger your sample will be. But the relationship between the two is much more complicated than that. In some instances, a short amount of time is sufficient to gather a relatively large sample, while in other cases a lot of time can pass and the sample will remain small. You should consider time as independent from the size of the sample.
Evaluation of competition in sports illustrates this point. In U.S. men's college basketball, a game lasts forty minutes and each team takes possession of the ball an average of about sixty-five times during the game. Since the number of times each team possesses the ball is roughly equal, possession has little to do with who wins. The team that converts possessions into the most points will win. In contrast, a men's college lacrosse game is sixty minutes long but each team takes possession of the ball only about thirty-three times. So in basketball, each team gets the ball almost twice a minute, while in lacrosse each team gets the ball only once every couple of minutes or so. The size of the sample of possessions in basketball is almost double that of lacrosse. That means that luck plays a smaller role in basketball, and skill exerts a greater influence on who wins. Because the size of the sample in lacrosse is smaller and the number of interactions on the field so large, luck has a greater influence on the final score, even though the game is longer.4
The Two-Jar Model
Imagine that you have two jars filled with balls.5 Each ball has a number on it. The numbers in one jar represent skill, while the numbers in the other represent luck. Higher numbers are better. You draw one ball from the jar that represents skill, one from the jar that represents luck, and then add them together to get a score. Figure 3-2 shows a case where the numbers for skill and luck follow a classic bell curve. But the numbers can follow all sorts of distributions. The idea is to fill each jar with numbers that capture the essence of the activity you are