Understanding Pitching Data

Overview

This past week, I started talking to one of my classmates, Shabab Ahmed, about the possibility of doing a research project together. The one problem: it has to do with the sport of baseball. Shabab is a big cricket fan, which makes him more baseball-literate than perhaps the average person that you’d encounter in academia, but the project will have to do with some of the finer points of baseball strategy.

However, this realization is important to have early on, as discussing this project with people who aren’t familiar with baseball will require us to give them the basics quickly. The data that we have is also a little opaque with respect to documentation, so we need to walk through to figure out how to use it best. Thus, this post will be a combination of data exploration and explanation of how pitching works in baseball¹.

The Data

pitches_og[code != type | (is.na(type) & !is.na(code)) | (is.na(code) & !is.na(type))]

## Empty data.table (0 rows and 40 cols): px,pz,start_speed,end_speed,spin_rate,spin_dir...

table(pitches_og$spin_dir, useNA = 'always')

## 
##             placeholder        <NA> 
##        6629      722161           0

table(pitches_og$spin_rate, useNA = 'always')

## 
##             placeholder        <NA> 
##        6629      722161           0

table(pitches_og$nasty, useNA = 'always')

## 
##   <NA> 
## 728790

table(pitches_og$zone, useNA = 'always')

## 
##             placeholder        <NA> 
##        6629      722161           0

Pitching in Baseball

For the uninitiated to America’s Pastime, the goal of the game is to end nine innings with more runs than your opponent. You score runs by getting hits, and the job of the pitcher is to prevent hits (this is obviously extremely simplistic, but more detail isn’t necessary at the moment). The pitcher prevents hits by throwing pitches that are difficult for the batter to hit. However, the pitcher faces a constraint: if they throw four pitches that are not in the strike zone over the course of an at-bat as judged by the umpire (referee), the batter is allowed to advance to first base for free (this is called a walk). Such an outcome is not desirable for the pitcher, so their goal is to throw pitches that are maximally difficult to hit, while satisfying the constraint of being within the strike zone (as if the batter does not swing at a pitch judged to be in the strike zone, it’s counted as a strike).

To visualize an at-bat, I’m going to first merge all the data together to create the full_data dataset:

abs_og <- fread('~/Google Drive/Raw Data/mlb_pitch_data/2019_atbats.csv') %>% 
  mutate_at(vars(ends_with('_id')), list(~ as.character(.))) %>% 
  data.table()

names_og <- fread('~/Google Drive/Raw Data/mlb_pitch_data/player_names.csv') %>% 
  mutate_at(vars(ends_with('id')), list(~ as.character(.))) %>% 
  data.table()

games_og <- fread('~/Google Drive/Raw Data/mlb_pitch_data/2019_games.csv') %>% 
  mutate_at(vars(ends_with('_id')), list(~ as.character(.))) %>% 
  data.table()

full_data <- pitches_og %>% 
  left_join(abs_og,
            by = 'ab_id') %>% 
  left_join(names_og %>% 
              select(pitcher_id = id, 
                     pitcher_first_name = first_name, 
                     pitcher_last_name = last_name),
            by = 'pitcher_id') %>% 
  left_join(names_og %>% 
              select(batter_id = id, 
                     batter_first_name = first_name, 
                     batter_last_name = last_name),
            by = 'batter_id') %>% 
  left_join(games_og,
            by = 'g_id')

So what does an at-bat actually look like? Well, we can build a function using this data to visualize a given at-bat.

full_data_built <- full_data %>% 
  group_by(batter_id) %>% 
  mutate(sz_bot_mean = mean(sz_bot),
         sz_top_mean = mean(sz_top)) %>% 
  ungroup() %>% 
  mutate(date = as.Date(date)) %>% 
  data.table()

visualize_ab <- function(ab_id_var, box = FALSE){
  
  ab_data <- full_data_built[ab_id == ab_id_var]
  
  # strike zone/plate dimensions
  low_sz <- unique(ab_data$sz_bot_mean)
  high_sz <- unique(ab_data$sz_top_mean)
  
  plate_min = -17/12/2
  plate_max = 17/12/2
  
  # pitcher and batter name
  pitcher <- unique(ab_data$pitcher_last_name)
  batter <- unique(ab_data$batter_last_name)
  date <- unique(ab_data$date)
  
  # make url (need to figure out how to identify doubleheaders, probably just by date?)
  home_team <- toupper(unique(ab_data$home_team))
  url <- str_interp('https://www.baseball-reference.com/boxes/${home_team}/${home_team}${format(date,"%Y%m%d")}0.shtml')
  
  # formatting vectors
  values_vec <- c('B' = 'red',
                  '*B' = 'red',
                  'I' = 'red',
                  'P' = 'red',
                  'C' = 'green',
                  'S' = 'purple',
                  'W' = 'purple',
                  'M' = 'purple',
                  'Q' = 'purple',
                  'X' = 'blue',
                  'D' = 'blue',
                  'E' = 'blue',
                  'F' = 'orange',
                  'T' = 'orange',
                  'L' = 'orange',
                  'R' = 'orange',
                  'H' = 'grey',
                  'E' = 'blue')
  
  labels_vec <- c('B' = 'Ball',
                  '*B' = 'Ball in dirt',
                  'I' = 'Intentional Ball',
                  'P' = 'Pitchout',
                  'C' = 'Strike (Called)',
                  'S' = 'Strike (Swinging)',
                  'W' = 'Strike (Swinging, Blocked)',
                  'M' = 'Missed Bunt',
                  'Q' = 'Swinging Pitchout',
                  'X' = 'In Play, Out(s)',
                  'D' = 'In Play, No Out',
                  'E' = 'In Play, Run(s)',
                  'F' = 'Foul',
                  'T' = 'Foul Tip',
                  'L' = 'Foul Bunt',
                  'R' = 'Foul Pitchout',
                  'H' = 'Hit By Pitch',
                  'E' = 'In Play')
  
  if(box == TRUE){
    cat(url)
  }
  
  
  # plot
  ggplot(ab_data) + 
    scale_x_continuous(limits = c(min(-1, min(ab_data$px) - .25/2),
                                  max(1, max(ab_data$px) + .25/2)), 
                       expand = expansion(mult = .03)) + 
    scale_y_continuous(limits = c(min(1, min(ab_data$pz) - .25/2),
                                  max(4, max(ab_data$pz) + .25/2)),
                       expand = expansion(mult = .03)) +
    ggforce::geom_circle(aes(x0 = px, y0 = pz, color = code, fill = code, r = .25/2),
                         alpha = .5) + 
    geom_text(aes(x = px, y = pz, label=pitch_num), hjust=.5, vjust=.5) +
    geom_rect(xmin = plate_min, 
              xmax = plate_max,
              ymin = low_sz,
              ymax = high_sz,
              alpha = 0,
              color = 'black') +
    scale_color_manual(values = values_vec,
                       labels = labels_vec) + 
    scale_fill_manual(values = values_vec,
                      labels = labels_vec) + 
    theme(legend.position = 'bottom',
          legend.title = element_blank(),
          axis.title = element_blank()) + 
    coord_fixed() + 
    labs(title = str_interp('${pitcher} vs ${batter} (${abs_og[ab_id == ab_id_var]$stand}), ${ifelse(abs_og[ab_id == ab_id_var]$top == 0, "Bottom", "Top")} ${abs_og[ab_id == ab_id_var]$inning}'),
         subtitle = str_interp('Result: ${abs_og[ab_id == ab_id_var]$event}'))
} 

The function is sort of long – here are the only somewhat interesting decisions that I made when building it (the rest is just base ggplot):

• The use of the ggforce package’s function geom_circle instead of ggplot’s base function geom_point to plot. The only reason I did this was to be able to try to make the circles the actual size of a baseball to contextualize them better.
• The inclusion of a url parameter. I realized that I was spending a lot of time checking at-bats with https://www.baseballreference.com, so I decided to try to decrease the difficulty of accessing Baseball Reference by creating the game’s URL in the function if the user chooses.
• I plotted the strike zone for a batter by taking the average of all their sz_top and sz_bot observations in the data. The outer bounds of the plate are defined by the size of home plate (17 inches) and the fact that it’s centered in PITCHf/x data on 0.

A visualization will look something like this:

visualize_ab('2019000030')

On this at-bat, we see that there were 8 pitches. The first was a called strike that looks like it was slightly off the plate. The next pitch was a low ball, the next a foul, and so on, until on the eighth pitch of the at-bat, Semien hits a home run on a pitch in the center of the plate. This at-bat actually motivates the discussion of pitching strategy below.

# get the average strike zone for reference
zone <- full_data %>% 
  distinct(batter_id, sz_bot, sz_top) %>% 
  summarise(mean_low = mean(sz_bot),
            mean_high = mean(sz_top))

outcome_data <- full_data %>% 
  # filter to strikes
  filter(code %in% c('C', 'S', 'W', 'M', 'Q', 'X', 'D', 'E', 'F', 'T', 'L', 'R')) %>% 
  # calculate bases on those strikes
  mutate(bases = case_when(event == 'Single' & code %in% c('X', 'D', 'E') ~ 1,
                           event == 'Double' & code %in% c('X', 'D', 'E') ~ 2,
                           event == 'Triple' & code %in% c('X', 'D', 'E') ~ 3,
                           event == 'Home Run' & code %in% c('X', 'D', 'E') ~ 4,
                           TRUE ~ 0)) %>% 
  distinct(batter_id, batter_first_name, event, pitch_num, type, batter_last_name, ab_id, bases, px, pz) %>% 
  # each box is one square inches
  mutate(px_box = floor(px * 12)/12,
         pz_box = floor(pz * 12)/12) %>% 
  group_by(px_box, pz_box) %>% 
  summarise(mean_bases = mean(bases),
            n = n()) %>% 
  ungroup() %>% 
  # somewhat arbitrarily throw out any box that has fewer than 50 pitches
  filter(n >= 50, !is.na(mean_bases), !is.na(px_box), !is.na(pz_box)) %>% 
  data.table()

ggplot(data = outcome_data) +
  geom_tile(aes(x = px_box, y = pz_box, fill = mean_bases)) +
  scale_fill_gradient(low = 'red', high = 'green') +
  geom_rect(xmin = -17/12/2,
            xmax = 17/12/2,
            ymin = zone$mean_low,
            ymax = zone$mean_high,
            alpha = 0,
            color = 'black') +
  theme(axis.title = element_blank()) +
  guides(fill=guide_legend(title="Mean Bases"))

zone_mean <- (zone$mean_low + zone$mean_high)/2

reg_data <- full_data %>% 
  # filter to strikes
  filter(code %in% c('C', 'S', 'W', 'M', 'Q', 'X', 'D', 'E', 'F', 'T', 'L', 'R')) %>% 
  # calculate bases on those strikes
  mutate(bases = case_when(event == 'Single' & code %in% c('X', 'D', 'E') ~ 1,
                           event == 'Double' & code %in% c('X', 'D', 'E') ~ 2,
                           event == 'Triple' & code %in% c('X', 'D', 'E') ~ 3,
                           event == 'Home Run' & code %in% c('X', 'D', 'E') ~ 4,
                           TRUE ~ 0),
         abs_px = abs(px),
         abs_pz = abs(pz - zone_mean)) %>% 
  distinct(ab_id, pitch_num, bases, abs_px, abs_pz, px, pz, end_speed, break_angle, break_length)

basic_pitch_reg <- lm(bases ~ end_speed + abs_px + abs_pz + end_speed*break_length + break_angle + break_length, data = reg_data)

Summary

So what should we take away from this basic review? Pitchers are trying to throw balls that are at the edges of the strike zone. In addition, they want to throw pitches that break a lot or are really fast (or in theory, both!)

There are a few other components that we’ll want to investigate as part of the conventional knowledge. One is the sequence of pitches – is a pitcher keeping a hitter “off-balance” by throwing pitches in varying speeds and locations? We also want to look at (and likely control for) the platoon advantage, which is the idea that a righty pitcher vs. a righty batter or a lefty pitcher vs. a lefty batter is an advantageous matchup (in general) for a pitcher, while a righty pitcher vs. a lefty batter or a lefty pitcher vs. a righty batter is an advantageous situation for the batter.

I’ll probably dig into that a little more in a further post, but this is a good starting point for the theory and intuition of basic pitching in baseball.