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Mauboussin: I think this is a cool analysis. I learned from Tom Tango, a respected sabermetrician, and in statistics it’s called “true score theory.” It can be expressed with a simple equation:
Observed outcome = skill + luck
Here’s the intuition behind it. Say you take a test in math. You’ll get a grade that reflects your true skill — how much of the material you actually know — plus some error that reflects the questions the teacher put on the test. Some days you do better than your skill because the teacher happens to test you only on the material you studied. And some days you do worse than your skill because the teacher happened to include problems you didn’t study. So you grade will reflect your true skill plus some luck.
Of course, we know one of the terms of our equation — the observed outcome — and we can estimate luck. Estimating luck for a sports team is pretty simple. You assume that each game the team plays is settled by a coin toss. The distribution of win-loss records of the teams in the league follows a binomial distribution. So with these two terms pinned down, we can estimate skill and the relative contribution of skill.
To be more technical, we look at the variance of these terms, but the intuition is that you subtract luck from what happened and are left with skill. This, in turn, lets you assess the relative contribution of the two.
Some aspects of the ranking make sense, and others are not as obvious. For instance, if a game is played one on one, such as tennis, and the match is sufficiently long, you can be pretty sure that the better player will win. As you add players, the role of luck generally rises because the number of interactions rises sharply.