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FootballEurope_analysis_postreg.R
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FootballEurope_analysis_postreg.R
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# load packages---------------------------------
library(tidyverse)
library(rethinking)
library(ggnewscale)
library(cowplot)
library(ellipse)
# load data---------------------------
football_original <- read.csv("FootballEurope.csv", stringsAsFactors = F)
# should have dataset football_original with n=9127
# data downloaded from
# https://www.kaggle.com/jangot/ligue1-match-statistics/version/3
# by Jemilu Mohammed
# acknowledged scraped source is whoscored.com
# downloaded 6th July 2017 (version 3)
# licence CC0: Public Domain
# separate home and away formations, i.e. one formation per row (long format)
f <- gather(football_original, homeFormation, awayFormation, key = "homeaway", value = "formation")
f$homeaway[f$homeaway == "homeFormation"] <- "home"
f$homeaway[f$homeaway == "awayFormation"] <- "away"
f$homeaway <- factor(f$homeaway)
# OPTIONAL: create dummy data------------------------------
# keep overall structure, with same divisions, managers, dates, homeaway
# generate formations in proportion to their actual frequency in the dataset
# randomise win/draw/loss: need to do this in original wide dataset otherwise will have non-paired results (e.g. every win needs to have a corresponding loss in the long dataset)
# # create football_dummy with same structure as football_original
# football_dummy <- read.csv("FootballEurope.csv", stringsAsFactors = F)
#
# # dummy scores
# N <- nrow(football_dummy)
# football_dummy$homeGoalFT <- sample(0:10, N, replace = T, prob = table(football_dummy$homeGoalFT) / N)
# football_dummy$awayGoalFT <- sample(0:9, N, replace = T, prob = table(football_dummy$awayGoalFT) / N)
#
# # dummy formations
# football_dummy$homeFormation <- sample(levels(as.factor(football_dummy$homeFormation)), N, replace = T, prob = table(football_dummy$homeFormation) / N)
# football_dummy$awayFormation <- sample(levels(as.factor(football_dummy$awayFormation)), N, replace = T, prob = table(football_dummy$awayFormation) / N)
#
# # now run below command and repeat subsequent formatting and predictors
# f <- gather(football_dummy, homeFormation, awayFormation, key = "homeaway", value = "formation")
# f$homeaway[f$homeaway == "homeFormation"] <- "home"
# f$homeaway[f$homeaway == "awayFormation"] <- "away"
# f$homeaway <- factor(f$homeaway)
# various preprocessing-------------------------
# combine 343 and 343d
f$formation[f$formation == "343d"] <- "343"
# code 'result' based on homeGoalFT and awayGoalFT
f$result <- NA
f$result[f$homeGoalFT == f$awayGoalFT] <- "draw"
f$result[(f$homeGoalFT > f$awayGoalFT) & f$homeaway == "home"] <- "win"
f$result[(f$homeGoalFT < f$awayGoalFT) & f$homeaway == "home"] <- "loss"
f$result[(f$homeGoalFT > f$awayGoalFT) & f$homeaway == "away"] <- "loss"
f$result[(f$homeGoalFT < f$awayGoalFT) & f$homeaway == "away"] <- "win"
# collect team, managerName and goalFT to separate home and away stats
f$team <- ifelse(f$homeaway == "home", f$homeTeam, f$awayTeam)
f$opponent <- ifelse(f$homeaway == "away", f$homeTeam, f$awayTeam) # NEW
f$manager <- ifelse(f$homeaway == "home", f$homeManagerName, f$awayManagerName)
f$goalsScored <- ifelse(f$homeaway == "home", f$homeGoalFT, f$awayGoalFT)
f$goalsConceded <- ifelse(f$homeaway == "home", f$awayGoalFT, f$homeGoalFT)
# NEW: get opponent formation, taking advantage of fact that home and away are in same order
f$opponent_formation <- NA
f$opponent_formation[f$homeaway == "home"] <- f$formation[f$homeaway == "away"]
f$opponent_formation[f$homeaway == "away"] <- f$formation[f$homeaway == "home"]
# keep relevant variables, discard the rest
f <- select(f, date, division, homeaway, formation, team, opponent, opponent_formation, manager, goalsScored, goalsConceded, result)
# typos / inconsistencies
f$manager[f$manager == "Arsene Wenger"] <- "Arsène Wenger"
f$manager[f$manager == "André Villas-Boas"] <- "Andre Villas-Boas"
f$manager[f$manager == "Gustavo Poyet"] <- "Gus Poyet"
f$manager[f$manager == "Louis van Gaal"] <- "Louis Van Gaal"
f$manager[f$manager == "Maurizio Pellegrino"] <- "Mauricio Pellegrino"
f$manager[f$manager == "Rafael Benítez"] <- "Rafael Benitez"
# fill in two blanks (checked via wikipedia and sky sports)
f$manager[f$manager == ""] <- "François Ciccolini"
f$formation[is.na(f$formation)] <- "4231"
f$opponent_formation[is.na(f$opponent_formation)] <- "4231"
# make formations, divisions etc. factors
f$homeaway <- factor(f$homeaway)
f$division <- factor(f$division)
f$formation <- factor(f$formation)
f$opponent_formation <- factor(f$opponent_formation) # NEW
f$team <- factor(f$team)
f$opponent <- factor(f$opponent) # NEW
f$manager <- factor(f$manager)
f$result <- factor(f$result)
# make date a Date variable
f$date <- as.Date(f$date)
# create integer day variable from date, starting at one
f$day <- as.integer(f$date - min(f$date)) + 1
f$day <- match(f$day, sort(unique(f$day)))
# add season variable; useful for calculating e.g. strength during a season for a team
# obtained from wikipedia
f$season <- NA
f$season[f$division == "Bundesliga" & f$date > "2012-08-23" & f$date < "2013-05-19"] <- 1
f$season[f$division == "Bundesliga" & f$date > "2013-08-08" & f$date < "2014-05-11"] <- 2
f$season[f$division == "Bundesliga" & f$date > "2014-08-21" & f$date < "2015-05-24"] <- 3
f$season[f$division == "Bundesliga" & f$date > "2015-08-13" & f$date < "2016-05-15"] <- 4
f$season[f$division == "Bundesliga" & f$date > "2016-08-25" & f$date < "2017-05-21"] <- 5
f$season[f$division == "EPL" & f$date > "2012-08-17" & f$date < "2013-05-20"] <- 1
f$season[f$division == "EPL" & f$date > "2013-08-16" & f$date < "2014-05-12"] <- 2
f$season[f$division == "EPL" & f$date > "2014-08-15" & f$date < "2015-05-25"] <- 3
f$season[f$division == "EPL" & f$date > "2015-08-07" & f$date < "2016-05-18"] <- 4
f$season[f$division == "EPL" & f$date > "2016-08-12" & f$date < "2017-05-22"] <- 5
f$season[f$division == "La_Liga" & f$date > "2012-08-01" & f$date < "2013-06-02"] <- 1
f$season[f$division == "La_Liga" & f$date > "2013-08-01" & f$date < "2014-05-31"] <- 2
f$season[f$division == "La_Liga" & f$date > "2014-08-01" & f$date < "2015-05-31"] <- 3
f$season[f$division == "La_Liga" & f$date > "2015-08-01" & f$date < "2016-05-31"] <- 4
f$season[f$division == "La_Liga" & f$date > "2016-08-01" & f$date < "2017-05-31"] <- 5
f$season[f$division == "Ligue_1" & f$date > "2012-08-01" & f$date < "2013-06-02"] <- 1
f$season[f$division == "Ligue_1" & f$date > "2013-08-01" & f$date < "2014-05-31"] <- 2
f$season[f$division == "Ligue_1" & f$date > "2014-08-01" & f$date < "2015-05-31"] <- 3
f$season[f$division == "Ligue_1" & f$date > "2015-08-01" & f$date < "2016-05-31"] <- 4
f$season[f$division == "Ligue_1" & f$date > "2016-08-01" & f$date < "2017-05-31"] <- 5
f$season[f$division == "Serie_A" & f$date > "2012-08-01" & f$date < "2013-06-02"] <- 1
f$season[f$division == "Serie_A" & f$date > "2013-08-01" & f$date < "2014-05-31"] <- 2
f$season[f$division == "Serie_A" & f$date > "2014-08-01" & f$date < "2015-06-01"] <- 3
f$season[f$division == "Serie_A" & f$date > "2015-08-01" & f$date < "2016-05-31"] <- 4
f$season[f$division == "Serie_A" & f$date > "2016-08-01" & f$date < "2017-05-31"] <- 5
# make season a factor to avoid treating as continuous
f$season <- factor(f$season)
# create 4231 variable 0 or 1
f$fourtwothreeone <- ifelse(f$formation == 4231, 1, 0)
# NEW: same for opponent
f$opponent4231 <- ifelse(f$opponent_formation == 4231, 1, 0)
# create win variable 0 or 1
f$win <- ifelse(f$result == "win", 1, 0)
# reduce German mid-season breaks to 10 days, in line with other leagues (except EPL), to make X-day window work
# season 1 mid-break ends 2012-12-16 starts 2013-01-18 (33 days, reduce by 23)
f$date[f$division == "Bundesliga" & f$season == 1 & f$date > "2012-12-16"] <- f$date[f$division == "Bundesliga" & f$season == 1 & f$date > "2012-12-16"] - 23
# s2 ends 2013-12-22 starts 2014-01-24 (33 days, reduce by 23)
f$date[f$division == "Bundesliga" & f$season == 2 & f$date > "2013-12-22"] <- f$date[f$division == "Bundesliga" & f$season == 2 & f$date > "2013-12-22"] - 23
# s3 ends 2014-12-21 starts 2015-01-30 (40 days, reduce by 30)
f$date[f$division == "Bundesliga" & f$season == 3 & f$date > "2014-12-21"] <- f$date[f$division == "Bundesliga" & f$season == 3 & f$date > "2014-12-21"] - 30
# s4 ends 2015-12-20 starts 2016-01-22 (33 days, reduce by 23)
f$date[f$division == "Bundesliga" & f$season == 4 & f$date > "2015-12-20"] <- f$date[f$division == "Bundesliga" & f$season == 4 & f$date > "2015-12-20"] - 23
# s5 ends 2016-12-21 starts 2017-01-20 (30 days, reduce by 20)
f$date[f$division == "Bundesliga" & f$season == 5 & f$date > "2016-12-21"] <- f$date[f$division == "Bundesliga" & f$season == 5 & f$date > "2016-12-21"] - 20
# check: all cases are complete
sum(!complete.cases(f))
# should have dataset f with n=18254
# fig 1: decline of 4231 over time--------------------
# overall frequencies over time: 4231 gets less common, replaced by first 433 and 442, then 433 gets more common than 442
# with day rather than date, no inter-season gaps
cbPalette <- c("#E69F00", "#56B4E9", "#009E73")
# create matrix containing proportion of each formation during a time bin (B days)
B <- 30
nbins <- round(max(f$day)/B) + 1
f$bin <- f$day %/% B + 1
plot_data <- matrix(NA, nbins, length(levels(f$formation)), dimnames = list(1:nbins,paste("f",levels(f$formation),sep="")))
for (i in 1:nbins) {
plot_data[i,] <- table(f$formation[f$bin == i]) / sum(table(f$formation[f$bin == i]))
}
plot_data <- as.data.frame(plot_data) # convert to dataframe
plot_data$day <- 1:nbins * B
plot_data <- plot_data[1:29,] # new code for revision: remove last row which only has 20 days
plot_data <- pivot_longer(plot_data, -day, names_to = "formation", values_to = "frequency", names_prefix = "f") # convert from wide to long
# all divisions
all_divs <- ggplot() +
theme_cowplot() +
ylim(0,0.6) +
geom_line(data = plot_data[plot_data$formation == "4231" | plot_data$formation == "442" | plot_data$formation == "433",], aes(x = day, y = frequency, colour = formation), alpha = 0.8, lwd = 1.2) + theme(legend.position = c(0.8, 0.8)) +
scale_colour_manual(values=cbPalette) +
new_scale_colour() +
geom_line(data = plot_data[plot_data$formation != "4231" & plot_data$formation != "442" & plot_data$formation != "433",], aes(x = day, y = frequency, group = formation), alpha = 0.2, lwd = 1, show.legend = F)
# by division
B <- 30
nbins <- round(max(f$day)/B) + 1
nformations <- length(levels(f$formation))+2
f$bin <- f$day %/% B + 1
plot_data <- matrix(NA, nbins*5, length(levels(f$formation))+2, dimnames = list(rep(1:nbins, each=5),c("division","bin",paste("f",levels(f$formation),sep=""))))
plot_data <- as.data.frame(plot_data) # convert to dataframe
plot_data$division <- rep(1:5,nbins)
plot_data$bin <- rep(1:nbins, each=5)
for (i in 1:nbins) {
for (j in 1:5) {
plot_data[plot_data$bin == i & plot_data$division == j,3:nformations] <- table(f$formation[f$bin == i & f$division == levels(f$division)[j]]) / sum(table(f$formation[f$bin == i & f$division == levels(f$division)[j]]))
}
}
plot_data <- pivot_longer(plot_data, -c(bin, division), names_to = "formation", values_to = "frequency", names_prefix = "f") # convert from wide to long
plot_data$day <- plot_data$bin * B # replace bin with day
plot_data$bin <- NULL
# add in division names
for (i in 1:5) {
plot_data$division[plot_data$division == i] <- c("Bundesliga", "EPL", "La Liga", "Ligue 1", "Serie A")[i]
}
plot_data <- plot_data[plot_data$day < 900,] # new code for revision: remove last row which only has 20 days
# by division
sep_divs <- ggplot() +
theme_cowplot(12) +
# ylim(0,1) +
scale_y_continuous(limits = c(0,1), breaks=c(0, 0.5,1)) +
geom_line(data = plot_data[plot_data$formation == "4231" | plot_data$formation == "442" | plot_data$formation == "433",], aes(x = day, y = frequency, colour = formation), alpha = 0.8, lwd = 1, show.legend = F) +
scale_colour_manual(values=cbPalette) +
new_scale_colour() +
geom_line(data = plot_data[plot_data$formation != "4231" & plot_data$formation != "442" & plot_data$formation != "433",], aes(x = day, y = frequency, group = formation), alpha = 0.2, lwd = 1, show.legend = F) +
facet_grid(rows = vars(division))
plot_grid(all_divs, sep_divs, rel_widths = c(2,1))
ggsave2("figures/fig1_frequencies.png", width = 8, height = 5, dpi = 600)
# create predictors--------------------------------------
# time window: number of days prior to game i to build variables
X <- 30
# create empty predictor variables
f$pers_use <- NA # frequency of that manager's use of 4231, for that season and division in the X-day window, centred on 0.5
f$pop_use <- NA # use frequency of 4231 in that division and season in the X-day window, centred on 0.5
#f$pop_use_R <- NA # use frequency of 4231 in that division and season in the X-day window, centred on 0.5, excluding own team
f$pers_win <- NA # manager's win rate with 4231 in that division and season in the X-day window, centred on mean win rate of non4231
f$pop_win <- NA # division-wide win rate with 4231 in that season in the X-day window, centred on mean win rate of non4231
#f$pop_win_R <- NA # division-wide win rate with 4231 in that season in the X-day window, centred on mean win rate of non4231, excluding own team
f$pers_win_all <- NA # manager's win rate for all their games, centred on mean win rate for all managers in that season and division
f$team_strength <- NA # proportion of games won by that team in a season, centred on mean win rate of all teams in that league
f$opponent_strength <- NA # NEW: proportion of games won by the opposing team in a season, centred on mean win rate of all teams in that league
f$n_division <- NA # variable to check how many games in window for game i
f$n_manager <- NA # variable to check how many games in window for manager of team in game i
# cycle through each match and create predictors
for (i in 1:nrow(f)) {
# first day of season for game i
first_day <- min(f$date[f$season == f$season[i] & f$division == f$division[i]])
# first X days remain NA
if (f$date[i] - X > first_day) {
window_division <- f$date < f$date[i] & f$date > (f$date[i] - X) & f$season == f$season[i] & f$division == f$division[i]
window_manager <- window_division & f$manager == f$manager[i] & f$team == f$team[i]
# number of games in previous X days (validity check, not used in analysis)
f$n_division[i] <- sum(window_division)
# and by that manager for that team in the window
f$n_manager[i] <- sum(window_manager)
# mean games played using 4231 in window by that manager for that team
f$pers_use[i] <- mean(f$fourtwothreeone[window_manager]) - 0.5
# mean games played using 4231 in window in that division
f$pop_use[i] <- mean(f$fourtwothreeone[window_division]) - 0.5
# NEW: pop_use excluding own team
#f$pop_use_R[i] <- mean(f$fourtwothreeone[window_division & f$team != f$team[i]]) - 0.5
# mean games won with 4231 by that manager in the window, relative to non4231 win rate
f$pers_win[i] <- mean(f[window_manager,]$win == 1 & f[window_manager,]$fourtwothreeone == 1) - mean(f[window_manager,]$win == 1 & f[window_manager,]$fourtwothreeone == 0)
# mean number of games in which 4231 was played that were won, relative to mean number of non-4231 games that were won
f$pop_win[i] <- mean(f[window_division & f$fourtwothreeone == 1,]$win) - mean(f[window_division & f$fourtwothreeone == 0,]$win)
# NEW: pop_win excluding own team
#f$pop_win_R[i] <- mean(f[window_division & f$fourtwothreeone == 1 & f$team != f$team[i],]$win) - mean(f[window_division & f$fourtwothreeone == 0 & f$team != f$team[i],]$win)
# mean games won by that manager in the window, relative to mean win rate of all managers
f$pers_win_all[i] <- mean(f[window_manager,]$win) - mean(f[window_division,]$win)
# mean games won by that team in the season, relative to overall win rate by all teams (not windowed)
f$team_strength[i] <- mean(f[f$team == f$team[i] & f$season == f$season[i],]$win) - mean(f[f$division == f$division[i] & f$season == f$season[i],]$win)
# NEW: strength of opponents
f$opponent_strength[i] <- mean(f[f$opponent == f$opponent[i] & f$season == f$season[i],]$win) - mean(f[f$division == f$division[i] & f$season == f$season[i],]$win)
}
}
# create use*win interaction variables
f$pers_useXpers_win <- f$pers_use * f$pers_win
f$pers_useXpers_win_all <- f$pers_use * f$pers_win_all
f$pop_useXpop_win <- f$pop_use * f$pop_win
f$pop_useXpers_win_all <- f$pop_use * f$pers_win_all
# NEW: use*win interactions using revised pop variables
#f$pop_useXpop_win_R <- f$pop_use_R * f$pop_win_R
#f$pop_useXpers_win_all_R <- f$pop_use_R * f$pers_win_all
# remove temp vars
rm(window_manager, window_division, first_day, i)
# retain complete cases only
football_full <- f
f <- football_full[complete.cases(football_full), ]
rownames(f) <- NULL # reset row names
f$manager <- factor(f$manager) # re-factor as some managers have been lost, messes with rethinking later otherwise
# gives n=16003 with X=30 (n=15988 with new _R variables)
# ORIGINAL ANALYSES AS IN PREREG--------------------------------------
# m1: null model with varying effects for division and manager, with homeaway and team_strength------
dat_list <- list(
fourtwothreeone = as.integer(f$fourtwothreeone),
homeaway = as.integer(ifelse(f$homeaway == "home", 1, 2)), # home=1, away=2,
manager_id = as.integer(f$manager),
division_id = as.integer(f$division),
team_strength = f$team_strength
)
m1 <- ulam(
alist(
fourtwothreeone ~ dbinom( 1 , p ) ,
logit(p) <- a_homeaway[homeaway] + b_team_strength*team_strength + a_manager[manager_id]*sigma_manager + a_division[division_id]*sigma_division,
a_homeaway[homeaway] ~ dnorm( 0 , 1 ) ,
b_team_strength ~ dnorm( 0 , 1 ) ,
a_manager[manager_id] ~ dnorm( 0 , 1 ) ,
a_division[division_id] ~ dnorm( 0 , 1 ) ,
sigma_manager ~ dexp( 1 ) ,
sigma_division ~ dexp( 1 )
) ,
data=dat_list , chains=4 , log_lik = T, cores=4, iter = 2000 )
traceplot(m1)
pairs(m1, depth = 2, pars = c("a_homeaway", "b_team_strength", "sigma_manager", "sigma_division"))
precis(m1, depth = 2, pars = c("a_homeaway", "b_team_strength", "a_division", "sigma_manager", "sigma_division"))
# mean sd 5.5% 94.5% n_eff Rhat
# a_homeaway[1] -0.53 0.47 -1.23 0.26 724 1.00
# a_homeaway[2] -0.64 0.47 -1.34 0.13 729 1.00
# b_team_strength -0.01 0.26 -0.42 0.39 1438 1.00
# a_division[1] 0.57 0.48 -0.12 1.39 781 1.00
# a_division[2] -0.70 0.39 -1.34 -0.11 901 1.00
# a_division[3] 0.63 0.49 -0.08 1.48 727 1.00
# a_division[4] -0.16 0.40 -0.79 0.47 694 1.00
# a_division[5] -1.74 0.58 -2.72 -0.87 1291 1.00
# sigma_manager 1.85 0.10 1.70 2.01 468 1.01
# sigma_division 1.26 0.46 0.72 2.10 1242 1.00
post <- extract.samples(m1)
inv_logit(colMeans(post$a_homeaway)) # slightly more likely to play 4231 at home
# [1] 0.3701951 0.3444764
# much lower prob of 4231 in Serie A, highest in Bundesliga and La Liga
data.frame(division = levels(f$division), prob_4231 = inv_logit(colMeans(post$a_division)))
# division prob_4231
# 1 Bundesliga 0.6393390
# 2 EPL 0.3317791
# 3 La_Liga 0.6525862
# 4 Ligue_1 0.4589095
# 5 Serie_A 0.1494498
# same for managers; lots of variation
data.frame(division = levels(f$manager), prob_4231 = inv_logit(colMeans(post$a_manager)))
# save as RDS file, use readRDS to load
saveRDS(m1, file="modelfits/m1.rds")
#m1 <- readRDS("modelfits/m1.rds")
# m2: personal variables model, varying slopes with pers_use------------------------
# non-centred parameterisation
dat_list <- list(
fourtwothreeone = as.integer(f$fourtwothreeone),
homeaway = as.integer(ifelse(f$homeaway == "home", 1, 2)), # home=1, away=2,
team_strength = f$team_strength,
manager_id = as.integer(f$manager),
division_id = as.integer(f$division),
pers_use = f$pers_use,
pers_win = f$pers_win,
pers_useXpers_win = f$pers_useXpers_win,
pers_useXpers_win_all = f$pers_useXpers_win_all
)
m2 <- ulam(
alist(
fourtwothreeone ~ dbinom( 1 , p ) ,
logit(p) <- a_homeaway[homeaway] + b_team_strength*team_strength + a_manager[manager_id,1] + a_manager[manager_id,2]*pers_use + a_division[division_id,1] + a_division[division_id,2]*pers_use + b_pers_use*pers_use + b_pers_win*pers_win + b_pers_useXpers_win*pers_useXpers_win + b_pers_useXpers_win_all*pers_useXpers_win_all,
a_homeaway[homeaway] ~ dnorm( 0 , 1 ) ,
b_team_strength ~ dnorm( 0 , 1 ) ,
# adaptive priors - non-centered
transpars> matrix[manager_id,2]:a_manager <-
compose_noncentered( sigma_manager , L_Rho_manager , z_manager ),
transpars> matrix[division_id,2]:a_division <-
compose_noncentered( sigma_division , L_Rho_division , z_division ),
matrix[2,manager_id]:z_manager ~ normal( 0 , 1 ),
matrix[2,division_id]:z_division ~ normal( 0 , 1 ),
b_pers_use ~ dnorm( 0 , 1 ) ,
b_pers_win ~ dnorm( 0 , 1 ) ,
b_pers_useXpers_win ~ dnorm( 0 , 1 ) ,
b_pers_useXpers_win_all ~ dnorm( 0 , 1 ) ,
vector[2]:sigma_manager ~ dexp(1),
cholesky_factor_corr[2]:L_Rho_manager ~ lkj_corr_cholesky( 2 ),
vector[2]:sigma_division ~ dexp(1),
cholesky_factor_corr[2]:L_Rho_division ~ lkj_corr_cholesky( 2 )
) ,
data=dat_list , chains=4 , log_lik = T, cores=4, iter = 2000 )
pairs(m2, pars = c("a_homeaway","b_team_strength", "b_pers_use", "b_pers_win", "b_pers_useXpers_win", "b_pers_useXpers_win_all"))
precis(m2, depth = 2)
# mean sd 5.5% 94.5% n_eff Rhat
# a_homeaway[1] -0.10 0.24 -0.46 0.30 900 1
# a_homeaway[2] -0.22 0.24 -0.58 0.18 923 1
# b_team_strength 0.08 0.25 -0.31 0.49 2969 1
# b_pers_use 2.28 0.67 0.99 3.16 1291 1
# b_pers_win 0.82 0.13 0.61 1.03 4102 1
# b_pers_useXpers_win -0.52 0.21 -0.85 -0.19 5010 1
# b_pers_useXpers_win_all 0.06 0.34 -0.48 0.61 3979 1
# sigma_manager[1] 0.65 0.07 0.55 0.76 820 1
# sigma_manager[2] 1.33 0.14 1.11 1.56 1141 1
# sigma_division[1] 0.50 0.21 0.26 0.90 1193 1
# sigma_division[2] 1.32 0.61 0.62 2.44 1409 1
# save as RDS file, use readRDS to load
saveRDS(m2, file="modelfits/m2.rds")
#m2 <- readRDS("modelfits/m2.rds")
# m3: population variables model, varying slopes with pop use-----------------
# non-centred parameterisation
dat_list <- list(
fourtwothreeone = as.integer(f$fourtwothreeone),
homeaway = as.integer(ifelse(f$homeaway == "home", 1, 2)), # home=1, away=2
team_strength = f$team_strength,
manager_id = as.integer(f$manager),
division_id = as.integer(f$division),
pop_use = f$pop_use,
pop_win = f$pop_win,
pop_useXpop_win = f$pop_useXpop_win,
pop_useXpers_win_all = f$pop_useXpers_win_all
)
m3 <- ulam(
alist(
fourtwothreeone ~ dbinom( 1 , p ) ,
logit(p) <- a_homeaway[homeaway] + b_team_strength*team_strength + a_manager[manager_id,1] + a_manager[manager_id,2]*pop_use + a_division[division_id,1] + a_division[division_id,2]*pop_use + b_pop_use*pop_use + b_pop_win*pop_win + b_pop_useXpop_win*pop_useXpop_win + b_pop_useXpers_win_all*pop_useXpers_win_all,
a_homeaway[homeaway] ~ dnorm( 0 , 1 ) ,
b_team_strength ~ dnorm( 0 , 1 ) ,
# adaptive priors - non-centered
transpars> matrix[manager_id,2]:a_manager <-
compose_noncentered( sigma_manager , L_Rho_manager , z_manager ),
transpars> matrix[division_id,2]:a_division <-
compose_noncentered( sigma_division , L_Rho_division , z_division ),
matrix[2,manager_id]:z_manager ~ normal( 0 , 1 ),
matrix[2,division_id]:z_division ~ normal( 0 , 1 ),
b_pop_use ~ dnorm( 0 , 1 ) ,
b_pop_win ~ dnorm( 0 , 1 ) ,
b_pop_useXpop_win ~ dnorm( 0 , 1 ) ,
b_pop_useXpers_win_all ~ dnorm( 0 , 1 ) ,
vector[2]:sigma_manager ~ dexp(1),
cholesky_factor_corr[2]:L_Rho_manager ~ lkj_corr_cholesky( 2 ),
vector[2]:sigma_division ~ dexp(1),
cholesky_factor_corr[2]:L_Rho_division ~ lkj_corr_cholesky( 2 )
) ,
data=dat_list , chains=4 , log_lik = T, cores=4, iter = 2000 )
pairs(m3, pars = c("a_homeaway", "b_team_strength", "b_pop_use", "b_pop_win", "b_pop_useXpop_win", "b_pop_useXpers_win_all"))
precis(m3, depth = 2)
# mean sd 5.5% 94.5% n_eff Rhat
# a_homeaway[1] -0.16 0.35 -0.72 0.41 927 1.01
# a_homeaway[2] -0.28 0.35 -0.84 0.29 928 1.01
# b_team_strength -0.08 0.30 -0.55 0.40 2745 1.00
# b_pop_use 1.54 1.03 -0.12 3.18 2685 1.00
# b_pop_win 0.34 0.19 0.03 0.63 4737 1.00
# b_pop_useXpop_win -0.46 0.64 -1.49 0.55 4863 1.00
# b_pop_useXpers_win_all 0.60 0.45 -0.12 1.33 6415 1.00
# sigma_manager[1] 1.89 0.12 1.71 2.09 765 1.00
# sigma_manager[2] 5.73 0.46 5.01 6.49 1007 1.00
# sigma_division[1] 0.70 0.30 0.35 1.24 2091 1.00
# sigma_division[2] 3.58 1.22 1.84 5.75 1912 1.00
# save as RDS file, use readRDS to load
saveRDS(m3, file="modelfits/m3.rds")
#m3 <- readRDS("modelfits/m3.rds")
# m4: full model, varying slopes with pers & pop use-----------------
# non-centred parameterisation
dat_list <- list(
fourtwothreeone = as.integer(f$fourtwothreeone),
homeaway = as.integer(ifelse(f$homeaway == "home", 1, 2)), # home=1, away=2
team_strength = f$team_strength,
manager_id = as.integer(f$manager),
division_id = as.integer(f$division),
pers_use = f$pers_use,
pers_win = f$pers_win,
pers_useXpers_win = f$pers_useXpers_win,
pers_useXpers_win_all = f$pers_useXpers_win_all,
pop_use = f$pop_use,
pop_win = f$pop_win,
pop_useXpop_win = f$pop_useXpop_win,
pop_useXpers_win_all = f$pop_useXpers_win_all
)
m4 <- ulam(
alist(
fourtwothreeone ~ dbinom( 1 , p ) ,
logit(p) <- a_homeaway[homeaway] + b_team_strength*team_strength + a_manager[manager_id,1] + a_manager[manager_id,2]*pers_use + a_manager[manager_id,3]*pop_use + a_division[division_id,1] + a_division[division_id,2]*pers_use + a_division[division_id,3]*pop_use + b_vars,
b_vars <- b_pers_use*pers_use + b_pers_win*pers_win + b_pers_useXpers_win*pers_useXpers_win + b_pers_useXpers_win_all*pers_useXpers_win_all + b_pop_use*pop_use + b_pop_win*pop_win + b_pop_useXpop_win * pop_useXpop_win + b_pop_useXpers_win_all * pop_useXpers_win_all,
a_homeaway[homeaway] ~ dnorm( 0 , 1 ) ,
b_team_strength ~ dnorm( 0 , 1 ) ,
# adaptive priors - non-centered
transpars> matrix[manager_id,3]:a_manager <-
compose_noncentered( sigma_manager , L_Rho_manager , z_manager ),
transpars> matrix[division_id,3]:a_division <-
compose_noncentered( sigma_division , L_Rho_division , z_division ),
matrix[3,manager_id]:z_manager ~ normal( 0 , 1 ),
matrix[3,division_id]:z_division ~ normal( 0 , 1 ),
b_pers_use ~ dnorm( 0 , 1 ) ,
b_pers_win ~ dnorm( 0 , 1 ) ,
b_pers_useXpers_win ~ dnorm( 0 , 1 ) ,
b_pers_useXpers_win_all ~ dnorm( 0 , 1 ) ,
b_pop_use ~ dnorm( 0 , 1 ) ,
b_pop_win ~ dnorm( 0 , 1 ) ,
b_pop_useXpop_win ~ dnorm( 0 , 1 ) ,
b_pop_useXpers_win_all ~ dnorm( 0 , 1 ) ,
vector[3]:sigma_manager ~ dexp(1),
cholesky_factor_corr[3]:L_Rho_manager ~ lkj_corr_cholesky( 2 ),
vector[3]:sigma_division ~ dexp(1),
cholesky_factor_corr[3]:L_Rho_division ~ lkj_corr_cholesky( 2 )
) ,
data=dat_list , chains=4 , log_lik = T, cores=4, iter = 2000 )
pairs(m4, pars = c("a_homeaway", "b_team_strength", "b_pers_use", "b_pers_win", "b_pers_useXpers_win", "b_pers_useXpers_win_all", "b_pop_use", "b_pop_win", "b_pop_useXpop_win", "b_pop_useXpers_win_all"))
precis(m4, depth = 2)
# mean sd 5.5% 94.5% n_eff Rhat
# a_homeaway[1] -0.01 0.17 -0.27 0.24 1150 1.01
# a_homeaway[2] -0.14 0.17 -0.41 0.11 1156 1.01
# b_team_strength 0.03 0.27 -0.39 0.46 3150 1.00
# b_pers_use 2.08 0.63 0.96 2.92 1654 1.00
# b_pers_win 0.84 0.13 0.63 1.06 4788 1.00
# b_pers_useXpers_win -0.64 0.21 -0.98 -0.30 5283 1.00
# b_pers_useXpers_win_all 0.11 0.35 -0.46 0.66 4518 1.00
# b_pop_use 1.34 0.48 0.55 2.03 2284 1.00
# b_pop_win -0.11 0.20 -0.43 0.22 5007 1.00
# b_pop_useXpop_win -0.62 0.67 -1.69 0.45 5673 1.00
# b_pop_useXpers_win_all -1.07 0.51 -1.87 -0.24 6213 1.00
# sigma_manager[1] 0.71 0.07 0.60 0.83 1133 1.00
# sigma_manager[2] 1.26 0.14 1.04 1.50 1506 1.00
# sigma_manager[3] 2.00 0.42 1.35 2.67 730 1.00
# sigma_division[1] 0.27 0.19 0.05 0.62 1637 1.00
# sigma_division[2] 1.25 0.59 0.57 2.32 1281 1.00
# sigma_division[3] 0.69 0.53 0.06 1.66 1735 1.00
# save as RDS file, use readRDS to load
saveRDS(m4, file="modelfits/m4.rds")
#m4 <- readRDS("modelfits/m4.rds")
# test hypotheses----------------------
# H1------
# the full model (m4) will be the best supported model as measured using WAIC, relative to personal-only, population-only and null models (m1, m2 and m3)
mcomparison <- compare(m1, m2, m3, m4)
mcomparison
# supported
# WAIC pWAIC dWAIC weight SE dSE
# m4 12273.1 338.3 0.0 1 144.03 NA
# m2 12346.3 298.2 73.2 0 144.19 15.16
# m3 13547.7 356.9 1274.6 0 137.23 88.05
# m1 14331.9 251.0 2058.8 0 135.11 101.69
saveRDS(mcomparison, file="modeloutputs/mcomparison.rds")
# mcomparison <- readRDS(file="modeloutputs/mcomparison.rds")
# H1. in the full model, there are effects of (a) personal 4231 use and (b) win rate, (c) population 4231 use and (d) win rate, and interactions between (e) personal 4231 use and win, and between (f) population 4231 use and win rates. Effects are indicated by the parameter estimates' 89% CI not including zero in the full model.
precis_m4 <- precis(m4, prob = 0.89, depth = 2)
precis_m4
saveRDS(precis_m4, file="modeloutputs/precis_m4.rds")
# precis_m4 <- readRDS(file="modeloutputs/precis_m4.rds")
# mean sd 5.5% 94.5% n_eff Rhat
# b_team_strength 0.03 0.27 -0.39 0.46 3150 1
# b_pers_use 2.08 0.63 0.96 2.92 1654 1 (a) yes
# b_pers_win 0.84 0.13 0.63 1.06 4788 1 (b) yes
# b_pers_useXpers_win -0.64 0.21 -0.98 -0.30 5283 1 (e) yes
# b_pers_useXpers_win_all 0.11 0.35 -0.46 0.66 4518 1
# b_pop_use 1.34 0.48 0.55 2.03 2284 1 (c) yes
# b_pop_win -0.11 0.20 -0.43 0.22 5007 1 (d) no
# b_pop_useXpop_win -0.62 0.67 -1.69 0.45 5673 1 (f) no
# b_pop_useXpers_win_all -1.07 0.51 -1.87 -0.24 6213 1
# plot effects of b variables
post <- extract.samples(m4)
# fig 2: plots of pers_use and pop_use, in interaction with win rates-------------
png("figures/fig2_pers_pop_interactions.png", width = 8, height = 4, units = 'in', res = 600)
par(mfrow=c(1,2))
# plot of pers_use: when pers 4231 use is low, then win rate makes a (small) difference
b.seq <- seq( from=0 , to=1 , by=0.01 )
logodds <- matrix(nrow = 4000, ncol = length(b.seq))
for (i in 1:length(b.seq)) {
logodds[,i] <- rowMeans(post$a_homeaway) + post$b_pers_use*b.seq[i]
}
logodds <- inv_logit(logodds)
p_mu <- apply( logodds , 2 , mean )
p_ci <- apply( logodds , 2 , PI )
plot( NULL , xlab="personal 4231 use" , ylab="probability of 4231" ,
ylim = c(0,1) , xlim = c(0,1) )
lines( b.seq , p_mu , col = "black", lwd = 2)
shade( p_ci , b.seq , col=col.alpha("black",0.2))
#text(0.5,0.7,"average performance")
# add pers use at +W% and -W% win rate compared to non-4231 win rate
W <- 0.5
for (i in 1:length(b.seq)) {
logodds[,i] <- rowMeans(post$a_homeaway) + post$b_pers_use * b.seq[i] + post$b_pers_win * W + post$b_pers_useXpers_win * b.seq[i] * W
}
logodds <- inv_logit(logodds)
p_mu <- apply( logodds , 2 , mean )
p_ci <- apply( logodds , 2 , PI )
lines( b.seq , p_mu , col = "chocolate1", lwd = 2)
shade( p_ci , b.seq , col=col.alpha("chocolate1",0.2))
text(0.3, 0.9, paste("+",W*100,"% performance", sep = ""), col = "chocolate1")
for (i in 1:length(b.seq)) {
logodds[,i] <- rowMeans(post$a_homeaway) + post$b_pers_use * b.seq[i] + post$b_pers_win * -W + post$b_pers_useXpers_win * b.seq[i] * -W
}
logodds <- inv_logit(logodds)
p_mu <- apply( logodds , 2 , mean )
p_ci <- apply( logodds , 2 , PI )
lines( b.seq , p_mu , col = "deepskyblue2", lwd = 2)
shade( p_ci , b.seq , col=col.alpha("deepskyblue2",0.2))
text(0.6, 0.4, paste("-",W*100,"% performance", sep = ""), col = "deepskyblue2")
par(xpd=NA)
text(-0.3,1.1,"A",cex=2)
# plot of pop_use: slight difference due to win rate at high pop 4231 use, but opposite to expected (higher performance->lower use)
b.seq <- seq( from=0 , to=1 , by=0.01 )
logodds <- matrix(nrow = 4000, ncol = length(b.seq))
for (i in 1:length(b.seq)) {
logodds[,i] <- rowMeans(post$a_homeaway) + post$b_pop_use*b.seq[i]
}
logodds <- inv_logit(logodds)
p_mu <- apply( logodds , 2 , mean )
p_ci <- apply( logodds , 2 , PI )
plot( NULL , xlab="population 4231 use" , ylab="probability of 4231" ,
ylim = c(0,1) , xlim = c(0,1) )
lines( b.seq , p_mu , col = "black", lwd = 2)
shade( p_ci , b.seq , col=col.alpha("black",0.2))
#text(0.5,0.6,"average performance")
# add pop use at +W% and -W% win rate compared to non-4231 win rate
for (i in 1:length(b.seq)) {
logodds[,i] <- rowMeans(post$a_homeaway) + post$b_pop_use * b.seq[i] + post$b_pop_win * W + post$b_pop_useXpop_win * b.seq[i] * W
}
logodds <- inv_logit(logodds)
p_mu <- apply( logodds , 2 , mean )
p_ci <- apply( logodds , 2 , PI )
lines( b.seq , p_mu , col = "chocolate1", lwd = 2)
shade( p_ci , b.seq , col=col.alpha("chocolate1",0.2))
text(0.7, 0.35, paste("+",W*100,"% performance", sep = ""), col = "chocolate1")
for (i in 1:length(b.seq)) {
logodds[,i] <- rowMeans(post$a_homeaway) + post$b_pop_use * b.seq[i] + post$b_pop_win * -W + post$b_pop_useXpop_win * b.seq[i] * -W
}
logodds <- inv_logit(logodds)
p_mu <- apply( logodds , 2 , mean )
p_ci <- apply( logodds , 2 , PI )
lines( b.seq , p_mu , col = "deepskyblue2", lwd = 2)
shade( p_ci , b.seq , col=col.alpha("deepskyblue2",0.2))
text(0.4, 0.9, paste("-",W*100,"% performance", sep = ""), col = "deepskyblue2")
par(xpd=NA)
text(-0.3,1.1,"B",cex=2)
dev.off()
par(mfrow=c(1,1)) # reset
# H2----
# The ratio of population : personal use is greater than 1, indicating greater reliance on social information than personal information
post <- extract.samples(m4)
round(c(mean(post$b_pop_use / post$b_pers_use), PI(post$b_pop_use / post$b_pers_use, prob = 0.89)), 2)
# No, opposite: mean 0.68, but very uncertain
# 5% 94%
# 0.68 0.24 1.41
# H3----
# There is more variation between (a) managers in personal info use, (b) managers in population info use, (c) divisions in personal info use, and (d) divisions in population info use, than there is in a model of dummy data with randomised formation and win rates across managers and divisions, as indicated by sigma_manager[2,3] and sigma_division[2,3]
post.d <- extract.samples(m4d) # run dummy model using code above
post.r <- extract.samples(m4) # real data
sigma_diffs <- data.frame(
diff_pers_manager=post.r$sigma_manager[,2] - post.d$sigma_manager[,2],
diff_pop_manager=post.r$sigma_manager[,3] - post.d$sigma_manager[,3],
diff_pers_division=post.r$sigma_division[,2] - post.d$sigma_division[,2],
diff_pop_division=post.r$sigma_division[,3] - post.d$sigma_division[,3])
precis_sigmadiffs <- precis(sigma_diffs) # differences in all except population use & division
precis_sigmadiffs
plot(precis_sigmadiffs)
saveRDS(precis_sigmadiffs[,1:4], file="modeloutputs/precis_sigmadiffs.rds")
# precis_sigmadiffs <- readRDS(file="precis_sigmadiffs.rds")
# H4----
# There is an n-shaped relationship between information use ratio and personal win rate across managers, i.e. managers who combine personal and population information do better than managers who predominantly use one or the other. Model this with unit of analysis as a manager, predicting their personal win rate from their population:personal use ratio squared (negative b^2 coefficient in a quadratic polynomial)
post <- extract.samples(m4)
# mean pop use rate / mean pers use rate NB ADDED INV_LOGIT UNLIKE PREREG VERSION
info_ratio <- apply(inv_logit(post$a_manager[,,3]), 2, mean) / apply(inv_logit(post$a_manager[,,2]), 2, mean)
# info_ratio <- standardize(info_ratio) # standardise NB REMOVED THIS TOO
win_rate <- NA
for (i in 1:length(levels(f$manager))) win_rate[i] <- mean(f[f$manager == levels(f$manager)[i],]$win)
win_rate <- standardize(win_rate) # relative to mean win_rate
m <- data.frame(win_rate = win_rate, info_ratio = info_ratio, info_ratio_sq = info_ratio^2)
dat_list <- list(
info_ratio = m$info_ratio,
win_rate = m$win_rate,
info_ratio_sq = m$info_ratio_sq
)
m.manager <- ulam(
alist(
win_rate ~ dnorm( mu , sigma ) ,
mu <- a + b1*info_ratio + b2*info_ratio_sq,
a ~ normal( 0 , 1.5 ),
b1 ~ normal( 0 , 0.2),
b2 ~ normal( -0.1 , 0.2),
sigma ~ dexp( 1 )
) ,
data=dat_list , chains=4 , log_lik = T, cores=4, iter = 2000 )
# prior predictive simulation: slightly more likely to be n-shaped, but still allow u-shaped
# N <- length(levels(f$manager))
# a <- rnorm(N, 0, 1.5)
# b1 <- rnorm(N, 0, 0.2)
# b2 <- rnorm(N, -0.1, 0.2)
# plot( NULL , xlim=range(info_ratio) , ylim=range(win_rate) ,
# xlab="info_ratio" , ylab="win_rate" )
# #xbar <- mean(d2$weight)
# for ( i in 1:N ) curve( a[i] + b1[i]*x + b2[i]*x^2,
# from=min(info_ratio) , to=max(info_ratio) , add=TRUE ,
# col=col.alpha("black",0.2) )
precis_manager <- precis(m.manager)
precis_manager # H4 not supported: very slightly positive b2 coefficient. Mostly no relationship.
# mean sd 5.5% 94.5% n_eff Rhat
# a 0.03 0.14 -0.19 0.26 1601 1
# b1 -0.16 0.18 -0.44 0.11 1469 1
# b2 0.10 0.07 -0.01 0.21 1757 1
# sigma 1.00 0.04 0.94 1.06 2092 1
saveRDS(precis_manager[,1:4], file="modeloutputs/precis_manager.rds")
# fig 3: win rate and use ratio------------
png("figures/fig3_ratio_winrate.png", width = 5, height = 5, units = 'in', res = 600)
ratio.seq <- seq( from=min(info_ratio) , to=max(info_ratio) , length.out=300 )
pred_dat <- list( info_ratio=ratio.seq , info_ratio_sq=ratio.seq^2 )
mu <- link( m.manager , data=pred_dat )
mu.mean <- apply( mu , 2 , mean )
mu.PI <- apply( mu , 2 , PI , prob=0.89 )
sim.win <- sim( m.manager , data=pred_dat )
win.PI <- apply( sim.win , 2 , PI , prob=0.89 )
plot( win_rate ~ info_ratio , xlab = "Manager population:personal information use", ylab = "Manager win rate")
lines( ratio.seq , mu.mean , lwd = 2)
shade( mu.PI , ratio.seq )
#shade( win.PI , ratio.seq )
abline(h = 0, lty = 3)
abline(v = 1, lty = 3)
dev.off()
# fig 4: plot of variation across divisions---------------
png("figures/fig4_divisions.png", width = 8, height = 4, units = 'in', res = 600)
par(mfrow=c(1,2))
# 4A: plot of pers_use in diff divisions
col_list <- c("gold2","chartreuse4","brown3","chocolate2","cornflowerblue") # yellow, green, red, orange, blue
b.seq <- seq( from=0 , to=1 , by=0.01 )
logodds <- matrix(nrow = 4000, ncol = length(b.seq))
plot( NULL , xlab="personal 4231 use" , ylab="probability of 4231" ,
ylim = c(0,1) , xlim = c(0,1) )
# for (i in 1:length(b.seq)) {
# logodds[,i] <- rowMeans(post$a_homeaway) + post$b_pers_use*b.seq[i]
# }
# logodds <- inv_logit(logodds)
# p_mu <- apply( logodds , 2 , mean )
# p_ci <- apply( logodds , 2 , PI )
# lines( b.seq , p_mu , col = "black", lwd = 2)
# shade( p_ci , b.seq , col=col.alpha("black",0.2))
for (j in 1:5) {
for (i in 1:length(b.seq)) {
logodds[,i] <- rowMeans(post$a_homeaway) + post$a_division[,j,1] + post$b_pers_use*b.seq[i] + post$a_division[,j,2]*b.seq[i]
}
logodds <- inv_logit(logodds)
p_mu <- apply( logodds , 2 , mean )
p_ci <- apply( logodds , 2 , PI )
lines( b.seq , p_mu , col = col_list[j], lwd = 2)
shade( p_ci , b.seq , col=col.alpha(col_list[j],0.2))
}
text(0.45,0.4,"Bundesliga", col = col_list[1])
text(0.6,0.5,"EPL", col = col_list[2])
text(0.75,0.6,"La Liga", col = col_list[3])
text(0.9,0.7,"Ligue 1", col = col_list[4])
text(0.2,0.9, "Serie A", col = col_list[5])
par(xpd=NA)
text(-0.3,1.1,"A",cex=2)
par(xpd=FALSE)
# plot variation across divisions
alpha <- 0.05
plot( NULL, xlim = c(0, 6), ylim = c(-2, 6), xlab = "reliance on personal info", ylab = "reliance on social info")
abline(h = 0, lty = 2)
abline(v = 0, lty = 2)
abline(a = 0, b = 1)
#points(apply(post$a_division[,,2], 1, mean) + post$b_pers_use, apply(post$a_division[,,3], 1, mean) + post$b_pop_use, col = col.alpha("black", alpha = alpha), pch = 20) # means
for (j in 1:5) {
points(post$a_division[,j,2] + post$b_pers_use, post$a_division[,j,3] + post$b_pop_use, col = col.alpha(col_list[j], alpha = alpha), pch = 20)
}
text(2.5,-1.5,"Bundesliga", col = col_list[1])
text(2.7,3.3,"EPL", col = col_list[2])
text(0.7,2.2,"La Liga", col = col_list[3])
text(2,4,"Ligue 1", col = col_list[4])
text(4.5,-0.5, "Serie A", col = col_list[5])
par(xpd=NA)
text(-1.8,6.6,"B",cex=2)
dev.off()
# explore between-manager variation in 4231 use
serieA_bymanager <- summarise( group_by(f[f$division == "Serie_A",], manager), mean = mean(fourtwothreeone) )
hist(serieA_bymanager$mean)
freq_bymanager <- summarise( group_by(f, manager, division), mean4231 = mean(fourtwothreeone) )
levels(freq_bymanager$division) <- c("Bundesliga", "EPL", "La Liga", "Ligue 1", "Serie A")
# 3 managers in Serie A used 4231 more than 50% of the time
sum(freq_bymanager$mean4231[freq_bymanager$division == "Serie A"] > 0.5)
# 10 more than 25%
sum(freq_bymanager$mean4231[freq_bymanager$division == "Serie A"] > 0.25)
# 35 never used it
sum(freq_bymanager$mean4231[freq_bymanager$division == "Serie A"] == 0)
# plot frequencies by division
ggplot( freq_bymanager, aes(mean4231)) +
geom_histogram(binwidth = 0.05) +
facet_grid(freq_bymanager$division) +
theme_cowplot() +
xlab("use of 4231 per manager")
# fig 5: plot of between manager variation-------------------------------
# list of managers and their win rates and number of games
View(summarise( group_by(f, manager), mean = mean(win), n = n() ))
# top 10 managers (level id) with >100 games ordered by win rate: Antonio Conte (25), Josep Guardiola (157), Carlo Ancelotti (40), Laurent Blanc (175), Massimiliano Allegri (206), Diego Simeone (72), Luis Enrique (185), Leonardo Jardim (176), Jose Mourinho (154), Arsene Wenger (28)
post <- extract.samples(m4)
png("figures/fig5_managers.png", width = 8, height = 4, units = 'in', res = 600)
par(mfrow=c(1,2))
textsize <- 0.7
alpha <- 0.03
plot( NULL, xlim = c(-5, 10), ylim = c(-10, 10), xlab = "reliance on personal info", ylab = "reliance on social info")
abline(h = 0, lty = 2)
abline(v = 0, lty = 2)
abline(a = 0, b = 1)
col_list <- c("gold2","chartreuse4","brown3","chocolate2","cornflowerblue") # yellow, green, red, orange, blue
k <- c(25, 157, 40, 154, 28) # conte, guardiola, ancelotti, mourinho, wenger
m.names <- levels(f$manager)[k[1]]
for (j in 1:5) {
points(post$a_manager[,k[j],2] + post$b_pers_use, post$a_manager[,k[j],3] + post$b_pop_use, col = col.alpha(col_list[j], alpha = alpha), pch = 4)
lines(ellipse(cor(post$a_manager[,k[j],2] + post$b_pers_use, post$a_manager[,k[j],3] + post$b_pop_use), scale = c(sd(post$a_manager[,k[j],2] + post$b_pers_use), sd(post$a_manager[,k[j],3] + post$b_pop_use)), centre = c(mean(post$a_manager[,k[j],2] + post$b_pers_use), mean(post$a_manager[,k[j],3] + post$b_pop_use)), level = 0.80), col = col.alpha(col_list[j], alpha = 1), lwd = 2)
}
text(-0.1,7.5, levels(f$manager)[k[1]], col = col_list[1], cex = textsize)
text(-2.9,4, levels(f$manager)[k[2]], col = col_list[2], cex = textsize)
text(4,-5.5, levels(f$manager)[k[3]], col = col_list[3], cex = textsize)
text(3,6.5, levels(f$manager)[k[4]], col = col_list[4], cex = textsize)
text(8.2,3, levels(f$manager)[k[5]], col = col_list[5], cex = textsize)
par(xpd=NA)
text(-9.5,11,"A",cex=2)
par(xpd=FALSE)
# now worst managers
alpha <- 0.03
plot( NULL, xlim = c(-5, 10), ylim = c(-10, 10), xlab = "reliance on personal info", ylab = "reliance on social info")
abline(h = 0, lty = 2)
abline(v = 0, lty = 2)
abline(a = 0, b = 1)
col_list <- c("gold2","chartreuse4","brown3","chocolate2","cornflowerblue") # yellow, green, red, orange, blue
k <- c(264, 278, 179, 7, 198) # donadoni, allardyce, alcaraz, pardew, hughes
m.names <- levels(f$manager)[k[1]]
for (j in 1:5) {
points(post$a_manager[,k[j],2] + post$b_pers_use, post$a_manager[,k[j],3] + post$b_pop_use, col = col.alpha(col_list[j], alpha = alpha), pch = 4)
lines(ellipse(cor(post$a_manager[,k[j],2] + post$b_pers_use, post$a_manager[,k[j],3] + post$b_pop_use), scale = c(sd(post$a_manager[,k[j],2] + post$b_pers_use), sd(post$a_manager[,k[j],3] + post$b_pop_use)), centre = c(mean(post$a_manager[,k[j],2] + post$b_pers_use), mean(post$a_manager[,k[j],3] + post$b_pop_use)), level = 0.80), col = col.alpha(col_list[j], alpha = 1), lwd = 2)
}
text(7.5,2, levels(f$manager)[k[1]], col = col_list[1], cex = textsize)
text(-0.5,-3.5, levels(f$manager)[k[2]], col = col_list[2], cex = textsize)
text(4.9,-3, levels(f$manager)[k[3]], col = col_list[3], cex = textsize)
text(-2.5,2.5, levels(f$manager)[k[4]], col = col_list[4], cex = textsize)
text(2.2,6.5, levels(f$manager)[k[5]], col = col_list[5], cex = textsize)
par(xpd=NA)
text(-9.5,11,"B",cex=2)
dev.off()
# REVISED ANALYSIS R1 WITH POPULATION VARIABLES EXCLUDING OWN TEAM---------------
# m1R1: null model with varying effects for division and manager, with homeaway and team_strength------