David M. Brown's Blog

August 9, 2016

The “odds” that what has already happened has happened are 100%

Filed under: Science — davidmbrowndotcom @ 7:15 am

Instapundit Glenn Reynolds repeats in apparent agreement a claim that the odds of there having been no major hurricane in the U.S. over the past 11 years are one in 2,300.

This is wrongheaded. Statistical guesstimations pertain only to what may happen in the future, and only when we don’t know enough about the relevant causal factors to say with certainty what must happen under given conditions. The “odds” of what has already verifiably happened are never one in anything, including one in 2,300, unless you want to say that they’re one in one. But the notion of statistical probability doesn’t apply at all to those known past events. Whatever causal factors were operative, they’ve already operated, and the outcome is now a datum. The erstwhile ignorance about what would happen–the ignorance about how causal factors would precisely interact, the ignorance about the individual case which alone makes the application of statistics relevant to our assessments and actions–no longer exists.

Similarly, there are no one-in-two “odds” that a coin that has already come up heads would have come up heads. We already know the result of all the interacting, not fully perceptible and not fully calculable factors. With respect to future events, statistics are irrelevant if our knowledge of causal factors is adequate enough to say with certainty what must happen under defined circumstances. We don’t have to calculate “the odds” that a weighted coin will come up on just one side if the falling coin falls a large enough distance. We can, in fact, then predict what the statistics must be in all like circumstances given our knowledge of the coin and the atmosphere and how we’re tossing it.

Knowledge always trumps ignorance. Our means of navigating ignorance when we don’t have the relevant knowledge are beside the point when we do have the knowledge. Statistics are relevant only when we know too little about individual cases to make predictions on the basis of our knowledge of the case alone, but we do know something about the statistical patterns of groups of similar events.

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