Lab 05 - MLB Wins

Due: Friday, Feb 28 at 11:59pm

Introduction

You will work with yearly baseball statistics for each team from the years 2014 to 2018. You do not need any deep insight into the sport of baseball to successfully complete this lab. However, if you think you do not understand a specific variable and how it relates to baseball then feel free to ask.

A baseball team beats its opponent when it outscores its opponent. This happens when a team scores more runs than it allows in a game. The win percentage (percentage of games played that resulted in a win) of a team is related to the number of runs a team scores versus the number of runs a team allows over the course of a full season (usually 162 games). Runs scored and runs allowed are a function of hits and walks, and hits allowed and walks allowed, respectively. You will explore some models that investigate the relationship between win percentage, and runs scored and runs allowed.

Getting started

Clone your assignment repo into RStudio Cloud and open the R Markdown file. Don’t forget to load in the necessary packages and configure git:

If you would like your git password cached for a week for this project, type the following in the Terminal:

You will need to enter your GitHub username and password one more time after caching the password. After that you won’t need to enter your credentials for 604800 seconds = 7 days. Note that this is only good for this single RStudio Cloud project – you will need to cache your credentials for each project you create.

The data

The data is made available by package Lahman. This package has dozens of data frames on MLB baseball metrics. The data we will work with is a subset of the Teams data frame - yearly statistics and standings for MLB teams.

If you have further interest in baseball data, I have installed package Lahman for you to explore some of the other datasets.

To get started, read in the data and save it as an object named teams_default.

Exercises

Write all R code according to the style guidelines discussed in class. Be especially careful about staying within the 80 character limit.

All team members must commit and push to receive full credit.

In addition to lm() and cor(), your code should only contain functions from the loaded R packages.

Exploratory data analysis

  1. Add the following variables to teams_default. Save the resulting object as teams.
New variable Name Definition
win_pct win percentage w / g, proportion of wins among all games played
rd run differential r− ra, runs scored minus runs allowed
hd hit differential h− ha, hits minus hits allowed
bbd walk differential bb− bba, walks minus walks allowed
sod strike out differential so − soa, strikeouts minus strikeouts allowed

  1. Create scatter plots of win percentage versus the four differential variables you created in Task 1: rd, hd, bbd, sod. Which variable appears to have the strongest correlation with a team’s win percentage? Which variable appears to have the weakest correlation with a team’s win percentage? Compute these correlations.

  2. Create a scatter plot to visualize the relationship between rank and win_pct. Describe the relationship you observe.

  3. Recreate your visualization in Exercise 3, but this time use geom_boxjitter() from package ggpol. Briefly describe what this geom does and if the resulting visualization is more or less informative than that in Exercise 3.

Model building (quantitative predictor)

The linear model is of the form \(\hat{y} = b_0 + b_1 x\).

  1. Fit a linear model called lm_rd, where run differential is the explanatory variable and win percentage is the response. Based on the regression output, write out the linear model.

  2. Recreate your visualization in Exercise 2 for only the variable run differential, but now add the fitted regression line to the plot in a contrasting color to that of your points.

  3. Interpret the slope and intercept of this linear model in the context of the data. Comment on whether or not the intercept interpretation makes sense with regards to this data.

  4. Determine the \(R^2\) of the model and interpret it in context of the data.

  5. Fit a linear model called lm_sod, where strike out differential is the explanatory variable and win percentage is the response. Based on the regression output, write out the linear model.

You will need to get statistics R and SO from Team Standard Batting and Team Standard Pitching, and then take their respective differences to get the 2019 run and strikeout differentials.

  1. Choose an MLB team. Go to https://www.baseball-reference.com/leagues/MLB/2019.shtml#all_teams_standard_batting and get their 2019 statistics for run differential and strikeout differential. Using each of your models, lm_rd and lm_sod, which model does better at predicting your selected team’s actual 2019 win percentage?

Model building (categorical predictor)

  1. Fit a linear model called lm_rank, where rank is the explanatory variable and win percentage is the response. Based on the regression output, write out the linear model.

  2. Interpret the coefficients of model lm_rank.

Try mutate() and fct_relevel().

  1. Refit your model from Exercise 11, but set the baseline level to when the rank is 5. Save this linear model as an object called lm_rank_base5. How do the coefficients of this model compare to those in Exercise 11?

  2. Compare \(R^2\) for models lm_rank and lm_rank_base5. Is this what you would expect? Explain your answer.

Submission

Knit to PDF to create a PDF document. Stage and commit all remaining changes, and push your work to GitHub. Make sure all files are updated on your GitHub repo.

Please only upload your PDF document to Gradescope. Associate the “Overall” graded section with the first page of your PDF, and mark where each answer is to the exercises. If any answer spans multiple pages, then mark all pages.

Only one team member needs to submit for the group. After you hit submit, go to View or edit group and select all your team members from the drop-down menu.