Fluctuating Batting Averages
When Miguel Cabrera came up to the plate in the fifth inning of last night’s Tigers-Rays game, he was 0-for-1 in the game and his up-to-the-minute batting average was announced as .349. I found this strange because, when the game started, Cabrera’s batting average was .350.
A player’s batting average is equal to (total hits) / (total at-bats). Thus the effect of one more at-bat without a hit dropped his average by .001, or 1/1000 (Note: rounding probably plays an important role here).
I wondered if this information uniquely determined both Cabrera’s hits and at-bats this season. Or maybe some combination of mathematics, baseball knowledge, and guessing could help me get those numbers. I did get the numbers–unfortunately, they were wrong.
An interesting question here is “What is the smallest possible number of hits such that one more hitless at-bat results in one’s rounded batting average dropping by .001?”