Golf Scramble Simulation

This is a simulation of a standard best-ball golf scramble. Conventional wisdom has it that the best golfer (A) should hit last, the idea being that one of the lesser golfers may have a decent shot already so the best golfer can take a risky shot. This simulation suggests that the worst golfer should indeed go first, but after that the order should be best on down (D, A, B, C). Perhaps a rationale is that golfer A will likely make a decent safe shot, which allows the other two medium skilled golfers a chance at a risky shot.

This is one of my first cracks at a sports simulation in R, so I welcome any comments about errors or constructive criticism.

Prepare

library(combinat)

## Attaching package: 'combinat'

## The following object is masked from 'package:utils':
## 
## combn

library(ggplot2)
set.seed(4444)
n <- 10000

Create golfer attributes

safe.attributes <- data.frame(golfer = c("a", "b", "c", "d"), mean = c(8, 7, 
    6, 5), sd = c(1.5, 1.5, 1.5, 1.5))
risk.attributes <- data.frame(golfer = c("a", "b", "c", "d"), mean = c(7, 6, 
    5, 4), sd = c(3, 3, 3, 3))

safe.densities <- apply(safe.attributes[, -1], 1, function(x) sort(rnorm(n = 1000, 
    mean = x[1], sd = x[2])))
colnames(safe.densities) <- safe.attributes$golfer
safe.df <- data.frame(safe.densities)

risk.densities <- apply(risk.attributes[, -1], 1, function(x) sort(rnorm(n = 1000, 
    mean = x[1], sd = x[2])))
colnames(risk.densities) <- risk.attributes$golfer
risk.df <- data.frame(risk.densities)

Plot golfer attributes

par(mfrow = c(2, 2))
par(mar = rep(2, 4))

plot(density(safe.df$a), col = "blue", xlim = c(0, 16), ylim = c(0, 0.3), main = "Golfer A", 
    col.main = "black", font.main = 4)
lines(density(risk.df$a), col = "red")
legend("topright", c("safe", "risk"), cex = 0.8, col = c("blue", "red"), lty = 1)

plot(density(safe.df$b), col = "blue", xlim = c(0, 16), ylim = c(0, 0.3), main = "Golfer B", 
    col.main = "black", font.main = 4)
lines(density(risk.df$b), col = "red")
legend("topright", c("safe", "risk"), cex = 0.8, col = c("blue", "red"), lty = 1)

plot(density(safe.df$c), col = "blue", xlim = c(0, 16), ylim = c(0, 0.3), main = "Golfer C", 
    col.main = "black", font.main = 4)
lines(density(risk.df$c), col = "red")
legend("topright", c("safe", "risk"), cex = 0.8, col = c("blue", "red"), lty = 1)

plot(density(safe.df$d), col = "blue", xlim = c(0, 16), ylim = c(0, 0.3), main = "Golfer D", 
    col.main = "black", font.main = 4)
lines(density(risk.df$d), col = "red")
legend("topright", c("safe", "risk"), cex = 0.8, col = c("blue", "red"), lty = 1)

Create holes dataframe

golfPerms <- permn(letters[1:4])
holes <- data.frame(matrix(NA, nrow = n, length(golfPerms)))

for (i in 1:length(golfPerms)) {
    colnames(holes)[i] <- paste0(golfPerms[[i]][1], golfPerms[[i]][2], golfPerms[[i]][3], 
        golfPerms[[i]][4])
}

Process

for (j in 1:n) {
    for (i in 1:length(golfPerms)) {
        shot1 <- sample(safe.df[, substr(golfPerms[[i]][1], 1, 1)], 1, T)

        if (shot1 >= 6) {
            shot2 <- max(shot1, sample(risk.df[, substr(golfPerms[[i]][2], 1, 
                1)], 1, T))
        } else {
            shot2 <- max(shot1, sample(safe.df[, substr(golfPerms[[i]][2], 1, 
                1)], 1, T))
        }

        if (shot2 >= 6) {
            shot3 <- max(shot2, sample(risk.df[, substr(golfPerms[[i]][3], 1, 
                1)], 1, T))
        } else {
            shot3 <- max(shot2, sample(safe.df[, substr(golfPerms[[i]][3], 1, 
                1)], 1, T))
        }

        if (shot3 >= 6) {
            shot4 <- max(shot3, sample(risk.df[, substr(golfPerms[[i]][4], 1, 
                1)], 1, T))
        } else {
            shot4 <- max(shot3, sample(safe.df[, substr(golfPerms[[i]][4], 1, 
                1)], 1, T))
        }

        holes[j, i] <- shot4
    }
}

Find winning order per hole

winners <- data.frame(matrix(NA, nrow = n, ncol = 1))
names(winners) <- "winner"
for (k in 1:n) {
    winners[k, 1] <- colnames(holes)[(which.max(holes[k, ]))]
}
winnerCounts <- data.frame(table(winners))
winnerCounts$winners <- reorder(winnerCounts$winners, -winnerCounts$Freq)

Plot results

par(mfrow = c(1, 1))
ggplot(data = winnerCounts, aes(x = winners, y = Freq)) + geom_bar(colour = "black", 
    fill = "#DD8888", width = 0.7, stat = "identity") + guides(fill = FALSE) + 
    xlab("Order") + ylab("Wins") + ggtitle("Golf Scramble Simulation")

ddunn801 at gmail dot com