Visualizing the Strike Zone

In this problem set, we will continue to use heatmaps (introduced briefly in Module 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’.
> library(tidyverse)
> pitches <- read_csv("data/pitchfx_2015.csv")
Parsed with column specification:
cols(
  Description = col_character(),
  X = col_double(),
  Z = col_double(),
  COUNT = col_character(),
  P_HAND = col_character(),
  B_HAND = col_character()
)

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:

> g <- ggplot(data = called_pitches)
  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

> g <- g + stat_summary_2d(mapping = aes(x = X, y = Z, z = Call))
> g

  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.
> g <- g + scale_fill_distiller("P(Called Strike)", palette = "RdBu")
> g

  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
> g <- g + annotate("rect", xmin = -8.5, xmax = 8.5, ymin = 19, ymax = 41.5, alpha = 0, 
+     color = "black")

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

> g <- g + theme_classic()
> g <- g + theme(axis.title.x = element_blank())
> g <- g + theme(axis.title.y = element_blank())
> g <- g + labs(title = "Estimated Strike Zone")
> g

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_integer(),
  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.

> table(raw_boxscore[["Tm"]])

 ATL  BOS  BRK  CHA  CHH  CHI  CHO  CLE  DAL  DEN  DET  GSW  HOU  IND  LAC 
 347  350   72  183  101  335   34  359  356  354  321  355  359  319  347 
 LAL  MEM  MIA  MIL  MIN  NJN  NOH  NOK  NOP  NYK  OKC  ORL  PHI  PHO  POR 
 319  271  348  337  328  298  161   34   63  345  144  340  352  348  338 
 SAC  SAS  SEA  TOR  TOT  UTA  VAN  WAS  WSB 
 332  342  195  366 1047  309   80  333   15

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

> filter(raw_boxscore, Tm == "WSB")
# A tibble: 15 x 22
   Season Player     Pos     Age Tm        G    GS    MP   FGM   FGA   TPM
    <int> <chr>      <chr> <int> <chr> <int> <int> <int> <int> <int> <int>
 1   1997 Ashraf Am… PF       25 WSB      31     0   144    12    40     1
 2   1997 Calbert C… SG       25 WSB      79    79  2411   369   730     4
 3   1997 Matt Fish  C        27 WSB       5     0     7     1     3     0
 4   1997 Harvey Gr… PF       31 WSB      78    25  1604   129   314    28
 5   1997 Juwan How… SF       23 WSB      82    82  3324   638  1313     0
 6   1997 Jaren Jac… SG       29 WSB      75     0  1133   134   329    53
 7   1997 Tim Legler SG       30 WSB      15     0   182    15    48     8
 8   1997 Gheorghe … C        25 WSB      73    69  1849   327   541     0
 9   1997 Tracy Mur… SF       25 WSB      82     1  1814   288   678   106
10   1997 Gaylon Ni… SG       27 WSB       1     0     6     1     3     0
11   1997 Rod Stric… PG       30 WSB      82    81  2997   515  1105    13
12   1997 Ben Walla… PF       22 WSB      34     0   197    16    46     0
13   1997 Chris Web… PF       23 WSB      72    72  2806   604  1167    60
14   1997 Chris Whi… PG       25 WSB      82     1  1117   139   330    58
15   1997 Lorenzo W… C        27 WSB      19     0   264    20    31     0
# ... with 11 more variables: TPA <int>, FTM <int>, FTA <int>, ORB <int>,
#   DRB <int>, AST <int>, STL <int>, BLK <int>, TOV <int>, PF <int>,
#   PTS <int>

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?