Combined Half No-Hitters

In August 2020 on Episode 1580 of “Effectively Wild”, there was a discussion about “Combined Half No-Hitters”, where neither team allows a hit through 4.5 innings, leading to 9 total half-innings without a hit. I did the queries in my Retrosheet database to find a list of every combined half no-hitter.

To look this up, I first read in attached my R session to my PostgreSQL database using the “dbcon.R” file, then read in the necessary columns of the play-by-play table.

library(tidyverse)
library(lubridate)
source("dbcon.R")
pbp <- dbGetQuery(con, "select game_id, away_team_id, inn_ct, bat_home_id, event_cd from retro_pbp_2")
games <- dbGetQuery(con, "select game_id, home_starting_pitcher_name, visitor_starting_pitcher_name from retro_games")

I then filter the play-by-play to the first 4.5 innings of the games, grouped by the game, and counted the number of hits (hits have an event code between 20 and 23). Games that fit the combined half no-hitter description will have no hits in the first 4.5 innings, so I filter to the games that have no hits and arrange by most recent date. The below table shows every combined half no-hitter in the database.

nohit <- pbp %>% 
  filter(inn_ct < 5 | (inn_ct == 5 & bat_home_id == 0)) %>% 
  group_by(game_id, away_team_id) %>% 
  summarize(n_hits = sum(event_cd %in% 20:23, na.rm = TRUE)) %>% 
  ungroup() %>% 
  filter(n_hits == 0) %>% 
  arrange(desc(as.numeric(substr(game_id, 4,11))))

nohit %>% 
  mutate(home_team = substr(game_id, 1,3)) %>% 
  mutate(date = ymd(as.numeric(substr(game_id, 4,11)))) %>% 
  left_join(games, by = "game_id") %>% 
  select(Date = date,
         "Home Team" = home_team, 
         "Home Starter" = home_starting_pitcher_name,
         "Away Team" = away_team_id,
         "Away Starter" = visitor_starting_pitcher_name) %>%
  kableExtra::kable() %>% 
  kableExtra::kable_styling() %>% 
  kableExtra::scroll_box(height = "500px")

There are 111 combined half no-hitters in the database, which is about half the number of true no-hitters. The below chart shows the number of no-hitters of each type for each season going back to 1970.

nohit_real <- pbp %>% 
  group_by(game_id, away_team_id, bat_home_id) %>% 
  filter(max(inn_ct) >= 8) %>% 
  summarize(n_hits = sum(event_cd %in% 20:23, na.rm = TRUE)) %>% 
  ungroup() %>% 
  filter(n_hits == 0) %>% 
  arrange(desc(as.numeric(substr(game_id, 4,11))))

ggplot() +
  geom_line(nohit %>% ungroup() %>% count(year = as.numeric(substr(game_id,4,7))) %>% complete(year = 1916:2020, fill = list(n=0)), mapping = aes(x=year, y = n, col = "4.5 Inning"), na.rm = TRUE) +
  geom_point(nohit %>% ungroup() %>% count(year = as.numeric(substr(game_id,4,7))) %>% complete(year = 1916:2020, fill = list(n=0)), mapping = aes(x=year, y = n, col = "4.5 Inning"), na.rm = TRUE) +
  geom_line(nohit_real %>% ungroup() %>% count(year = as.numeric(substr(game_id,4,7))) %>% complete(year = 1916:2020, fill = list(n=0)), mapping = aes(x=year, y = n, col = "Regular"), na.rm = TRUE) +
  geom_point(nohit_real %>% ungroup() %>% count(year = as.numeric(substr(game_id,4,7))) %>% complete(year = 1916:2020, fill = list(n=0)), mapping = aes(x=year, y = n, col = "Regular"), na.rm = TRUE) +
  theme_light() +
  xlim(c(1970,2020)) +
  labs(x= "Year", y = "Number of Games",
       col = "No-Hitter Type")

In the episode, Ben Lindbergh and Sam Miller talked about why there are about half as many of these combined half no-hitters as there are regular no-hitters. My theory is that in each game, there are two opportunities for a regular no-hitter (one for the home team, one for the away team), but only one opportunity for a combined half no-hitter.