Stapidity
We need to have a name for the pairing, in current sports reporting, of absolute worship of "statistics" combined with absolute ignorance about how to do probabilistic reasoning. "Stapidity"?
For instance, the NBA draft lottery is a domain in which we can be sure pure probabilistic reasoning applies, since it is deliberately set up that way. If a team has a 42.3% chance of getting the top pick, that's that: there is no point looking at "recent history" to see how teams in that position did, since in a random sampling, we expect to see subsets with different distributions of results than we will get as our sample size approaches infinity. And we know with certainty (unless we suspect the NBA has a broken random number generator) that in the limit, 42.3% of such teams will wind up with the top pick. And yet:
"And as the fine folks at ESPN Stats & Information pointed out, recent history says not to be too confident the Lakers will keep the pick should they enter the lottery in that fourth spot, even though 82.8 percent seems like a solid figure.
"Over the past five years, teams that had a pre-lottery position of fourth dropped to sixth on two occasions: the Golden Warriors in 2010 and Washington Wizards in 2011." (Italics mine.)
The implication is that 82.8% is really only about the same as 60%, since if we look at the last five cases, that is the percentage we get. And if a fair coin comes up heads twice in a row, we know it isn't really fair!
For instance, the NBA draft lottery is a domain in which we can be sure pure probabilistic reasoning applies, since it is deliberately set up that way. If a team has a 42.3% chance of getting the top pick, that's that: there is no point looking at "recent history" to see how teams in that position did, since in a random sampling, we expect to see subsets with different distributions of results than we will get as our sample size approaches infinity. And we know with certainty (unless we suspect the NBA has a broken random number generator) that in the limit, 42.3% of such teams will wind up with the top pick. And yet:
"And as the fine folks at ESPN Stats & Information pointed out, recent history says not to be too confident the Lakers will keep the pick should they enter the lottery in that fourth spot, even though 82.8 percent seems like a solid figure.
"Over the past five years, teams that had a pre-lottery position of fourth dropped to sixth on two occasions: the Golden Warriors in 2010 and Washington Wizards in 2011." (Italics mine.)
The implication is that 82.8% is really only about the same as 60%, since if we look at the last five cases, that is the percentage we get. And if a fair coin comes up heads twice in a row, we know it isn't really fair!
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