# Golf Scramble Simulation in R

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# 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 <- 10000Create 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

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