University of Minnesota, Twin Cities School of Statistics

Playoff Probability Calculator

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ngame <- 7   # number of games in the series
n1 <- "Twins"
n2 <- "Angels"
w1 <- 1   # number of wins, team 1
w2 <- 0   # number of wins, team 2
p1 <- 0.5 # probability of team 1 win (see comments)
hfa <- 0.55  # probability of home team win (see comments)

if (ngame == 7) {
   g <- c(TRUE, TRUE, FALSE, FALSE, FALSE, TRUE, TRUE)
   g.to <- 4
} else if (ngame == 5) {
   g <- c(TRUE, TRUE, FALSE, FALSE, TRUE)
   g.to <- 3
} else {
   stop("we only do 5 or 7 game series")
}
logit <- function(p) {
   if (any(p <= 0 | p >= 1))
      stop("probability out of range")
   log(p / (1 - p))
}
invlogit <- function(theta) {
   foo <- max(theta)
   bar <- exp(theta - foo)
   bar / (bar + exp(- foo))
}
p1home <- invlogit(logit(p1) + logit(hfa))
p1road <- invlogit(logit(p1) - logit(hfa))
print(p1home)
print(p1road)

w1 <- as.integer(w1[1])
w2 <- as.integer(w2[1])
if (w1 < 0 | w2 < 0)
   stop("negative number of wins impossible")
ngplayed <- w1 + w2
if (ngplayed > ngame)
   stop("total wins greater than games impossible")
if (ngplayed == ngame)
   stop("nothing to do, series over")
x.g <- ngplayed
x.w1 <- w1
x.w2 <- w2
x.p <- 1.0
foo <- NULL
for (i in (ngplayed + 1):ngame) {
   p1now <- ifelse(g[i], p1home, p1road)
   l <- length(x.g)
   y.w1 <- c(x.w1 + 1, x.w1[l])
   y.w2 <- c(x.w2[1], x.w2 + 1)
   y.g <- c(x.g + 1, x.g[1] + 1)
   y.p <- c(x.p * p1now, 0)
   y.p <- y.p + c(0, x.p * (1 - p1now))
   inies <- y.w1 < g.to & y.w2 < g.to
   if (any(! inies)) {
      bar <- cbind(y.g, y.w1, y.w2, y.p)
      foo <- rbind(foo, bar[! inies, ])
   }
   x.g <- y.g[inies]
   x.w1 <- y.w1[inies]
   x.w2 <- y.w2[inies]
   x.p <- y.p[inies]
   print(p1now)
   print(cbind(x.g, x.w1, x.w2, x.p))
}
cat("probability", n1, "win at home", p1home, "\n")
cat("probability", n2, "win at home", 1 - p1road, "\n")
cat("probability", n1, "win on road", p1road, "\n")
cat("probability", n2, "win on road", 1 - p1home, "\n")
print(foo)
print(sum(foo[, 4]))
print(sum(foo[foo[ , 2] == g.to, 4]))
print(sum(foo[foo[ , 3] == g.to, 4]))