Functions to Simulate a Half-Inning of Baseball

simulation_half_inning.R

# to simulate the number of runs in one half-inning
# st <- runs_setup() 
# simulate_half_inning(st)

runs_setup <- function(){
  # based on 2015 season data
  Prob_Single <- matrix(0, 8, 8)
  dimnames(Prob_Single)[[1]] <- c("000", "100", "010", "001",
                       "110", "101", "011", "111")
  dimnames(Prob_Single)[[2]] <- c("000", "100", "010", "001",
                       "110", "101", "011", "111")
  Prob_Single["000", "100"] <- 1
  Prob_Single["100", c("101", "110")] <- 
       round(c(1411,  3940) / (1411 + 3940), 3)
  Prob_Single["010", c("100", "101")] <- 
       round(c(1044,  768) / (1044 + 768), 3)
  Prob_Single["001", "100"] <- 1 
  Prob_Single["110", c("101", "110", "111")] <- 
       round(c(403, 605, 675) / (403 + 605 + 675), 3)
  Prob_Single["101", c("101", "110")] <- 
       round(c(178, 583) / (178 + 583), 3)
  Prob_Single["011", c("100", "101")] <- 
       round(c(215, 200) / (215 + 200), 3)
  Prob_Single["111", c("101", "110", "111")] <- 
       round(c(137, 211, 266) / (137 + 211 + 266), 3)

  Prob_Double <- matrix(0, 8, 8)
  dimnames(Prob_Double)[[1]] <- c("000", "100", "010", "001",
                                "110", "101", "011", "111")
  dimnames(Prob_Double)[[2]] <- c("000", "100", "010", "001",
                                "110", "101", "011", "111")
  Prob_Double[c("000", "010", "001", "011"), "010"] <- 1 
  Prob_Double["100", c("011", "010")] <- 
       round(c(817, 591) / (817 + 591), 3)
  Prob_Double["110", c("010", "011")] <- 
       round(c(212, 260) / (212 + 260), 3)
  Prob_Double["101", c("010", "011")] <- 
       round(c(107, 132) / (107 + 132), 3)
  Prob_Double["111", c("010", "011")] <- 
      round(c(74, 95) / (74 + 95), 3)
  
  Prob_Walk <- matrix(0, 8, 8)
  dimnames(Prob_Walk)[[1]] <- c("000", "100", "010", "001",
                                "110", "101", "011", "111")
  dimnames(Prob_Walk)[[2]] <- c("000", "100", "010", "001",
                                "110", "101", "011", "111")
  Prob_Walk["000", "100"] <- 1
  Prob_Walk["100", "110"] <- 1
  Prob_Walk["010", "110"] <- 1
  Prob_Walk["001", "101"] <- 1
  Prob_Walk[c("110", "101", "011", "111"), "111"] <- 1

  # outcomes are out, walk, single, double, triple, home run

  prob <- c(86304 + 37446, 13122 + 951 + 1602,
          28016, 8241, 939, 4909)
  prob <- prob / sum(prob)
  names(prob) <- c("OUT", "BB", "1B", "2B", "3B", "HR")
  list(Prob_Single=Prob_Single, Prob_Double=Prob_Double, 
       Prob_Walk=Prob_Walk, prob=prob)
}

simulate_half_inning <- function(setup){
  runs.transition <- function(s1, s2){
    before <- sum(as.numeric(unlist(strsplit(s1, split=""))))
    after <- sum(as.numeric(unlist(strsplit(s2, split=""))))
    before - after + 1
  }
  outs <- 0
  bases <- "000"
  runs <- 0
  all_bases <- c("000", "100", "010", "001",
               "110", "101", "011", "111")
 while(outs < 3){
   event <- sample(names(setup$prob), size=1, prob=setup$prob)
   if (event=="1B") new_bases <- sample(all_bases, 1, 
                              prob=setup$Prob_Single[bases, ])
   if (event=="2B") new_bases <- sample(all_bases, 1, 
                              prob=setup$Prob_Double[bases, ])
   if (event=="BB") new_bases <- sample(all_bases, 1, 
                              prob=setup$Prob_Walk[bases, ])
   if (event=="3B") new_bases <- "001"
   if (event=="HR") new_bases <- "000"
   if (event=="OUT") new_bases <- bases
   outs <- outs + (event == "OUT")
   runs <- runs - (event == "OUT") + 
           runs.transition(bases, new_bases) 
   bases <- new_bases
 }
  runs
}