How Not to Be Fooled by Odds

The New York Times ran an article recently titled “How Not to Be Fooled by Odds” in which the author defines what is meant by a statement such as “the odds of a Republican takeover of the Senate is about 74%.”  Stating that “there really is a difference between saying something will almost certainly happen and saying that it is more likely to happen than not,” the author goes on to explain what is and is not meant by the statement.  Concluding that “…a prediction that puts a 74 percent chance on an outcome should be “wrong” about 26 percent of the time,” he presents a list of situations that occur about 26% of the time, including:

  • The odds that a National Football League defense prevents a first down on third-and-one.
  • The percentage of full-time graduate students in electrical engineering in this country who are American citizens
  • The percentage of mothers with children under 18 who stay home with their children
  • The share of Americans who live in California, Texas or New York

rain-bowIn the same way, we need to be careful about what is actually being asserted by other statistics.  For example, in the third year of California’s drought, we are quite focused on rain.  So what is meant by the statement “There is a 40% chance of rain” (technically, the PoP or ‘Probability of Precipitation’)?  Consulting the National Weather Service, we find the following:

Mathematically, PoP is defined as follows:

PoP = C x A where “C” = the confidence that precipitation will occur somewhere in the forecast area, and where “A” = the percent of the area that will receive measureable precipitation, if it occurs at all.

So… in the case of the forecast above, if the forecaster knows precipitation is sure to occur ( confidence is 100% ), he/she is expressing how much of the area will receive measurable rain. ( PoP = “C” x “A” or “1” times “.4” which equals .4 or 40%.)

But, most of the time, the forecaster is expressing a combination of degree of confidence and areal coverage. If the forecaster is only 50% sure that precipitation will occur, and expects that, if it does occur,it will produce measurable rain over about 80 percent of the area, the PoP (chance of rain) is 40%. ( PoP = .5 x .8 which equals .4 or 40%. )

In either event, the correct way to interpret the forecast is: there is a 40 percent chance that rain will occur at any given point in the area.

As you present your quality control findings to others, be sure that everyone understands what they mean.  A clear definition of your terms at the beginning or end of any report is a good first step.

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