Review

We understand that it’s been quite a busy week and that we’ve thrown a ton of material your way. We’d like you to take some time today and this weekend to go through the notes of the first four lectures and first three problem sets carefully with your team and RTA.

Visualizing the Strike Zone

In this part, we will continue to use heatmaps (introduced briefly in Lecture 2) to explore the strike zone in baseball. We will focus on data collected by PITCHf/x. At a high-level, PITCHf/x consists of a set of cameras installed at every ballpark which tracks the motion of each pitch. For more information about the system, check out this article by Mike Fast The data collected by PITCHf/x is then transmitted to the MLB Gameday application along with contextual information about the pitch. The data contains the measurements from the PITCHf/x system recorded in 2015.

  1. Read the data into a tbl called `pitches’.

The columns are: * Description: Records the outcome of the pitch (Called Strike, Swinging Strike, Foul, etc.) * X and Z: the horizontal and vertical coordinates of the pitch in inches. Note that the center of home plate corresponds to X = 0. Note that the X coordinate are recorded from the catcher’s perspective, with negative values on the left and positive values on the right. In this coordinate system, a right-handed batter will line up to the left (i.e. negative X values). * COUNT: The ball-strike count for each pitch * P_HAND and B_HAND: the handedness of the batter and pitcher.

  1. To visualize the strike zone, we are going to want to filter out only the called strikes and balls. Moreover, it will be helpful to convert the Description to numeric values (1 for called strikes, 0 for balls). Use the pipe operator, filter(), mutate(), and case_when() to create a new tbl called_pitches containing only the called strike and balls and that includes a new column “Call” whose value is 0 for balls and 1 for called strike.

  2. To get started, we will create a plot and then add to it sequentially:

  1. To estimate the probability of a called strike given the pitch location, we will use a strategy similar to what we used to make heatmaps in Module 2. Essentially, we divide the plane into several small rectangular bins and compute the proportion of called strikes within each bin. To compute this, we use the stat_summary_2d() function, which takes three aesthetics:

By default, stat_summary_2d() divides the plane into rectangles based on the aesthetics x and y, and then computes the average value of z for observations in the bin. We can add this layer to our plot g as follows and obtain the following plot

  1. You’ll notice in the plot above that stat_summary_2d() has added a legend to our plot. However, the title of the legend is a somewhat non-informative. The color scheme does not distinguish between different values particularly well.

  1. According to the official rule book, the strike zone is a rectangular region that spans the width of home plate and extends vertically from the batter’s knee to the middle of his chest. From the plot above, we see that the region in which the strike zone probability is higher than 90% is definitely not rectangular. To better visualize the discrepancy, we can add another layer to plot which delimits an approximation of the rule book strike zone. The code below does just that. The xmin and xmax arguments give the horizontal limits of the strike zone (in this case, the coordinates of the edges of the strike zone) and the ymin and ymax arguments are the average vertical limits measured by PITCHf/x. Note: these values were pre-computed using a much larger dataset

We can additionally make the plot a bit more attractive visually as follows:

NBA Team Shooting Statistics

The file “nba_boxscore.csv” lists detailed box score information about every NBA player in every season ranging from 1996–97 season and 2015-16 season. We will look at team shooting statistics over this 20-season span.

  1. Load the data into a tbl called raw_boxscore.
Parsed with column specification:
cols(
  .default = col_double(),
  Player = col_character(),
  Pos = col_character(),
  Tm = col_character()
)
See spec(...) for full column specifications.

The column “Tm” lists the team on which each player played. We can look at the relative frequencies of the teams using the table() function. This function takes a vector and returns the frequencies of each unique value.

Looking at the list of teams you may see a few that you don’t recognize. For instance, there are 15 players listed as playing on “WSB”. We can use filter() to take a closer look at these players

These fifteen players during the 1996-97 season on the Washington Bullets, which was renamed the Washington Wizards at the end of that season. There are a few other examples: VAN refers to the Vancouver Grizzlies who moved to Memphis and CHH refers to the original Charlotte Hornets franchise, which ultimately relocated to New Orleans.

One of the teams listed is “TOT”. This does not refer any specific team. Instead these rows record the total statistics recorded by a player if he played for multiple teams in a single season. For the purposes of understanding how team shooting statistics changed over time, we will not want to include these rows in our analysis.

  1. Use filter(), group_by(), summary(), and mutate() to create a new tbl called team_boxscore that does the following:
  1. Use filter() to create a new tbl called reduced_boxscore that pulls out the rows of team_boxscore corresponding to the following teams: BOS, CLE, DAL, DET, GSW, LAL, MIA, and SAS. Then create a plot of these teams’ three point percentage in each season. Be sure to color the points according to the team. What patterns do you notice?

Work with new data

Once you finish reviewing the material from earlier this week, we’d like you to use some of the tools we introduced in Lecture 4 to read in new data into R. Then, using the skills you’ve learned in the first four lectures, we’d like to you do some type of analysis with this data. It doesn’t need to be sophisticated – even making a few interesting visualizations or computing some interesting summaries is enough. We just want you to get some practice working with some data that you’ve collected yourselves!