Football ex-2

### Thanks to Martin Eastwood

df <- read.csv("http://www.football-data.co.uk/mmz4281/1516/E0.csv")

##  Format compatible with glms 
df <- apply(df, 1, function(row){
  data.frame(team=c(row['HomeTeam'], row['AwayTeam']),
             opponent=c(row['AwayTeam'], row['HomeTeam']),
             goals=c(row['FTHG'], row['FTAG']),
             home=c(1, 0))
})
df <- do.call(rbind, df)
head(df)

##                  team    opponent goals home
## HomeTeam  Bournemouth Aston Villa     0    1
## AwayTeam  Aston Villa Bournemouth     1    0
## HomeTeam1     Chelsea     Swansea     2    1
## AwayTeam1     Swansea     Chelsea     2    0
## HomeTeam2     Everton     Watford     2    1
## AwayTeam2     Watford     Everton     2    0

##  numeric data not factors
df$goals <- as.numeric(as.character(df$goals))

##  fit the GLM
model <- glm(goals ~ home + team + opponent, 
             family = poisson(link = log), data = df)

##  Predictions Chelsea vs Arsenal
ave_home_goals <- predict(model, data.frame(home = 1, team = "Chelsea", opponent = "Arsenal", type = "response"))
ave_away_goals <- predict(model, data.frame(home = 0, team = "Arsenal", opponent = "Chelsea", type = "response"))

##  Probabilities per goal
home_goals <- dpois(0:10, ave_home_goals)
away_goals <- dpois(0:10, ave_away_goals)

##   Convert probability vectors into score matrix
score.matrix <- home_goals %o% away_goals

##   Probabilities for home and away win
draw <- sum(diag(score.matrix))
away <- sum(score.matrix[upper.tri(score.matrix)])
home <- sum(score.matrix[lower.tri(score.matrix)])

cat("Draw probability =", draw, "\nAway probability =", away, "\nHome Probability = ", home)

## Draw probability = 0.5677174 
## Away probability = 0.3101683 
## Home Probability =  0.1221143