R function to compute and plot the probability a MLB home team wins a game at the end of each inning given a particular lead.

plot.prob.home.R

plot.prob.home <- function(year, plot=TRUE){
  require(arm)
  require(ggplot2)
  load.gamelog <- function(season, headers){
    download.file(
      url=paste("http://www.retrosheet.org/gamelogs/gl", season, ".zip"
                , sep="")
      , destfile=paste("gl", season, ".zip", sep="")
    )
    unzip(paste("gl", season, ".zip", sep=""))
    gamelog <- read.table(paste("gl", season, ".txt", sep="")
                          , sep=",", stringsAsFactors=F)
    names(gamelog) <- names(headers)
    file.remove(paste("gl", season, ".zip", sep=""))
    file.remove(paste("gl", season, ".txt", sep=""))
    gamelog
  }
  
  headers <- read.csv("https://raw.githubusercontent.com/beanumber/baseball_R/master/data/game_log_header.csv")
  d <- load.gamelog(year, headers)
  
  # remove line scores for games when at least 10 runs are scored

  d <- subset(d, !grepl("\\(", as.character(d$VisitorLineScore)) &
              !grepl("\\(", as.character(d$HomeLineScore)))

  # for a particular game, extract individual inning runs for
  # visitor and home teams
  
  get.visitor.innings <- function(j)
    as.numeric(strsplit(as.character(d$VisitorLineScore[j]), 
                        split="")[[1]])[1:8]
  get.home.innings <- function(j)
    as.numeric(strsplit(as.character(d$HomeLineScore[j]), 
                        split="")[[1]])[1:8]
  
  # apply these functions for all games
  
  options(warn=-1) # turn off warnings
  N <- dim(d)[1]
  V <- t(sapply(1:N, get.visitor.innings))
  H <- t(sapply(1:N, get.home.innings))
  options(warn=0) # turn on warnings
  
  # compute running scores of visitor and home teams
  
  C.V <- t(apply(V, 1, cumsum))
  C.H <- t(apply(H, 1, cumsum))
  
  # compute running scores for each of 16 half-innings
  
  mf <- function(y) rep(y, each=2)
  CC.V <- t(apply(C.V, 1, mf))
  nf <- function(y) as.vector(matrix(c(0, y[1:(length(y) - 1)], y),
                                     2, length(y), byrow=TRUE))
  CC.H <- t(apply(C.H, 1, nf))
  
  # compute game outcome (1 if home team wins, 0 otherwise)
  
  O <- with(d, ifelse(HomeRunsScore > VisitorRunsScored, 1, 0))
  
  # run the logistic regression
  
  logistic.fit <- function(half.inning){
    visitor.runs <- CC.V[, half.inning]
    home.runs <- CC.H[, half.inning]
    B <- data.frame(Run.diff = home.runs - visitor.runs,
                    Outcome = O)
    coef(glm(Outcome ~ Run.diff, data=B, family=binomial))
  }
  
  S <- t(sapply(1:16, logistic.fit))
  
  D <- data.frame(Inning=0,
                  Run.Lead=0,
                  Prob.Win=mean(O))
  for (r in -4:4){
    hi <- seq(2, 16, 2)
    D <- rbind(D, data.frame(Inning=hi/2,
                             Run.Lead=r,
              Prob.Win=invlogit(S[hi, 1] + r * S[hi, 2])))
  }
  
  if(plot==TRUE){
  D$RUN.LEAD <- as.factor(D$Run.Lead)
  print(ggplot(D, aes(Inning, Prob.Win, color=RUN.LEAD)) + 
    geom_point(size=4) + geom_line(size=1.5) +
    labs(title=paste("Probability Home Team Wins At End of Each Inning:",
                  year, "Data")) +
      ylab("Probability Home Team Wins") +
    ylim(0, 1) + geom_hline(yintercept=0.5, size=1.5))}
  
  D$Season <- year
  D
}