May 25, 2011 | Q&AEvent Highlights

Untangling Skill and Luck

Michael Mauboussin explains how to improve decision making — and outcomes — by understanding how both contribute to our most important undertakings.


Why is it so important to distinguish skill from luck?

We all know that the outcomes in many activities in life combine both skill and luck. Understanding the relative contributions of each can help us assess past outcomes and, much more importantly, anticipate future outcomes.

It is axiomatic that outcomes will revert to the mean in a system that combines skill and luck. An extremely favorable or unfavorable single outcome is going to be followed by an outcome that has an expected value closer to the average of all results. If a system reverts quickly to the mean, you know that it has lots of luck. If a system is slow to revert to the mean, you know that a good amount of skill is contributing to the outcomes.

Sports provide us with some good examples. In baseball, over a long season the best teams win about 60 percent of their games. But over shorter stretches it’s not unusual to see a team win or lose a whole bunch in a row. Reversion to the mean tells you the expected value of the whole season is still closer to 50-50 or slightly above or below. The Red Sox started off 2011 by losing six games in a row, so their fans were fretting. The Baltimore Orioles started off winning four in a row and their fans are excited. It’s a long season. Reversion to the mean will ultimately assert itself because there’s a lot of randomness in baseball.

In contrast, running races are almost all skill. That means the fastest runners will dominate: line up the same people five or 10 times in a row and the fastest person will win every time. There is no reversion to the mean because there is no luck. Runners finish in the same order every time.

How do you sort out skill from luck?

In sports, you can use statistical analysis to calculate where a given activity falls on the skill-luck continuum. Basically, you figure out what the results would look like if only luck mattered — the win-loss records for teams in a league would follow a binomial distribution — and then you figure out what the results would look like in a world of pure skill. You can then blend the two distributions in a proportion that matches the empirical results. The weightings of the blend indicate the relative contributions of skill and luck.

This leads directly into defining what makes for a good statistic. You see statistics used in many realms, but not all stats are equally useful. Basically, a good statistic should have two features. First, it should be persistent — that is, the current period result should have a decent correlation with the prior result. Second, it should be predictive — that is, if you do well or poorly as measured by the stat, the outcome will be good or bad. You’d be amazed how many stats fail this simple two-feature test.

While measuring skill and luck in business or investing isn’t as simple as sports, you can use these methods to take concrete steps in understanding the relative contributions of both skill and luck in these realms.

Given that business and investing are more complex systems, can you talk more about how skill and luck play out there?

First, it’s important to understand the paradox of skill, which says that as people in an endeavor become more skillful, luck actually becomes more important in determining outcomes. This seems backwards, but another sports example can illustrate the point. Seventy years ago, Ted Williams was the last baseball player to have a full-year batting average over .400. He hit .406 in 1941 and no one’s really come close ever since. Why?

One possible explanation is that players aren’t as good as they used to be, but that’s implausible because training techniques and technology have improved dramatically.

No one has come close to the record because everyone has gotten better: pitchers, batters, fielders. Consequently, while the mean of the batting averages has been relatively stable over the decades, the standard deviation of batting averages is much smaller: neither the best nor worst hitters are as far away from the average hitters as they used to be. When you have more skill, results become more uniform and so luck has more room to influence outcomes. Since the right tail of batting averages is closer to the mean today than it was in 1941, no player has been good enough to sustain a batting average over .400. And Williams, were he playing today, wouldn’t be able to do it either.

The paradox of skill is one reason it is so hard to beat the market. Everybody is smart, has incredible technology, and the government has worked to ensure that the dissemination of information is uniform. So information gets priced into stocks quickly and it’s very difficult to find mispricing. By the way, the standard deviation of mutual fund returns has been declining for the last 50 years or so, just as it has for batting averages.

So where would you place business and investing on the continuum?

Some academics have argued that all market outperformance is attributable to luck. But it’s been demonstrated, by statistical tests and common sense, that there is a component of skill involved. There’s a big difference between saying investing is all luck and saying it has a lot of luck. But as an investor it is important to acknowledge that, on the continuum, investing is closer to the luck side. That doesn’t mean that investors aren’t skillful — it is rather a reflection of the paradox of skill.

This leads to an important mindset: whenever you observe any outcome, you should always ask, “What would I expect by chance?” If the actual outcomes are different than what chance would dictate, there’s likely some element of skill.

So what constitutes skill in a field where probability dominates? The key is to have a good process. In all probabilistic fields, the best performers dwell on process. This is true for great value investors, great poker players, or great sports team managers. It’s all process stuff. It’s hard to do psychologically, emotionally, organizationally, but that is how you get paid.

You highlight the market’s march toward efficiency, which suggests a much more competitive landscape. What does it mean for the future of investment management?

Until we change human nature, or evolution weeds out these kinds of behaviors — which isn’t going to happen anytime soon — there will be opportunities in markets.

Think about handicapping in horseracing. There are two separate issues to consider. One is how fast the horse is likely to run in a particular race. The second is the odds priced on the tote board. If the horse’s chances of success are fully reflected in the odds, you are not going to make any money. You are looking for discrepancies between the horse’s prospects and what’s priced on the board.

The failure to distinguish between the fundamentals of how a company will perform and expectations — that is, what is priced into the security — is probably the biggest error in the investment business. Our natural tendency is to buy when things are going well and sell when things are going badly, irrespective of what’s priced in.

So the behavioral piece will continue to be enormous. Our behavioral finance courses routinely address the common heuristics that humans use and the biases that emanate from these heuristics. These biases include overconfidence, anchoring, confirmation bias, and recency bias. If you’re a normal human being, you exhibit all of these biases. The goal is to develop a process that weaves in tools and techniques to allow you to mitigate or manage those biases.

Seth Klarman, founder of the Baupost Group, has a great line: “Value investing is at its core the marriage of a contrarian streak and a calculator.” The contrarian streak says that you must be willing and able to do something different than what the consensus is telling you to do. That’s extremely difficult. And sometimes the consensus is right: if the movie house is on fire, you should run out the door, not in. So adding the calculator part is key; being a contrarian makes sense if it leads to a mispricing between fundamentals and expectations. That is a market opportunity.

The types of opportunities that present themselves tend to evolve. Think about them like the game Whac-A-Mole, where the moles are opportunities in markets. A mole pops up, you whack it, another one pops up. If an academic publishes a paper on a certain strategy that generates alpha, investors will exploit the strategy and by their very actions will compete away the excess returns. But the good news is that another opportunity pops up somewhere else.

Michael Mauboussin is chief investment strategist at Legg Mason Capital Management and adjunct professor of finance and economics at Columbia Business School.

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