7.4 Where is the Strike Zone?

• Only part of the ball needs to cross home plate to be a strike
• Home plate is 17 inches wide and ball’s circumference is 9 inches
• Outside edges of strike zone vary by plus or minus 0.947 feet
• Top and bottom of strike zone varies by batter height (Midpoint between top of shoulders and top of players pants down to hollow beneath kneecap)

MLB Strike Zone

plate_width <- 17 + 2 * (9/pi)
k_zone_plot <- ggplot(
  NULL, aes(x = plate_x, y = plate_z)
) + 
  geom_rect(
    xmin = -(plate_width/2)/12, 
    xmax = (plate_width/2)/12, 
    ymin = 1.5, 
    ymax = 3.6, color = crcblue, alpha = 0
  ) + 
  coord_equal() + 
  scale_x_continuous(
    "Horizontal location (ft.)", 
    limits = c(-2, 2)
  ) + 
  scale_y_continuous(
    "Vertical location (ft.)", 
    limits = c(0, 5)
  )

k_zone_plot %+% 
  sample_n(taken, size = 2000) +
  aes(color = Outcome) +
  geom_point(alpha = 0.2) + 
  scale_color_manual(values = crc_fc)

zones <- taken |>
  group_by(zone) |>
  summarize(
    N = n(), 
    right_edge = min(1.5, max(plate_x)), 
    left_edge = max(-1.5, min(plate_x)),
    top_edge = min(5, quantile(plate_z, 0.95, na.rm = TRUE)), 
    bottom_edge = max(0, quantile(plate_z, 0.05, na.rm = TRUE)),
    strike_pct = sum(Outcome == "called_strike") / n(),
    plate_x = mean(plate_x), 
    plate_z = mean(plate_z)
  )

library(ggrepel)
k_zone_plot %+% zones + 
  geom_rect(
    aes(
      xmax = right_edge, xmin = left_edge,
      ymax = top_edge, ymin = bottom_edge,
      fill = strike_pct, alpha = strike_pct
    ), 
    color = "lightgray"
  ) +
  geom_text_repel(
    size = 3, 
    aes(
      label = round(strike_pct, 2),
      color = strike_pct < 0.5
    )
  ) + 
  scale_fill_gradient(low = "gray70", high = crcblue) + 
  scale_color_manual(values = crc_fc) +
  guides(color = FALSE, alpha = FALSE)