Mourinho results vs top 6 (2017-11-06).R

library(dplyr)
library(ggplot2)

probs <- c(home = 0.35, draw = 0.4, away = 0.25)
points <- c(home = 0, draw = 1, away = 3)

n_sim <- 1e4
n_games <- 11
samples <- sample(points, size = n_sim * n_games, prob = probs, replace = TRUE)

sims <- data_frame(
  sim = rep.int(1:n_sim, n_games),
  game = rep_len(1:n_games, n_sim * n_games),
  points = samples
)

observed_points <- 5

sims %>% 
  group_by(sim) %>% 
  summarise(points = sum(points)) %>% 
  ungroup() %>% 
  summarise(100 * mean(points <= observed_points))

sims %>% 
  group_by(sim) %>% 
  summarise(points = sum(points)) %>% 
  ggplot(aes(x = points)) + 
  geom_histogram(aes(y = 100 * ..count.. / sum(..count..)), 
                 binwidth = 1) +
  geom_vline(xintercept = observed_points, linetype = "dotted") +
  scale_x_continuous(breaks = seq(0, 50, 2)) + 
  theme_minimal() +
  ggtitle("Simulated points", 
          sprintf("Home/Draw/Away = %0.0f%% / %0.0f%% / %0.0f%%", 
                  100*probs["home"], 100*probs["draw"], 100*probs["away"])) +
  xlab("Points") +
  ylab("%")