R script for blog post on five-game playoffs

fivegameplayoffs.R

# plot my prior

curve(dnorm(x, .5, .05), .5, .8) 
title("My Prior")

# write a function to compute the log likelihood

log_likelihood <- function(p, f){
  prob3 <- p ^ 3 + (1 - p) ^ 3
  prob4 <- 3 * p ^ 3 * (1 - p) +
    3 * (1 - p) ^ 3 * p
  prob5 <- 6 * p ^ 3 * (1 - p) ^ 2 +
    6 * (1 - p) ^ 3 * p ^ 2
  f[1] * log(prob3) + f[2] * log(prob4) +
    f[3] * log(prob5)
}

# observed number of 3, 4, and 5 game series

f <- c(48, 42, 42)

# plot the likelihood

p <- seq(.5, .8, by = .001)
llike <- log_likelihood(p, f)
like <- exp(llike - max(llike))
plot(p, like, type = "l")
title("The Likelihood")

# function to compute the log posterior

log_posterior <-function(p, f){
  prob3 <- p ^ 3 + (1 - p) ^ 3
  prob4 <- 3 * p ^ 3 * (1 - p) +
    3 * (1 - p) ^ 3 * p
  prob5 <- 6 * p ^ 3 * (1 - p) ^ 2 +
    6 * (1 - p) ^ 3 * p ^ 2
  log_like <- f[1] * log(prob3) + f[2] * log(prob4) +
    f[3] * log(prob5) 
  log_prior <- dnorm(p, 0.5, 0.05, log = TRUE)
  log_like + log_prior
}

# plot the posterior

p <- seq(.5, .8, by = .001)
lpost <- log_posterior(p, f)
post <- exp(lpost - max(lpost))
plot(p, post, type = "l")
title("The Posterior")