In bayesball/ShinyBaseball: Shiny Baseball Applications

knitr::opts_chunk$set(echo = TRUE,
                      message = FALSE)

Introduction

This app illustrates Berkson's Paradox which might be better called the Selection-Distortion Effect. Two variables may appear to have some type of association. But when we select a portion of the data, the selected data may have a different association pattern. In other words, the pattern of association is distorted by the selection mechanism.

Using the BerksonBA App

In this app, we focus on data from the 2019 season, consider all hitters with at least 100 at-bats, and select hitters with at least a 0.200 batting average. We see a scatterplot of the in-play rate (1 - SO / AB) and the batting average on balls on contact (BACON) (H / (AB - SO)). We see a slight negative correlation of -0.37.

Now change the minimum batting average to 0.270. The app shows the selected points -- there is a stronger association pattern and the correlation value is now -0.76. So we have changed the association pattern by selecting the better hitters.

library(shiny)
library(ShinyBaseball)
library(broom)
shinyAppDir(
  system.file("shiny-examples/BerksonBA", 
              package = "ShinyBaseball"),
  options = list(
    width = "100%", height = 550
  )
)

Things to Try

1. Try to show this paradox by selecting data from a different season. Do you see a similar phenomena when you select players with at least a minimum BA?

2. One can observe a similar paradox by selecting players on the basis of the number of at-bats (AB). For a specific season, look at all hitters with say at least 50 at-bats. Does the association pattern between In-Play Rate and BACON change when you select players with at least 400 at-bats? Can you explain why the association pattern has or has not changed?

bayesball/ShinyBaseball documentation built on March 26, 2024, 9:26 a.m.