There is much to enjoy in Michael Mauboussin's latest book, The Success Equation: Untangling Skill and Luck in Business, Sports and Investing, but here are a few highlights.

How do you distinguish skill from luck? He writes that:

There's a quick and easy way to test whether an activity involves skill; ask whether you can lose on purpose. In games of skill, it's clear that you can lose intentionally but when playing roulette or the lottery you can't lose on purpose

The problem of sample size. Tell people that the US counties with the lowest rates for kidney cancer have small rural populations and they will come up with a number of explanations: healthy lifestyle, lack of pollution etc. Tell people that the US counties with the highest rates of kidney cancer have small, rural populations and they will come up with different explanations: low income, lack of access to healthcare and so on. Both statements are true. The reason that the variation of result will be greater in a small sample size, just as small opinion polls have a higher margin of error than large ones.

Mauboussin points out that this error led policymakers to favour small school sizes on the grounds that the best grade averages were achieved by establishments of limited size. But they failed to notice that small schools were also overrepresented in the list of worst schools.

The undersampling of failure, or survivorship bias. Business studies often look for ways of creating successful companies by studying the characteristics of the existing giants. One example is the idea that being a great company implies taking big risks. But when we look at companies that exist now that took big risks in the past, we fail to consider the many failed companies that also took risks and are no longer around. We need to consider the whole group.

We struggle with logical problems. Take a look at the following puzzle, which I got wrong until I read the explanation.

Jack is looking at Anne but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person? A)Yes, B)No or C)cannot be determined.

Like 80% of those tested, I went for C because we don't know the marital status of Anne. But if Anne is married, she is looking at the unmarried George, while if she is unmarried, then the married Jack is looking at her. So the answer is A.

This creates more serious problems, as with the well-known example of false positives in cancer screenings; doctors often make logical mistakes in assessing the probabilities.

Investors focus on the wrong measures. Studies find that earnings per share is the most popular measure of corporate performance and is often used for executive pay. They also find that "the majority of companies are willing to sacrifice long-run economic value to deliver short-run earnings" doubtless because of those executive incentives. But the correlation between eps growth in one three-year period and the next is actually negative; you can prop up the measure for a while but eventually growth reverts to the mean.

The same goes for mutual funds. The correlation between excess returns in one three year period and another is also negative, when applied to 1500 mutual funds. Fund managers revert to the mean as well (for some reasons, see this week's column). However, skill does play a role; streaks of outperformance by individual fund managers happen more frequently than chance would suggest.

Anyway, there is a lot of thought-provoking stuff in the book, for sports fans as well as investors.

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