## Archive for August 19, 2011

### Eddie Gaedel, a Man of Stature

Sixty years ago today, baseball player Eddie Gaedel stepped to the plate for the only at-bat of his major league career. Standing just 3’7″ tall, he drew a walk on four straight pitches.

Why mention this on a math jokes blog? Gaedel’s uniform number was 1/8.

This reminds me of a math question that my friend Harold Reiter likes to use to start a class discussion about size of numbers.

Which of the following is the largest fraction?

1/2

1/4

1/6

1/8

It also reminds me of the priest who tells his congregation that he understands how difficult it is to tithe. “If you can’t afford to give 1/10 of your salary to the church,” he tells them, “then just give 1/9 or 1/8.”

Officially, Gaedel had 1 base‑on‑balls (BB) and 0 at-bats (AB). In baseball, a plate appearance does not offically count as an at-bat if the player is walked. This gave Gaedel an on-base percentage (OBP) of 1.000, the highest possible. As it turns out, he’s not the only player with an OBP of 1.000; nearly 30 others have accomplished the same feat.

The official formula for on-base percentage is

OBP = (H + BB + HBP) ÷ (AB + BB + HBP + SF)

where

- H = hits
- HBP = hits-by-pitch
- SF = sacrifice flies

An interesting question is:

How can a player have a higher batting average than on-base percentage?

Though rare, it occasionally happens when a player has a relatively low number of at‑bats with few walks and several sacrifice flies. For instance, a player with 1 hit in 2 at-bats with a sacrifice fly would have a batting average of 0.500 and an on-base percentage of 0.333.