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Tuesday, November 20, 2012

Luck and Skill Untangled: The Science of Success | Wired Science |

When we post articles which aren’t interesting to you, consider it regression to the mean.

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.

Jim Furtado Posted: November 20, 2012 at 06:47 AM | 5 comment(s) Login to Bookmark
  Tags: sabermetrics

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   1. depletion Posted: November 20, 2012 at 08:37 AM (#4306599)
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.

Of course it's impossible to know if the grade is because of luck so obviously you try to determine why she got the grade: didn't do the homework, test was poorly worded, bad noise/odor in the test room, never really grapsed the material, etc. It's pretty mindless to write off results to "luck" without first seeing if they're "trend".
   2. AROM Posted: November 20, 2012 at 09:53 AM (#4306640)
Depends on the way the test is set up. If it's all multiple choice, with many difficult questions that lead to guessing, then luck is a big factor.

Back in my day, after those of us lucky enough to avoid sabre-tooth tigers made it to school, most of the tests were pretty easy if you read what you were supposed to read and moderately tough if you didn't.
   3. valuearbitrageur Posted: November 20, 2012 at 12:49 PM (#4306814)
In Poker the results = skill + luck works out slightly differently,

because mother ####### donkeys always get way more luck.
   4. Walt Davis Posted: November 20, 2012 at 01:08 PM (#4306836)
Not that it matters much but team outcomes (or batter outcomes) do not strictly meet the assumptions of the binomial distribution. The binomial is (almost certainly) a reasonable approximation. The independence of tests is probably the most "controversial" of the binomial assumptions for baseball (hot and cold streaks).

Also one doesn't normally think of discrete variables in a classical test theory (or "true score theory") way. It doesn't matter much once you're talking outcomes of 162 games or 600 PA but O = T + E is more conformable with continuous variables. For a discrete variable, P(O) = T (not usually expressed as a "true" score but go with it) or in the case of the binomial, E(O) = NT where N is the number of trials, T the true p of success and O the number of successes. As N gets large, the binomial approximates a normal distribution for most baseball-y values of T.
   5. dr. scott Posted: November 20, 2012 at 02:47 PM (#4306912)
Daniel Kahneman descirbes this quite well in thinking fast and Slow when an Israeli general tells him that positive feedback never works and negative feedback always works. when he praised cadets for a clean execution of some maneuver, the next time they try they usually dont do nearly as good, and whever he yelled at someone for screwing up, they always did better.

Kahneman was quite excited by this as he saw this as a perfect example of regression to the mean, but realized that regression ot the mean is one of the main reasons why people think megative feedback is so effective. This of course is most true in cases where you only praise or reprimand serious outliers. Yhere will always be a distribution of talent of course.

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