MLB Home Plate Umpires
Motivation
Baseball is a popular American sport played on a diamond-shaped field. Games are 9 innings long and each inning has two halves, the first in which the visiting team bats and the second where the home team bats. Innings end after three outs. An out is when a player from the hitting team is removed from play for the half of the inning due to various reasons. Batters aim to get on base by hitting a ball pitched to them by the pitcher. Batters can get to first, second, or third base depending on how far they hit the ball and how fast they run. If a batter hits the ball past the outfield fences, they, along with any runners on base, automatically score, this is called a home run. Runners can also score if another player hits the ball and then they reach home. The team with the most runs wins the game.
There are 9 defensive positions in baseball, the layout of these positions is labeled in the below diagram.
Behind the catcher, at home plate is an official known as the home plate umpire. The umpire’s role is to enforce the rules and make decisions during a game. Many of these decisions involve calling balls and strikes. Pitches that are considered strikes are pitched within the zone outlined below. Anything outside of that zone is called a ball. If a batter gets 3 strikes, they are out on a strike out. If the batter gets 4 balls they get to go to first base on what is called a walk.
Major League Baseball (MLB) is a professional baseball league with 30 teams and a 162 game season. The MLB has 76 umpires in total with four umpires in each game. Umpires are stationed at 1st, 2nd, and 3rd base in addition to home plate but the home plate umpire is the only one who makes calls on pitches.
The mlb_umpires.csv dataset looks at cumulative data from MLB homeplate umpires dating as far back as 2008. The boost statistics in the dataset investigate how certain umpires compare to the “average” Major League Baseball umpire. The dataset provides insight on if umpires favor defensive players or offensive plaeyrs more.
Data
The data set has 954 rows with 11 variables. Each row is an MLB home plate umpire combined with a boost_stat ranking how they compare with the average umpire. There are 159 umpires in the dataset with 6 rows per umpire. The data is cumulative from 2008 until 2024.
| Variable | Description |
|---|---|
Umpire |
The name of the umpire. |
Games |
The number of games the umpire has umpired since 2008. |
k_pct |
The strike out percentage of batters and pitchers when the umpire is umpiring. (Career Strike Outs Called/Career Plate Appearances Umpired) |
bb_pct |
The walk percentage of batters when the umpire is umpiring. (Career Walks Called/Career Plate Appearances Umpired) |
RPG |
The career runs scored per game when the umpire is umpiring. (Career Runs While Umpiring/Career Games Umpired) |
BA |
The batting average of batters in games when the umpire is umpiring. (Career Hits While Umpiring/Career Plate Appearances Umpired) |
OBP |
The on base percentage of batters when the umpire is umpiring. ((Career Hits While Umpiring + Career Walks While Umpiring + Career Hit by Pitches While Umpiring)/(Career At Bats Umpired + Career Walks While Umpired + Career Hit by Pitches While Umpiring + Career Sacrifice Flies While Umpiring)) |
SLG |
The slugging percentage of batters when the umpire is umpiring. ((Singles While Umpiring + (Doubles While Umpiring * 2) + (Triples While Umpiring * 3) + (Home Runs While Umpiring * 4))/Career At Bats Umpired) |
boost_stat |
The statistic being “boosted” by the umpire when they are behind home plate. This can be strikeouts (K), walks (BB), runs (R), batting average (BA), on base percentage (OBP), and slugging percentage (SLG). |
boost_pct |
The percentage that the boost_stat is being boosted. In other words how much the umpire is above or below the average umpire in calling that statistic. |
Rating |
Whether or not the umpire favors offensive or defensive players in that statistic. The Rating is Defensive if the umpire has a boost_pct above zero and the boost_stat is K or if the boost_pct is below zero and the stat is BB, R, BA, OBP, or SLG. The Rating is Offensive if the umpire has a boost_pct below zero and the boost_stat is K or if the boost_pct is above zero and the stat is BB, R, BA, OBP, or SLG. It will be Neither if the boost_pct is zero. |
Questions
Describe the distribution of
k_pctbased on a histogram.What is the mean
k_pctfor all umpires?What is the standard deviation of
k_pctfor all umpires?Use the IQR method to determine if any of the ‘k_pct’ values should be considered outliers.
Fit a model to predict
RPGwithGames,k_pct,BA, andbb_pct. Write down fitted prediction equation.Predict the
RPGfor an umpire that has umpired 255 games, with aBAfor hitters of 0.270, ak_pctof 15%, and abb_pctof 10%.Obtain the p-values for each of the predictors in the model. Are all of the predictors effective? If not, which ones and why?
Perform a test for the overall fit of the model.
Record and comment on the multiple R-squared and adjusted R-squared values for the model.
Drop
bb_pctfrom the model and record the new multiple R-squared and adjusted R-squared values. Is the model withoutbb_pctbetter or worse?Find the VIFs for the original model, are any of the values concerning? Explain why or why not.
Find and interpret the 95% confidence interval for the mean
RPGfor all umpires who have umpired 400 games, with aBAfor hitters of 0.215, ak_pctof 18%, and abb_pctof 9%.Find and interpret the 95% prediction interval for the
RPGof an umpire who has umpired 400 games, with aBAfor hitters of 0.215, ak_pctof 18%, and abb_pctof 9%.
References
Data obtained from swishanalytics.com