University of Minnesota, Twin Cities School of Statistics

Playoff and World Series Probability Calculator

Just Do It

This web page implements a playoff probability calculator. Given assumptions about the probabilities for single games, it calculates probabilities for a 5 or 7 game series.

To check out what it does, just click the submit button below.

Ignore everything but the last six lines, which will look something like

Rweb:> cat("currently,", n1, w1, n2, w2, "\n") 
currently, Yankees 2 Twins 1  
Rweb:> cat("probability", n1, "win series:", p1total, "\n") 
probability Yankees win series: 0.7525  
Rweb:> cat("probability", n2, "win series:", 1 - p1total, "\n") 
probability Twins win series: 0.2475

To modify what it does, look at the section on modifying the calculation below.

ngame <- 5     # number of games in the series
n1 <- "Yankees" # name of team 1
n2 <- "Twins"  # name of team 2
w1 <- 2        # number of wins, team 1
w2 <- 1        # number of wins, team 2
p1home <- 0.55 # probability of team 1 win at home
p1road <- 0.45 # probability of team 1 win on road

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")
}
if (p1home < 0 | p1home > 1)
   stop("impossible p1home probability")
if (p1road < 0 | p1road > 1)
   stop("impossible p1road probability")

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))
}
dimnames(foo) <- list(NULL, c("games", "w1", "w2", "prob"))
print(foo)
p1total <- sum(foo[foo[ , 2] == g.to, 4])
cat("currently,", n1, w1, n2, w2, "\n")
cat("probability", n1, "win series:", p1total, "\n")
cat("probability", n2, "win series:", 1 - p1total, "\n")

Modifying the Calculation

The whole calculation is determined by 5 numbers, which are assigned in the statements at the top of the web form and which you can edit.

ngame <- 7     # number of games in the series
w1 <- 0        # number of wins, team 1
w2 <- 1        # number of wins, team 2
p1home <- 0.55 # probability of team 1 win at home
p1road <- 0.45 # probability of team 1 win on road

The meaning of these numbers is as follows.

ngame is the number of games in the whole series (including games already played), right now only 5 or 7 is allowed.
w1 is the number of wins for team 1 in the games already played. Team 1 is the team with home field advantage in the series (the team at home in the first game).
w2 is the number of wins for team 2 in the games already played.
p1home is the probability of team 1 winning a game at home. The default (0.55) is about right for two evenly matched baseball teams (the home field/court advantage is much higher in basketball).
p1road is the probability of team 1 winning a game on the road. The default (0.45) is about right for two evenly matched baseball teams (the home field/court advantage is much higher

Basically, your opinion only enters the two numbers p1home and p1road. If you don't believe the teams are evenly matched, change these numbers and see what happens.

You can also edit the team names, but this doesn't affect any calculated numbers.

n1 <- "Angels" # name of team 1
n2 <- "Giants" # name of team 2