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?
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)
- 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.