The Batting Average Paradox

In the nor­mal course of my web brows­ing, I stum­bled upon the home page of Stephen E. Schwartz, an atmos­pheric sci­en­tist at Brookhaven National Lab­o­ra­tory and chief sci­en­tist of the Depart­ment of Energy’s Atmos­pheric Sci­ence Pro­gram.

The page gets pretty tech­ni­cal for those of us who are not atmos­pheric sci­en­tists, but near the bot­tom of the page he men­tions “the bat­ting aver­age para­dox” – which con­tains a sur­pris­ing bit of math that any of us can appreciate…

The bat­ting aver­age para­dox. Able has a higher bat­ting aver­age than Baker in the first half of the sea­son and also in the sec­ond half. You might think that that means that Able has a higher aver­age for the sea­son. But you would be wrong. Click here to see why aver­ag­ing ratios can be mis­lead­ing.”

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