What Baseball Can Teach About Statistics

5323" target=external>New York Yankees with more than 300 at bats-in the previous year, the authors (Langford, Schwertman, and Owens) found that the number of triples hit by a player correlated positively with the number of base hits he had, which in turn correlated positively with the number of home runs he hit. Yet the number of triples a player hit correlated negatively with the number of home runs he hit.

Stated differently, players who got a lot of triples generally got a lot of hits of all kinds, and players who got a lot of hits also tended to hit a lot of home runs.

The reason triples and home runs were nevertheless negatively correlated is that players who hit a lot of triples were usually lithe and fast, traits that do not lend themselves to home run hitting, and players who homered a lot were generally big and slow, traits that do not lend themselves to hitting a lot of triples.

In general, even if a quantity X correlates positively with another quantity Y, and Y correlates positively with a third quantity Z, we can't conclude that X correlates positively with Z. Transitivity may not hold.

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