Question: A baseball team is comparing two of its hitters, Hernandez and Dimock. Hernandez hit .250 in 2017 and .275 in 2018. Dimock did worse in both years – .245 in 2017 and .270 in 2018. Overall, though, Dimock hit better across the two years, .263 versus .258 for Hernandez. How can this be?

Answer: Note that 2018 was a better year than 2017, for both hitters. This is an example of Simpson’s Paradox, in which Dimock had relatively more at-bats in the better year, and relatively fewer in the worse year. For example, the numbers might be as follows:

2018

• • • Hernandez:  65 hits in 241 at-bats in 2018 (.275)
    • Dimock: 105 hits in 389 at-bats in 2018 (.270)

2017

• • • Hernandez: 80 hits in 320 at-bats in 2017 (.250)
    • Dimock: 35 hits in 143 at-bats in 2017 (.245)

Overall

• • • Hernandez: hit 145/561 = .258,
    • Dimock: hit 140/532 = .263