Tuesday, March 29, 2011

Margins and Statistics

In a recent posting at Econlog, my former student David Henderson writes about "at the margin" and the use of statistics. He's writing about the NCAA basketball tournament but everything he says applies equally to curling (see this, where I become mired in pedantry). David writes:

The economic principal is the idea that the margin matters. Think of how some of the outcomes would have changed had a few little things changed. I'm thinking, for example, of the close University of Arizona game against U Conn. (U Conn won 65-63.) What if Arizona's star, Derrick Williams, hadn't been called for just one touch foul? Then he would have been on the floor longer and Arizona might have won. Or, in some of the other games, what if two of a team's 3-point attempts had been a few inches shorter or longer and gone in? Again a different outcome. Margins can matter a lot. [EE: or in curling think how often an eighth of an inch one way or another affects the outcome]

And the statistical principle, which is related to the above, is how much randomness there is. One team can be a little off its game for most of a half and, although it is a better team generally than the team it's playing against, this can make a difference. There's always randomness. So much that happens in the world is random. So the moral of the story is that the degree of certainty otherwise-intelligent people have about their bracket choices is just not justified.

A related moral is that when you play a lot of games and win enough to get to be one of the 20 or so top picks in the choice of 68 teams, you've done a good job. What happens from then on is a mix of skill and randomness.



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