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@bayesball bayesball/model.data.sim.R
Last active Sep 19, 2015

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Illustrates Model-Data Simulation to Learn About a Player's Batting Ability Based on a "ofer" Slump
# Script to Learn About Ryan Howard's Batting Ability from a "0 for 35" Slump
# Uses a function from the BayesTestStreak package
# install_github("bayesball/BayesTestStreak")
library(MASS)
library(BayesTestStreak)
# Simulate 500 at-bats with a constant hitting probability p = 0.250
# -- find the longest ofer.
one.sim <- function(p=.25, n=500){
require(BayesTestStreak)
max(find.spacings(rbinom(n, size=1, prob=p))$y)
}
# Repeat this simulation 1000 iterations
# graph the maximum ofers and overlay the observed value.
S <- replicate(1000, one.sim())
truehist(S,
main="Longest Ofer in 500 AB if p = 0.250")
abline(v=35, lwd=3, col="red")
text(30, .07, "OBSERVED", col="red")
# Here is a different question.
# What can we learn about Howard's true batting average on the
# basis of the data "oh for 35 or greater"?
# Illustrate model/data simulation.
# Suppose Howard's true batting p is any value between
# p=.10 and p=.40 and we assign each value the same prior probability.
# Here is the prior:
p <- seq(.1, .4, .01)
prior <- 1/length(p) + 0 * p
plot(p, prior, type="h", col="red",
lwd=6, main="The Prior on Howard's True AVG")
model.data.sim <- function(){
require(BayesTestStreak)
p <- sample(seq(.1, .4, .01), size=1)
x <- max(find.spacings(rbinom(500, size=1, prob=p))$y)
c(p, x)
}
many.sim <- function(ofer, iter=100000){
S <- replicate(iter, model.data.sim())
S.p <- S[1, S[2, ] >= ofer]
truehist(S.p,
main=paste("Howard's Posterior Given Ofer =", ofer))
}
# What is a player goes "0 for 15+" in a 500-AB season?
many.sim(15)
# What if a player goes "0 for 35+" in a 500-AB season?
many.sim(35)
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