R Code for Visualizing Baseball

Author

Jim Albert

Published

February 1, 2024

1 Gentle Introduction to ggplot2

1.1 Introduction

ggplot2 is a R package for graphing data based on the “The Grammar of Graphics” framework introduced by Leland Wilkinson. This package is used to construct all of the graphs for the book Visualizing Baseball. The purpose of this document to introduce ggplot2 for a familiar baseball dataset. In this document, I introduce the basic framework and illustrate the use of ggplot2 to construct graphs for different types of variables.

1.2 Some Baseball Data

Collect hitting data for all teams in the 2015 baseball season. For each team, I compute its slugging percentage SLG and its on-base percentage OBP.

library(dplyr)
library(Lahman)
teams2015 <- filter(Teams, yearID == 2015)
names(teams2015)[18:19] <- c("X2B", "X3B")
teams2015$SF <- as.numeric(teams2015$SF)
teams2015$HBP <- as.numeric(teams2015$HBP)
teams2015 <- mutate(teams2015,
                    X1B = H - X2B - X3B - HR,
                    TB = X1B + 2 * X2B + 3 * X3B + 4 * HR,
                    SLG = TB / AB,
                    OBP = (H + BB + HBP) / 
                      (AB + BB + HBP + SF))

1.3 Three Basic Components of a ggplot2 Graph

To construct a graph using ggplot2, one needs …

  • A data frame that contains the data that you want to graph.

  • Aesthetics or roles assigned to particular variables in the data frame.

  • A geometric object (or geom for short) which is what you are plotting.

For example, suppose we wish to construct a scatterplot of the on-base percentage and the slugging percentages for all teams in the 2015 season.

  1. The data frame teams2015 contains the data and OBP and SLG are the variables of interest.

  2. To construct a scatterplot, you need to have a variable on the horizontal axis (x) and a variable on the vertical axis (y). If I want OBP to be the horizontal axis variable and SLG the vertical axis variable, I would assign the aesthetics OBP to x and SLG to y.

These two steps are communicated by the command

library(ggplot2)
ggplot(data=teams2015, aes(x=OBP, y=SLG))

The ggplot2 function only sets up the axis – it does not plot anything. To construct a scatterplot, we need to add a point geometric object which is the function geom_point. Now we see the scatterplot. There is a clear positive association between a team’s OBP and its SLG.

ggplot(data=teams2015, aes(x=OBP, y=SLG)) +
  geom_point()

1.4 Other Aesthetics (color, shape, and size)

There are other roles or aesthetics that you can assign to variables.

For example, the variable lgID gives the league (AL or NL). We can assign lgID to the color aesthetic – so the points are colored by the league variable. This tells us that the team with the highest OBP and highest SLG was from the American League.

ggplot(data=teams2015, 
       aes(x=OBP, y=SLG, color=lgID)) +
  geom_point()

There are other aesthetics like shape and size.

Here I can use different plotting symbols for each league by assigning lgID to the shape aesthetic. Personally, I think the different shapes are harder to distinguish than the different colors.

ggplot(data=teams2015, 
       aes(x=OBP, y=SLG, shape=lgID)) +
  geom_point()

The variable W is the number of team wins. Here I assign the variable W to the size aesthetic. Notice that the team with the highest OBP and SLG values appeared to win a lot of games in the 2015 season.

ggplot(data=teams2015, 
       aes(x=OBP, y=SLG, size=W)) +
  geom_point()

1.5 Facetting

In ggplot2, it is easy to break the plot into several panels defined by a categorical variable – these different panels are called facets. Suppose I want to construct panels of scatterplots of OBP by SLG, where the panels are defined by the league variable.

From this graph, it appears that the AL teams generally had higher SLG values than the NL teams.

ggplot(data=teams2015, 
       aes(x=OBP, y=SLG)) +
  geom_point() +
  facet_grid(~ lgID)

1.6 Some Plot Geoms

There are many possible geometric objects (geoms) that one can use depending on the number of variables and variable types.

1.6.1 A Single Numeric Variable

Suppose one wants to construct a histogram of the OBP’s for the 30 times. Here the single aesthetic is x and we use geom_histogram. I indicate that we want to apply five bins in the histogram.

ggplot(data=teams2015, aes(x=OBP)) + 
  geom_histogram(bins=5)

1.6.2 A Single Categorical Variable

A bar chart is a graph of a single categorical variable that we can produce using the geom_bar geom. This graph confirms that there are 15 teams in each league.

ggplot(data=teams2015, aes(x=lgID)) + geom_bar()

1.6.3 One Categorical Variable and One Numeric Variable

We said earlier that it appeared that the slugging percentages were greater for teams in the American League. A more direct way to graphically compare the two groups of SLG values is by parallel boxplots. Here we assign the x aesthetic to lgID, the y aesthetic to SLG, and use the geom_boxplot geom.

ggplot(data=teams2015, aes(x=lgID, y=SLG)) +
  geom_boxplot()

Another geom that one can use in this scenario is geom_jitter which produces jittered points. The width option controls the width of the horizontal range of the jittering.

ggplot(data=teams2015, aes(x=lgID, y=SLG)) +
  geom_jitter(width=0.1)

1.7 Modifying the Axes

In ggplot2, it is possible to modify all aspects of the graph. I illustrate some basic modificaitons here. I use the ggtitle function to add a plot title, and use the ylab and xlab functions to add x and y labels.

ggplot(data=teams2015, aes(x=lgID, y=SLG)) +
  geom_jitter(width=0.1) +
  ggtitle("Slugging Percentages in the 2015 Season by League") +
  xlab("League") + ylab("Slugging Percentage")

1.8 Learning More About ggplot2

Hopefully this introduction gets you interested in trying out ggplot2 for your own graphs. I encourage you to try out some of the ggplot2 example scripts for the different chapters and then apply ggplot2 for your own problems.

2 Chapter 1 - History of Baseball

2.1 History of Home Run Hitting

We load the packages Lahman, dplyr and ggplot2.

library(Lahman)
library(dplyr)
library(ggplot2)

2.1.1 The Data

The Lahman package contains season to season data for players and teams from the Sean Lahman database. For this history of home runs graph, want to collect the number of home runs hit (variable HR) and number of games played (variable G) for all teams for all seasons since 1900.

Here are a few sample rows of our data.

select(sample_n(Teams, 8), yearID, teamID, HR, G)
  yearID teamID  HR   G
1   1974    SFN  93 162
2   1951    PHA 102 154
3   2008    SFN  94 162
4   2018    DET 135 162
5   1881    CHN  12  84
6   1983    CHA 157 162
7   2014    COL 186 162
8   1987    BOS 174 162

2.1.2 Creating the Variables of Interest

I use the summarize function to collect the total number of home runs hit and the total number of games played for each season.

S <- summarize(group_by(Teams, yearID),
               HR = sum(HR),
               G = sum(G))

I use the filter function to select the summary data for only seasons 1900 or later.

S2 <- filter(S, yearID >= 1900)

2.1.3 Constructing the Graph

Now I can construct the plot. I construct a scatterplot of yearID (horizontal) against the number of home runs hit for each team per game (variable HR / G). I add a smoothing loess curve to the plot to see the general pattern.

ggplot(S2, aes(yearID, HR / G)) +
  geom_point() +
  geom_smooth(method="loess", span=0.3, se=FALSE)

2.2 History of Home Run Leaders

Next suppose we want to graph the leading number of home runs against season for all seasons past 1900.

2.2.1 The Data

The Batting data frame in the Lahman package contains the number of home runs hit by each player each season.

2.2.2 Creating the Variables of Interest

Actually, the Batting table contains more than one row for players who play for more than one team in a given season. So the first use the summarize function to find the number of home runs for each player each season.

S <- summarize(group_by(Batting, yearID, playerID),
                 HR=sum(HR, na.rm=TRUE))

Next, for each season, we collect the maximum number of home runs that are hit. Also we select only the rows of the data frame where the season is at least 1900.

S1 <- summarize(group_by(S, yearID),
                 HR=max(HR, na.rm=TRUE))
S2 <- filter(S1, yearID >= 1900)

Here are the first few rows of our table.

head(S2)
# A tibble: 6 × 2
  yearID    HR
   <int> <int>
1   1900    12
2   1901    16
3   1902    16
4   1903    13
5   1904    10
6   1905     9

2.2.3 Constructing the Graph

Now I can construct the plot. I construct a scatterplot of yearID (horizontal) against the maximum number of home runs hit (variable HR). I add a smoothing loess curve to the plot to see the general pattern.

ggplot(S2, aes(yearID, HR)) +
    geom_point() +
    geom_smooth(method="loess", span=0.3, se=FALSE)

3 Chapter 2 - Career Trajectories

3.1 Plotting a Career Trajectory

Here is a function plot_hr_trajectory() that will graph a specific player’s home run trajectory. It uses three packages: Lahman contains the season-to-season data, dplyr helps with data management, stringr helps with one string operation, and ggplot2 does the graphing.

Here is some insight how plot_hr_trajectory() works:

  • The input is the player’s full name in quotes.

  • Using the People data frame in the Lahman package, I find the playerID and birth information for that player.

  • From the Batting data frame of hitting data, I collect HR, AB for all seasons of the player’s career.

  • I find the Age variable by first finding the player’s birthyear, adjusting the birthyear depending on the birthmonth, and then defining Age.

  • I use ggplot2 to construct a scatterplot and smoothing curve for the home run rate HR / AB.

plot_hr_trajectory <- function(playername){
  require(Lahman)
  require(dplyr)
  require(stringr)
  require(ggplot2)
  names <- unlist(str_split(playername, " "))
  info <- filter(People, nameLast==names[2],
                       nameFirst==names[1])

  bdata <- filter(Batting, playerID==info$playerID)
  bdata <- mutate(bdata,
          birthyear = ifelse(info$birthMonth >= 7, 
                  info$birthYear + 1, info$birthYear),
          Age = yearID - birthyear)

  ggplot(bdata, aes(yearID, HR / AB)) + 
    geom_point() +
    geom_smooth(method="loess", se=FALSE)
}

3.2 Plotting Two Trajectories

I illustrate using this function for two players. Note that I am saving the ggplot2 plotting object in a variable. By just typing the variable name, I see the graph.

p1 <- plot_hr_trajectory("Mickey Mantle")
p1

p2 <- plot_hr_trajectory("Mike Schmidt")
p2

3.3 Comparing Trajectories

The ggplot2 object contains the plotting data. So I combine the data from the two earlier plotting objects to construct a graph that compares the two trajectories.

ggplot(rbind(p1$data, p2$data), aes(Age, HR / AB)) +
  geom_point() +
  geom_smooth(method="loess", se=FALSE) +
  facet_wrap(~ playerID, ncol=1)

4 Chapter 3 - Runs Expectancy

This chapter illustrates graphing the famous runs expectancy matrix.

First load some required packages.

library(readr)
library(knitr)
library(ggplot2)

4.1 The Data

To obtain the runs expectancy matrix, one needs the Retrosheet play-by-play data for a particular season. I have computed the runs expectancies using 2015 season data. I have stored the data into a csv file that we read into R and store in the variable RR.

RR <- read_csv("https://bayesball.github.io/VB/data/runs2015.csv")

Use the kable function to display the data frame containing the runs expectancies.

kable(RR)
…1 STATE Mean Outs Bases O
1 000 0 0.4738828 OUTS = 0 000 0
2 000 1 0.2514400 OUTS = 1 000 1
3 000 2 0.0988068 OUTS = 2 000 2
4 001 0 1.4011407 OUTS = 0 003 0
5 001 1 0.9643617 OUTS = 1 003 1
6 001 2 0.3630464 OUTS = 2 003 2
7 010 0 1.1109418 OUTS = 0 020 0
8 010 1 0.6637977 OUTS = 1 020 1
9 010 2 0.3036562 OUTS = 2 020 2
10 011 0 2.0450000 OUTS = 0 023 0
11 011 1 1.3655761 OUTS = 1 023 1
12 011 2 0.5598688 OUTS = 2 023 2
13 100 0 0.8577522 OUTS = 0 100 0
14 100 1 0.5046115 OUTS = 1 100 1
15 100 2 0.2266157 OUTS = 2 100 2
16 101 0 1.7113951 OUTS = 0 103 0
17 101 1 1.1209412 OUTS = 1 103 1
18 101 2 0.4528302 OUTS = 2 103 2
19 110 0 1.4727344 OUTS = 0 120 0
20 110 1 0.8881782 OUTS = 1 120 1
21 110 2 0.4296086 OUTS = 2 120 2
22 111 0 2.2865412 OUTS = 0 123 0
23 111 1 1.5900901 OUTS = 1 123 1
24 111 2 0.7925729 OUTS = 2 123 2

4.2 Graph of the Matrix

Here I am constructing a scatterplot of the Bases variable against the mean runs variable Mean where the plotting symbol is the O variable (number of outs).

ggplot(RR, aes(Bases, Mean, label=O)) +
    geom_point(size=3) + 
    geom_label(color="black", size=4,
               fontface="bold") +
    ylab("Runs Scored in \n Remainder of Inning") +
    xlab("Runners on Base") +
    theme(axis.text = element_text(size=16),
          axis.title = element_text(size=16))

5 Chapter 4 - Count Effects

Load in a few helpful packages.

library(readr)
library(ggplot2)
library(dplyr)

5.1 The Data

Using the Retrosheet play-by-play data for the 2015 season, I found the expected runs in the remainder of the inning for plate appearances that pass through each possible count. I store these expected runs values in the csv file “count2015a.csv”.

I read this file into R – variable name of data frame is d – and show the first few lines.

d <- read_csv("https://bayesball.github.io/VB/data/count2015a.csv")
head(d)
# A tibble: 6 × 6
  count strikes balls N.Pitches Type         Runs
  <chr>   <dbl> <dbl>     <dbl> <chr>       <dbl>
1 0-0         0     0         0 Neutral -0.000798
2 1-0         0     1         1 Batter   0.0339  
3 0-1         1     0         1 Pitcher -0.0387  
4 2-0         0     2         2 Batter   0.0940  
5 1-1         1     1         2 Pitcher -0.0153  
6 0-2         2     0         2 Pitcher -0.0894

5.2 The Graph

In this graph, the Pitch Number (variable N.Pitches) is graphed against the Runs Value (variable Runs), using the Count (variable count) as the plotting label.

ggplot(d, aes(N.Pitches, Runs, label=count)) +
  geom_point() +
  geom_path(data=filter(d, strikes==0),
     aes(N.Pitches, Runs), color="blue") +
  geom_path(data=filter(d, strikes==1),
     aes(N.Pitches, Runs), color="blue") +
  geom_path(data=filter(d, strikes==2),
     aes(N.Pitches, Runs), color="blue") +
  geom_path(data=filter(d, balls==0),
     aes(N.Pitches, Runs), color="blue") +
  geom_path(data=filter(d, balls==1),
     aes(N.Pitches, Runs), color="blue") +
  geom_path(data=filter(d, balls==2),
     aes(N.Pitches, Runs), color="blue") +
  geom_path(data=filter(d, balls==3),
     aes(N.Pitches, Runs), color="blue") +
  xlab("Pitch Number") +
  ylab("Runs Value") +
  ggtitle("") +
  geom_hline(yintercept=0, color="black") +
  geom_label()

5.3 Data

Above we considered the runs value of plate appearances that pass through each possible count. Here we consider the runs values of balls put in play on each possible count. These runs values are found using 2016 Retrosheet play-by-play data. The data is saved in the csv file “count2015b.csv”. We read in this data and save in the variable S.

S <- read_csv("https://bayesball.github.io/VB/data/count2015b.csv")
head(S)
# A tibble: 6 × 6
  count   Runs strikes balls N.Pitches     N
  <chr>  <dbl>   <dbl> <dbl>     <dbl> <dbl>
1 0-0   0.0402       0     0         0 20668
2 0-1   0.0163       1     0         1 16560
3 0-2   0.0162       2     0         2  8374
4 1-0   0.0506       0     1         1 12366
5 1-1   0.0369       1     1         2 15601
6 1-2   0.0184       2     1         3 14508

5.4 The Graph

In this graph, the Pitch Number (variable N.Pitches) is graphed against the Runs Value (variable Runs), using the Count (variable count) as the plotting label.

ggplot(S, aes(N.Pitches, Runs, label=count, size=N)) +
  xlab("Number of Pitch") +
  ylab("Runs Value") +
  geom_hline(yintercept=0, color="black") +
  geom_label()

6 Chapter 5 - PITCHf/x Data

6.1 The Data

Using the pitchRX package, I downloaded all of the pitch data for all games in the 2016 season. From this large dataset, I collected the data for 2044 pitches thrown by Clayton Kershaw.

Here I read in the pitchFX data and show a few lines.

library(readr)
CK <- read_csv("https://bayesball.github.io/VB/data/kershaw2016.csv")
head(CK)
# A tibble: 6 × 15
  pitch_type     px     pz des             num gameday_link start_speed spin_dir
  <chr>       <dbl>  <dbl> <chr>         <dbl> <chr>              <dbl>    <dbl>
1 FF          0.089  2.75  Called Strike     7 gid_2016_04…        90.1     187.
2 FF          0.083  2.72  Swinging Str…     7 gid_2016_04…        92.3     159.
3 FF         -2.65   2.69  Ball              7 gid_2016_04…        91.3     206.
4 CU         -0.644 -0.231 Ball              7 gid_2016_04…        73.5     354.
5 FF          0.642  4.52  Ball              7 gid_2016_04…        93.1     180.
6 FF         -1.41   2.33  Swinging Str…     7 gid_2016_04…        94.3     155.
# ℹ 7 more variables: spin_rate <dbl>, pfx_x <dbl>, pfx_z <dbl>, type <chr>,
#   pitcher_name <chr>, event <chr>, stand <chr>

Here are the variables in the data frame CK.

  • pitch_type - type of pitch thrown
  • px - horizontal location in zone
  • pz - vertical location in zone
  • des - outcome of pitch
  • start_speed - speed of pitch as it leaves the pitcher’s hand
  • event - outcome of the plate appearance
  • stand

Load several packages.

library(ggplot2)
library(dplyr)
library(stringr)

6.2 Pitch Types Thrown

To get an understanding of what pitch types are thrown, we construct a dotplot of the frequencies of the pitch types (variable pitch_type).

S_CK <- filter(summarize(group_by(CK, pitch_type),
                  N=n()),
            pitch_type %in% c("SL", "FF", "CU", "CH"))
ggplot(S_CK, aes(pitch_type, N)) +
  geom_point(size=3, color="blue") +
  coord_flip() +
  ggtitle("Frequencies of Pitch Type of Clayton Kershaw") +
  theme(plot.title = element_text(size = 14,
                hjust = 0.5))

6.3 Pitch Speeds

These different pitch types are thrown at different speeds. The following display is a boxplot of the speeds (varialbe start_speed) of the four types of pitches thrown by Kershaw.

ggplot(filter(CK, pitch_type %in%
                c("SL", "FF", "CU", "CH")),
       aes(pitch_type, start_speed)) +
  geom_boxplot() + coord_flip() +
  ggtitle("Pitch Speeds") +
  theme(plot.title = element_text(size = 14,
                                  hjust = 0.5)) +
     ylim(70, 100)

6.4 Pitch Breaks

These pitch types are also distinguished by their movement or break. The variables pfx_x and pfx_z give the horizontal and vertical break amounts. (The perspective is from the catcher behind the plate.) The following graph shows the movements for each type of pitch.

CK <- filter(CK, pitch_type %in% c("CU",
                          "FF", "SL"))
ggplot(CK,
  aes(pfx_x, pfx_z, shape=pitch_type)) +
  geom_point(color="blue", size=2, alpha=0.5) +
  ggtitle("Pitch Breaks") +
  theme(plot.title = element_text(size = 14,
                                  hjust = 0.5)) +
  xlab("Horizontal Break") + ylab("Vertical Break")

6.5 Pitch Locations

The variables px and pz give the horizontal and vertical locations of the pitch viewed from the catcher’s perspective. The zone for an average hitter is added to the plots so we can see which pitches are inside and outside of the zone.

topKzone <- 3.5
botKzone <- 1.6
inKzone <- -0.85
outKzone <- 0.85
kZone <- data.frame(
  x=c(inKzone, inKzone, outKzone, outKzone, inKzone),
  y=c(botKzone, topKzone, topKzone, botKzone, botKzone)
)
ggplot(CK) +
  geom_point(data= filter(CK, pitch_type=="CU"),
             aes(px, pz), shape=1) +
  geom_point(data= filter(CK, pitch_type=="FF"),
             aes(px, pz), shape=2) +
  geom_point(data= filter(CK, pitch_type=="SL"),
             aes(px, pz), shape=3) +
  geom_path(aes(x, y), data=kZone, lwd=1, col="blue") +
  facet_wrap(~ pitch_type, ncol=2) +
  xlim(-2, 2) + ylim(-0.5, 5) +
  theme(strip.text = element_text(size = rel(1.5),
                                  hjust=0.5,
                                  color = "black")) +
  ggtitle("Pitch Locations") +
  theme(plot.title = element_text(size = 14,
                                  hjust = 0.5))

Two-dimensional contour plots (from fitting a two-dimensional density estimate) are helpful for visualizing the locations of the different types of pitches.

ggplot(CK) +
  geom_density_2d(aes(px, pz), color="black") +
  geom_path(aes(x, y), data=kZone, lwd=1, col="blue") +
  facet_wrap(~ pitch_type, ncol=2) +
  xlim(-2, 2) + ylim(-0.5, 5) +
  theme(strip.text = element_text(size = rel(1.5),
                                  hjust=0.5,
                                  color = "black")) +
  ggtitle("Pitch Locations") +
  theme(plot.title = element_text(size = 14,
                                  hjust = 0.5))
Warning: Removed 35 rows containing non-finite values (`stat_density2d()`).

6.6 Pitch Outcomes

What are the outcomes of these different types of pitches? We use the variable des which gives a description of the pitch outcome.

SO <- summarize(group_by(CK, pitch_type, des), N=n())
SO <- mutate(SO,
      Outcome=ifelse(str_detect(des, "Foul") == TRUE, "Foul",
      ifelse(str_detect(des, "Swing") == TRUE |
               des == "Missed Bunt", "Swing and Miss",
      ifelse(str_detect(des, "Ball") == TRUE, "Ball",
      ifelse(str_detect(des, "In play") == TRUE, "In play",
             des)))))
SOS <- summarize(group_by(SO, pitch_type, Outcome),
                 F=sum(N))
SOS1 <- summarize(group_by(SO, pitch_type),
                 Total=sum(N))
inner_join(SOS, SOS1) %>%
  mutate(Percentage = 100 * F / Total) -> SOS
ggplot(SOS,
        aes(Outcome, Percentage)) +
  geom_point(size=3, color="blue") +
  coord_flip() + facet_wrap(~ pitch_type, ncol=1) +
  theme(strip.text = element_text(size = rel(1.5),
                                  hjust=0.5,
                                  color = "black"))

6.7 Outcome of a Swing

What if the batter swings at the pitch? We focus on the frequencies of the three outcomes “Foul”, “In play”, and “Miss” for each pitch type.

CK <- mutate(CK,
             Foul = str_detect(des, "Foul"),
             InPlay = str_detect(des, "In play"),
             Miss = str_detect(des, "Swing"),
             Swing = Foul | InPlay | Miss)
CK_swing <- filter(CK, Swing == TRUE)
ggplot(CK_swing, aes(px, pz, color=Miss)) +
  geom_point(alpha=0.75) +
  facet_wrap(~ pitch_type, ncol=2) +
  geom_path(aes(x, y), data=kZone, lwd=1, col="black") +
  facet_wrap(~ pitch_type, ncol=2) +
  xlim(-2, 2) + ylim(-0.5, 5) +
  scale_colour_manual(values = c("gray60", "blue")) +
  theme(strip.text = element_text(size = rel(1.5),
                                  hjust=0.5,
                                  color = "black"))

7 Chapter 6 - Batted Balls

Load some necessary packages.

library(dplyr)
library(ggplot2)
library(stringr)
library(Lahman)
library(readr)

7.1 The Data

The ESPN home run tracker http://www.hittrackeronline.com/ contains a number of variables for each home run hit during the current season. I collected this data for five baseball seasons (2012 through 2016) and the csv file homeruns.csv contains data on 24,299 home runs hit during these five seasons.

d <- read_csv("https://bayesball.github.io/VB/data/homeruns.csv")
head(d)
# A tibble: 6 × 16
  Date    Video Path  Hitter   H_Team Pitcher P_Team Inning Ballpark `Type/Luck`
  <chr>   <chr> <chr> <chr>    <chr>  <chr>   <chr>   <dbl> <chr>    <chr>      
1 10/3/12 Video View  Longori… TB     Arriet… BAL         6 Tropica… JE         
2 10/3/12 Video View  Johnson… CHW    Huff, … CLE         2 Progres… ND         
3 10/3/12 Video View  Maybin,… SD     Kintzl… MIL         6 Miller … PL         
4 10/3/12 Video View  Cano, R… NYY    Morten… BOS         5 Yankee … ND         
5 10/3/12 Video View  Moore, … WSH    Lee, C… PHI         6 Nationa… ND         
6 10/3/12 Video View  Longori… TB     Tillma… BAL         4 Tropica… ND         
# ℹ 6 more variables: True_Dist <dbl>, Speed_off_Bat <dbl>,
#   Elevation_Angle <dbl>, Horiz_Angle <dbl>, Apex <dbl>, N_Parks <dbl>

7.2 (Figure 6.4) distribution of horizontal angle

In the book, I define the horizontal angle which is 180 - Horiz_Angle where Horiz_Angle is the definition of the horizontal angle on the website.

Here is a density plot of the collection of horizontal angles.

ggplot(d, aes(180 - Horiz_Angle)) +
  geom_density() +
  xlim(30, 180 - 30) +
  xlab("Horizontal Angle") +
  ylab("Density") +
  geom_vline(xintercept=90) +
  annotate("text", x=40, y=0.015,
           label="Left\nField", size=6) +
  annotate("text", x=140, y=0.015,
           label="Right\nField", size=6)

7.3 (Figure 6.5) relationship of distance and horizontal angle

Here I graph the horizontal angle against the home run distance and add a smoothing curve to show the general pattern.

ggplot(d, aes(180 - Horiz_Angle, True_Dist)) +
  geom_point(alpha=0.1) + geom_smooth() +
  ylim(300, 500) + xlim(45, 130) +
  xlab("Horizontal Angle") +
  ylab("Distance")

7.4 Relationship of direction and handedness of batter

Here I get information about the batting side of each hitter and merge this information with the main dataset.

Names <- str_split(d$Hitter, ",")
one_row <- function(j, k)
  str_trim(Names[[j]][k])
d$LastName <- sapply(1:24299, one_row, 1)
d$FirstName <- sapply(1:24299, one_row, 2)
d2 <- inner_join(d,
                 select(People, nameLast, nameFirst, bats),
                 by=c("LastName"="nameLast",
                      "FirstName"="nameFirst"))
d2$Batting <- ifelse(d2$bats=="R",
                     "Right-Handed Hitter",
                     "Left-Handed Hitter")

Here I look the right and left batter effects – show how the distribution of the horizontal angle varies among right and left-handed hitters.

ggplot(filter(d2, bats=="R" | bats=="L"),
       aes(180 - Horiz_Angle)) +
  geom_density(size=1.0)  + xlim(45, 130) +
  xlab("Horizontal Angle") +
  ylab("Density") +
  facet_wrap(~ Batting, ncol=1) +
  theme(strip.text = element_text(face="bold", size=16))

7.5 Ballpark effects

Here I look at the proportion of left-sided hr for all parks (Figure 6.7)

S <- summarise(group_by(d2, Ballpark),
               NL=sum(180 - Horiz_Angle < 90),
               NR=sum(180 - Horiz_Angle > 90),
               PL=NL / (NL + NR))
ggplot(filter(S, NL + NR > 200), aes(Ballpark, PL)) +
  geom_point() + coord_flip() +
  ylab("Proportion of Home Runs to Left") +
  geom_hline(yintercept = 0.5)

I focus on 12 extreme parks

S200 <- filter(S, NL + NR > 200)
S200 <- arrange(S200, desc(PL))
Sextreme <- rbind(slice(S200, 1:8),
                  slice(S200, 28:31))
ballparks <- as.character(arrange(Sextreme, PL)$Ballpark)
d2$Ballpark <- factor(d2$Ballpark,
                      levels=ballparks)

(Figure 6.8) This shows the distribution of the horizontal angle for each of these extreme parks.

ggplot(filter(d2, bats=="R" | bats=="L",
              Ballpark %in% Sextreme$Ballpark),
       aes(180 - Horiz_Angle)) +
  geom_density() +
  facet_wrap(~ Ballpark, ncol=4) +
  geom_vline(xintercept = 90, color="blue") +
  xlab("Horizontal Angle") + ylab("Density")

8 Chapter 7 - Plate Discipline

8.1 Plate Discipline Statistics for Batters

Load several useful packages.

library(tidyverse)
library(ggplot2)

8.2 The Data

Collect several useful tables from Fangraphs. The first dataset contains basic hitting statistics and the second dataset has stats related to plate discipline. We merge the two datasets, creating a single data frame, 146 observations and 33 variables.

d1 <- read_csv("https://bayesball.github.io/VB/data/Dashboard_2016.csv")
d2 <- read_csv("https://bayesball.github.io/VB/data/Plate_Discipline_2016.csv")
d <- inner_join(d1, d2, by="playerid")
vars <- c(14, 25:33)
d_subset <- d[, vars]
names(d_subset) <- c("OBP", "O_Swing", "Z_Swing", "Swing",
                     "O_Contact", "Z_Contact",
                     "Contact", "Zone",
                     "F_Strike", "SwStr")
names(d)[c(14, 25:33)] <- names(d_subset)

8.3 Swing and Contact Rates

Following graph constructs a scatterplot of the swing and contact rates for all hitters with a smoothing curve added.

ggplot(d, aes(Swing, Contact)) +
  geom_point(size=2) +
  geom_smooth(se=FALSE) +
  xlab("Swing Rate") + ylab("Contact Rate")

8.4 Relationship with Strikeout Rate

We divide the players into “high” and “low” strikeout groups. We use contact and swing rates to predict (by a logistic model) the probability a hitter is in the high strikeout group. A line is added to the scatterplot – points above (below) the line are predicted to be in the low (high) K groups.

d$K_Rate <- with(d, ifelse(K > .1875, "HI", "LO"))
d$y <- ifelse(d$K_Rate=="HI", 1, 0)
glm(y ~ Contact + Swing, data=d, family=binomial) -> F
ggplot(d, aes(Swing, Contact, 
              color=K_Rate)) +
  geom_point(size=3) +
  xlab("Swing Rate") + ylab("Contact Rate") +
  geom_abline(intercept = coef(F)[1] / (-coef(F)[2]),
              slope = coef(F)[3] / (-coef(F)[2])) +
  scale_shape(solid = FALSE) +
  scale_colour_manual(values = c("black", "grey60"))

8.5 Relationship with Walk Rate

We divide the players into “high” and “low” walk groups. We use contact and swing rates to predict (by a logistic model) the probability a hitter is in the high walk group. A line is added to the scatterplot – points to the left (to the right) of the line are predicted to be in the high (low) walk groups.

d$BB_Cat <- with(d, ifelse(BB > .082, "HI", "LO"))
d$y <- ifelse(d$BB_Cat=="HI", 1, 0)
glm(y ~ Contact + Swing, data=d, family=binomial) -> F
ggplot(d, aes(Swing, Contact, 
              color=BB_Cat)) +
  xlab("Swing Rate") + ylab("Contact Rate") +
  geom_point(size=3) +
  geom_abline(intercept = coef(F)[1] / (-coef(F)[2]),
              slope = coef(F)[3] / (-coef(F)[2])) +
  scale_shape(solid = FALSE) +
  scale_colour_manual(values = c("black", "grey60"))

8.6 Contrasting the top and bottom K hitters

We first identify the players who have the smallest (TOP) and largest (BOTTOM) strikeout rates.

d <- mutate(d,
            K_Type=ifelse(K < .12, "TOP",
                  ifelse(K > .25, "BOTTOM", NA)))
select(filter(d, K_Type == "TOP"),
       Name.x, Team.x, K)
# A tibble: 16 × 3
   Name.x           Team.x        K
   <chr>            <chr>     <dbl>
 1 Mookie Betts     Red Sox   0.11 
 2 Jose Altuve      Astros    0.098
 3 Adrian Beltre    Rangers   0.103
 4 Daniel Murphy    Nationals 0.098
 5 Dustin Pedroia   Red Sox   0.105
 6 Jose Ramirez     Indians   0.1  
 7 Buster Posey     Giants    0.111
 8 Ender Inciarte   Braves    0.118
 9 Martin Prado     Marlins   0.105
10 Yadier Molina    Cardinals 0.108
11 Joe Panik        Giants    0.089
12 Jose Iglesias    Tigers    0.097
13 Yunel Escobar    Angels    0.118
14 Melky Cabrera    White Sox 0.107
15 Brandon Phillips Reds      0.116
16 Albert Pujols    Angels    0.115
select(filter(d, K_Type == "BOTTOM"),
       Name.x, Team.x, K)
# A tibble: 16 × 3
   Name.x           Team.x           K
   <chr>            <chr>        <dbl>
 1 Jonathan Villar  Brewers      0.256
 2 Adam Duvall      Reds         0.27 
 3 Chris Davis      Orioles      0.329
 4 Khris Davis      Athletics    0.272
 5 Jake Lamb        Diamondbacks 0.259
 6 Leonys Martin    Mariners     0.259
 7 Mark Trumbo      Orioles      0.255
 8 Russell Martin   Blue Jays    0.277
 9 Danny Espinosa   Nationals    0.29 
10 Travis Shaw      Red Sox      0.251
11 Michael Saunders Blue Jays    0.281
12 Justin Upton     Tigers       0.286
13 Alex Gordon      Royals       0.292
14 Melvin Upton Jr. - - -        0.288
15 Mike Napoli      Indians      0.301
16 Chris Carter     Brewers      0.32

Similarly we identify the players with the largest (TOP) and smallest (BOTTOM) walk rates

d <- mutate(d,
            BB_Type=ifelse(BB > .13, "TOP",
                  ifelse(BB < .05, "BOTTOM", NA)))
select(filter(d, BB_Type == "TOP"),
       Name.x, Team.x, BB)
# A tibble: 13 × 3
   Name.x           Team.x          BB
   <chr>            <chr>        <dbl>
 1 Mike Trout       Angels       0.17 
 2 Josh Donaldson   Blue Jays    0.156
 3 Joey Votto       Reds         0.16 
 4 Paul Goldschmidt Diamondbacks 0.156
 5 Dexter Fowler    Cubs         0.143
 6 Brandon Belt     Giants       0.159
 7 Ben Zobrist      Cubs         0.152
 8 Carlos Santana   Indians      0.144
 9 Bryce Harper     Nationals    0.172
10 Matt Carpenter   Cardinals    0.143
11 Chris Davis      Orioles      0.132
12 Jose Bautista    Blue Jays    0.168
13 Joe Mauer        Twins        0.137
select(filter(d, BB_Type == "BOTTOM"),
       Name.x, Team.x, BB)
# A tibble: 15 × 3
   Name.x           Team.x       BB
   <chr>            <chr>     <dbl>
 1 Starling Marte   Pirates   0.043
 2 Kevin Pillar     Blue Jays 0.041
 3 Eduardo Nunez    - - -     0.049
 4 Didi Gregorius   Yankees   0.032
 5 Freddy Galvis    Phillies  0.04 
 6 Salvador Perez   Royals    0.04 
 7 Jonathan Schoop  Orioles   0.032
 8 Rougned Odor     Rangers   0.03 
 9 Josh Harrison    Pirates   0.034
10 Starlin Castro   Yankees   0.039
11 Brandon Phillips Reds      0.031
12 Adonis Garcia    Braves    0.043
13 Alcides Escobar  Royals    0.04 
14 Marwin Gonzalez  Astros    0.042
15 Alexei Ramirez   - - -     0.042

8.7 Comparing Top and Bottom Strikeout Hitters

This scatterplot compares the top and bottom K groups with respect to the contact rates in the zone and outside of the zone.

ggplot(filter(d, K_Type %in% c("TOP", "BOTTOM")),
        aes(Z_Contact, O_Contact, color=K_Type)) +
         geom_point(size=3) +
  scale_shape(solid = FALSE) +
  scale_colour_manual(values = c("grey50", "black" ))

8.8 Comparing Top and Bottom Walk Hitters

This scatterplot compares the top and bottom BB groups with respect to the swing rates in the zone and outside of the zone.

ggplot(filter(d, BB_Type %in% c("TOP", "BOTTOM")),
        aes(Z_Swing, O_Swing, color=BB_Type)) +
         geom_point(size=3) +
  scale_shape(solid = FALSE) +
  scale_colour_manual(values = c("grey50", "black" ))

9 Chapter 8 - Probability and Modeling

Load in some necessary packages.

library(dplyr)
library(ggplot2)
library(stringr)
library(readr)

9.1 The Data

The FanGraphs page http://www.fangraphs.com/plays.aspx?date=2016-11-02&team=Indians&dh=0 provides a play log for Game 7 of the 2016 World Series. The table on that page was downloaded and stored in a csv file that is read into R.

d <- read_csv("https://bayesball.github.io/VB/data/WSGame7.csv")
d$Play_Number <- 1:dim(d)[1]
d$WE  <- as.numeric(str_replace(d$WE, "%", ""))
head(d)
# A tibble: 6 × 13
  Pitcher  Player    Inn.  Outs Base  Score Play     LI    RE    WE    WPA  RE24
  <chr>    <chr>    <dbl> <dbl> <chr> <chr> <chr> <dbl> <dbl> <dbl>  <dbl> <dbl>
1 C Kluber D Fowler     1     0 ___   0-1   Dext…  0.87  0.48  39.8  0.102  1   
2 C Kluber K Schwa…     1     0 ___   0-1   Kyle…  0.79  0.48  36.7  0.032  0.37
3 C Kluber K Bryant     1     0 1__   0-1   Kris…  1.3   0.85  39.6 -0.029 -0.35
4 C Kluber A Rizzo      1     1 1__   0-1   Anth…  1.05  0.5   42.1 -0.025 -0.28
5 C Kluber K Schwa…     1     2 1__   0-1   Kyle…  0.72  0.22  41.2  0.009  0.09
6 C Kluber B Zobri…     1     2 _2_   0-1   Ben …  1.04  0.31  44.1 -0.029 -0.31
# ℹ 1 more variable: Play_Number <int>

9.2 Plot of Win Probabilities of a Game

The WE column of the data frame gives the win probability as a percentage. The below plot graphs the win probability against the Play_Number variable. I add additional text indicating the inning of the game.

ggplot(d, aes(Play_Number, WE / 100)) +
  geom_point(size=2) +
  geom_line() +
  ylim(0, 1) +
  ggtitle("") +
  ylab("Probability Indians Win") +
  geom_hline(yintercept = .50, color="blue", size=1.5) +
  annotate("text", x=cumsum(c(0, 10, 7, 9, 9, 12, 8,
                              8, 10, 8)) +
             c(10, 7, 9, 9, 12, 8,
               8, 10, 8, 14) / 2,
           y=0.90,
           label = as.character(1:10), size=5) +
  annotate("text", x=45, y=0.98, 
           label="INNING", size=6) +
  xlab("Play Number")

9.3 Plot of Leverages

The variable LI is the leverage of the game situation defined by the score, inning, runners on base and number of outs. This graph plots the leverage values against the play number.

ggplot(d, aes(Play_Number, LI)) +
  geom_segment(aes(xend = Play_Number, yend = 0),
               size = 2, lineend = "butt") +
  xlab("Play Number") +
  ylab("Leverage")  +
  ylim(0, 5.8) +
  annotate("text", x=cumsum(c(0, 10, 7, 9, 9, 12, 8,
                              8, 10, 8)) +
             c(10, 7, 9, 9, 12, 8,
               8, 10, 8, 14) / 2,
           y=5,
           label = as.character(1:10), size=5) +
  annotate("text", x=45, y=5.5, label="INNING", size=6)

9.4 Plot of Win Probability Added

The variable WPA provides the change in the win probability for each play. This graph plots WPA against the play number.

ggplot(d, aes(Play_Number, WPA)) +
  geom_segment(aes(xend = Play_Number, yend = 0),
               size = 2, lineend = "butt") +
  xlab("Play Number") +
  ylab("Win Probability Added") +
  ylim(-0.24, 0.6) +
  annotate("text", x=cumsum(c(0, 10, 7, 9, 9, 12, 8,
                              8, 10, 8)) +
             c(10, 7, 9, 9, 12, 8,
               8, 10, 8, 14) / 2,
           y=0.53,
           label = as.character(1:10), size=5) +
  annotate("text", x=45, y=0.60, label="INNING", size=6) +
  annotate('text', x=71, y=0.45, label="Davis\nHR") +
  annotate('text', x=85, y=0.38, label="Zobrist\n2B") +
  annotate('text', x=77, y=-0.22, label="Baez\nSO")

10 Chapter 9 - Streakiness and Clutch Play

10.1 Streakiness Graphs

Load the BayesTestStreak package (available on Github). This package will be used to generate the streakiness graphs of this chapter.

Note: One can install the BayesTestStreak package by use of the install_github() function from the remotes package. (The installation need be done only once.)

remotes::install_github("bayesball/BayesTestStreak")
library(BayesTestStreak)
library(gridExtra)

By the way, to see the R code, one just types the name of the function. For example, to see the code for the moving average function, type moving_average_plot.

moving_average_plot
function (mavg_data) 
{
    ggplot(mavg_data, aes(x = Index, ymax = Average, ymin = AVG)) + 
        geom_ribbon(fill = "blue") + theme_minimal()
}
<bytecode: 0x7fb26bb43fe0>
<environment: namespace:BayesTestStreak>

10.2 The Data

First I use the find_id function in the package to find the Retrosheet ids for these two hitters.

walker_id <- find_id("Neil Walker")
aoki_id <- find_id("Nori Aoki")

Collect the hit/out sequences for both players.

walker <- streak_data(walker_id, pbp2016, "H", AB=TRUE)
aoki <- streak_data(aoki_id, pbp2016, "H", AB=TRUE)

10.3 “Rug Plots”

Here are simple lines showing the AB occurrences of all seasons during the season

plot_streak_data(walker) + theme(plot.title = element_text(colour = "blue", size = 18, 
        hjust = 0.5)) + ggtitle("Walker")

plot_streak_data(aoki) + theme(plot.title = element_text(colour = "blue", size = 18, 
        hjust = 0.5)) + ggtitle("Aoki")

10.4 Moving average plots

The function moving_average computes the moving averages and moving_average_plot constructs the moving average plot.

walker_s_data <- moving_average(walker, 50)
moving_average_plot(walker_s_data) +  
  theme(plot.title = element_text(colour = "blue", 
                                  size = 18, 
        hjust = 0.5)) + ggtitle("Walker")

aoki_s_data <- moving_average(aoki, 50)
moving_average_plot(aoki_s_data) + 
  theme(plot.title = element_text(colour = "blue", size = 18, 
        hjust = 0.5)) + ggtitle("Aoki")

For comparison, better to put the two moving average plots on the same scale:

p1 <- moving_average_plot(walker_s_data) + 
  ylim(.1, .5) +
  annotate("text", x=200, y=0.45,
           label="Neil Walker", size=7) +
  ylab("Moving Average") + xlab("") 
p2 <- moving_average_plot(aoki_s_data) + 
  ylim(.1, .5) +
  annotate("text", x=200, y=0.45,
           label="Nori Aoki", size=7) +
  ylab("Moving Average") + xlab("At Bat Number")
grid.arrange(p1, p2)

10.5 Geometric Plots

sp <- find_spacings(walker)
geometric_plot(sp) + 
  theme(plot.title = element_text(colour = "blue", size = 18, 
        hjust = 0.5)) + ggtitle("Walker")

sp <- find_spacings(aoki)
geometric_plot(sp) + 
  theme(plot.title = element_text(colour = "blue", 
                                  size = 18, 
        hjust = 0.5)) + ggtitle("Aoki")