IMAGINING AN AT BAT AS A COIN FLIP. Nick finished his explanation of small samples by imagining at bats in the playoffs as coin flips. He took as an example Jayson Werth, who had one hit in 20 at bats in this year’s playoffs after having unusual success in 226 plate appearances in playoffs in previous years.
Nick wrote:
“Let’s say that all of Jayson Werth’s PAs were coin flips as to whether he’d reach base – i.e. giving him a “true talent” of a .500 OBP…. We will call this .500 OBP player Coin Werth.
“This is totally unscientific, but I went to random.org and flipped sets of 20 coins. Heads was “reached base” and tails was “out.” I did this 20 times. Each of these sets of 20 flips represents a theoretical 20 PAs, which is what Werth got this postseason.
“Three times the results were 10-10. Six times out of the 20, Coin Werth went absolutely berserk, reaching base 15, 12, 16, 13, 14, and 15 times out of 20. Amusingly, the first four of those happened in order – an 80 “PA” chunk of sheer dominance by Coin Werth.
“But then here’s something to keep in mind: If I had decided instead that heads was “out” and tails was “reached base” then all of a sudden this is 80 PAs where Coin Werth is unplayable garbage, despite the exact same odds of either one happening.”
Nick concluded his post: “There’s always next year.”