Data - Description

This dataset is a sample of Australian professional soccer players who have appeared in a matchday squad in the 2019/2020 A-League Season. The data is based on the html data tables taken from the squad details and stat pages from each teams Transfermarkt.com page located at https://www.transfermarkt.com/a-league/startseite/wettbewerb/AUS1.

Although this dataset contains additional, only 16 are relevant for the purposes of this analysis. These variables are:
Team [Character]: Name of team
TeamCode [Character]: Uniquee Team ID number
Name [Character]: Name of player
Position [Factor]: Categorical variable with 16 factors (Goalkeeper, Right-Back, Centre-Back, Defender, Left-Back, Defensive Midfield, Central Midfield, Midfielder, Attacking Midfield, Second Striker, Right Winger, Right Midfield, Left Midfield, Left Winger, Centre-Forward, Forward)
Date of Birth [Date]: Date of birth of player
Height [Integer]: Numerical variable, height of player
Foot [Factor]: Categorical variable with 4 factors (left, both, right, unknown)
Age [Integer]: Numerical variable, age of player
Squad_Selection [Integer]: Numerical value, number of matchday squads selected in during season
Games_Played [Integer]: Numerical value, number of games played in season
Goals [Integer]: Numerical value, number of goals in season
Assists [Integer]: Numerical value, number of goals in season
Minutes_Played [Integer]: Numerical value, number of minutes played in season

The remaining variables, superfluous to this analysis, were dropped after reading the file.

Data - Collecting Team Codes and Team Name

• The read_html function was used to scrape the data.
• The html_nodes function was used to extract the '.hide-for-pad .vereinprofil_tooltip' node set.
• The html_attr function was used to extract the 'href' attributes which provides links to each team page.
• The data.frame function was used to store the team links.
• The separate function was used to seperate the link into different columns in the data frame.
• The select function was used to remove the superfluous vaiables from the data frame.

teamcodes <- read_html("https://www.transfermarkt.com/a-league/startseite/wettbewerb/AUS1/plus/?saison_id=2019") %>%
  html_nodes(".hide-for-pad .vereinprofil_tooltip") %>%
  html_attr("href") %>% 
  data.frame() %>% 
  separate(.,.,into = c("blank","team","startseite","verein","teamcode","saison","year"), sep = "/") %>% 
  select(-1,-3,-4,-6,-7)
  head(teamcodes, n= 10)

Data - Collecting Squad Details

• The apply function was used to loop through the teamcodes and teamname and scrape squad details.
• The read_html function was used to scrape the squad details data fom th teams url, which was created using the paste function.
• The html_nodes and html_table function was used to extract the 2nd table and was then stored as a data frame.
• The select function and the drop_na function were used to remove the superfluous vaiables and rows containing missing values.
• The cbind funciton was used to add the teamname to the data frame.
  
• The do.call and rbind.data.frame were used to bind each team's squad data into one data frame.
• The names function was used to name each column in the squd data frame.

squadlist <- apply(teamcodes, 1, function(x){
  teamcodes <- (x['teamcode'])
  teamname <- (x['team'])
  starturl <- "https://www.transfermarkt.com/sydney-fc/kader/verein/"
  endurl <- "/plus/1/galerie/0?saison_id=2019"
  theurl <- paste(starturl,teamcodes,endurl, sep = "")
  squad <- read_html(theurl) %>%
    html_nodes(.,"table") %>%
    html_table(.,fill = TRUE)  %>% .[2] %>%
    data.frame() %>% 
    select(-1,-2,-3,-7,-8,-11,-12,-13,-14) %>%
    drop_na() %>%
    cbind(.,teamname)
})
squad <- do.call(rbind.data.frame, squadlist)
names(squad) <- c("Name", "Position","DOB","Height","Foot","Team")
head(squad, n=6)

Data - Collecting Squad Statistics

The same process and functions that were used to scrape the Squad Details were then used for the Player Statsitics which come from a different url and provide a different dataset.

# Get the stats data
statslist <- apply(teamcodes, 1, function(x){
  teamcodes <- (x['teamcode'])
  teamname <- (x['team'])
  starturl <- "https://www.transfermarkt.com/sydney-fc/leistungsdaten/verein/"
  endurl <- "/plus/1?reldata=%262019"
  theurl <- paste(starturl,teamcodes,endurl, sep = "")
  
stats <- read_html(theurl) %>%
         html_nodes(.,"table") %>%
         html_table(.,fill = TRUE)  %>% .[2] %>%
         data.frame() %>% 
         select(-1,-2,-3,-7,-12,-13,-14,-15,-16,-17,-19,-20,-21,-22,-23,-24,-25,-26,-27) %>%
         drop_na() %>%
         cbind(.,teamname)
})

stats <- do.call(rbind.data.frame, statslist)
names(stats) <- c("Name", "Position","Age", "Squad_Selections", "Games_Played","Goals","Assists","Minutes_Played","Team")
head(stats, n=8)

Data - Missing Data and Outliers

• The impute function was used to coerce the NA values into 0 across the Age, Squad_Selections, Games_Played, Goals, Assists, Minutes_Played variables.
• The impute function was then used to coerce the NA values in the Foot factor to "unknown".
• The is.na function was used to find the NA values in the Height variable and replace them with the mean Height.
• A filter was used to find any rows with likely errors.

team <- team_data
team[,c(3:8)] %<>% impute(., fun = 0)
team$Foot %<>% impute(., fun = "unknown")
team$Height[is.na(team$Height)] <- mean(team$Height, na.rm = TRUE)
team %>% filter(., Age < 15 | Age > 45 | Height < 160 | Height > 210) %>% select(Name, Age, Height, Minutes_Played)

• A data entry error was locaed in the Height variable and was repalced with the mean Height.

team$Height[which(team$Height <50)] <- mean(team$Height, na.rm = TRUE)
head(team)

Data - Creating Bins

• The seperrate function was used to create new numeric varirables for the "BirthYear", "BirthMonth" and "BirthDay".
• The discretize function was then used to discetize the new vairables into bins.

team %<>% separate(DOB, into =  c("BirthYear","BirthMonth","BirthDay"))
team[,10:12] <- sapply(team[,10:12],as.numeric)
BirthMonthQuartile <- discretize(team$BirthMonth, disc = "equalwidth", nbins=4)

names(BirthMonthQuartile) <- c("BirthMonthQuartile")
team <- cbind(team, BirthMonthQuartile)
str(team)

## 'data.frame':    339 obs. of  15 variables:
##  $ Name              : chr  "Tom GloverT Glover" "Dean BouzanisD Bouzanis" "Joe GauciJoe Gauci" "Jack HendryJ Hendry" ...
##  $ Position          : Factor w/ 10 levels "GK","RB","CB",..: 1 1 1 3 3 2 4 3 3 4 ...
##  $ Age               : num  21 28 18 24 28 20 24 27 26 30 ...
##  $ Squad_Selections  : num  25 25 11 2 15 29 30 27 31 25 ...
##  $ Games_Played      : num  15 15 0 2 9 23 24 26 28 24 ...
##  $ Goals             : num  0 0 0 0 0 1 1 1 1 0 ...
##  $ Assists           : num  0 0 0 0 1 0 1 0 1 2 ...
##  $ Minutes_Played    : num  1380 1350 0 180 670 ...
##  $ Team              : chr  "melbourneheartfc" "melbourneheartfc" "melbourneheartfc" "melbourneheartfc" ...
##  $ BirthYear         : num  1997 1990 2000 1995 1991 ...
##  $ BirthMonth        : num  12 10 7 5 4 6 4 3 3 10 ...
##  $ BirthDay          : num  24 2 4 7 2 13 10 15 23 13 ...
##  $ Height            : num  190 189 181 192 183 ...
##  $ Foot              : 'impute' chr  "unknown" "right" "unknown" "right" ...
##   ..- attr(*, "imputed")= int  1 3 8 11 12 13 19 20 21 22 ...
##  $ BirthMonthQuartile: int  4 4 3 2 2 2 2 1 1 4 ...

Analysis - Birth Month Frequencies

The BirthMonth variable is presented below in a frequency distribution and bar chart.
The data is displayed as proportions, f/n, where f = the count or frequency or a value, and n = sample size.

MonthCol = c("#D7191C","#D7191C","#D7191C","#FDAE61","#FDAE61","#FDAE61","#ABDDA4","#ABDDA4","#ABDDA4","#2B83BA","#2B83BA","#2B83BA")
BirthMonth <- team$BirthMonth %>% table() %>% prop.table()*100
knitr::kable(round(t(BirthMonth),2))

BirthMonth %>% barplot(main = "Birth Month - Percentage",ylab="Percent", ylim=c(0,15), col = MonthCol)

Analysis - Birth Quartile Frequencies

The BirthQuartile variable is presented below in a frequency distribution and bar chart.
The data is displayed as proportions, f/n, where f = the count or frequency or a value, and n = sample size.

BirthQuartile <- team$BirthMonthQuartile %>% table() %>% prop.table()*100
knitr::kable(round(t(BirthQuartile),2))

BirthQuartile %>% barplot(main = "Birth Quartile - Percentage",ylab="Percent", ylim=c(0,35), col = (brewer.pal(4,"Spectral")),)

Analysis - Birth Quartile by Position Frequencies

The BirthQuartile variable is presented below in a bar chart, grouped by Position. The data is displayed as proportions, f/n, where f = the count or frequency or a value, and n = sample size.

positiontable <- table(team$BirthMonthQuartile,team$Position) %>% prop.table(margin = 2)*100

positiontable %>% barplot(main = "Birth Quartile by Position", ylab="Percent",
                    ylim=c(0,50), legend=rownames(positiontable), beside=TRUE,
                    col = (brewer.pal(4,"Spectral")),
                    args.legend=c(x = "topright", horiz=TRUE, title="Birth Quartile"),
                    xlab="Position")

Analysis - Minutes Played

Box Plots have beeen used to depict the quartiles of distribution for Minutes Played by both the Birth Quartile and Birth Month variables.

par(mfrow=c(1,2))
team %>% boxplot(Minutes_Played ~ BirthMonthQuartile,data = ., main="Minutes Played of Birth Quartile", 
                     ylab="Minute Played", xlab="Birth Quartile", col = (brewer.pal(4,"Spectral")))


team %>% boxplot(Minutes_Played ~ BirthMonth,data = ., main="Minutes Played of Birth Month", 
                     ylab="Minute Played", xlab="Birth Month", col = MonthCol)

Hypothesis Testing - Birth Quartiles

H0: The population distribution of professional footballers in Austrlaia by birth quartile is 25% Q1, 25% Q2, 25% Q3, 25% Q4.
HA: The population distribution of professional footballers in Austrlaia by birth quartile is NOT 25% Q1, 25% Q2, 25% Q3, 25% Q4.

Chi-Square Goodness of Fit Test \[\chi^2 = ∑{\frac{(Obs−Exp)^2}{Exp}}\]

table(team$BirthMonthQuartile) %>% prop.table()

## 
##         1         2         3         4 
## 0.3303835 0.2448378 0.2241888 0.2005900

population_prop <- c(0.25,0.25,0.25,0.25)
chi1<-chisq.test(table(team$BirthMonthQuartile), p = population_prop)
chi1

## 
##  Chi-squared test for given probabilities
## 
## data:  table(team$BirthMonthQuartile)
## X-squared = 13.012, df = 3, p-value = 0.004611

chi1$observed

## 
##   1   2   3   4 
## 112  83  76  68

chi1$expected

##     1     2     3     4 
## 84.75 84.75 84.75 84.75

Hypothesis Testing - Birth Months

H0: The population distribution of professional footballers in Australia by birth month is 8% Jan, 8% Feb, 9% Mar, 8% Apr, 8% May, 8% Jun, 9% Jul, 8% Aug, 9% Sep, 9% Oct, 8% Nov, 8% Dec.
HA: The population distribution of professional footballers in Australia by birth month is NOT 8% Jan, 8% Feb, 9% Mar, 8% Apr, 8% May, 8% Jun, 9% Jul, 8% Aug, 9% Sep, 9% Oct, 8% Nov, 8% Dec.

Chi-Square Goodness of Fit Test \[\chi^2 = ∑{\frac{(Obs−Exp)^2}{Exp}}\]

table(team$BirthMonth) %>% prop.table()

## 
##          1          2          3          4          5          6          7 
## 0.13569322 0.08259587 0.11209440 0.09734513 0.06194690 0.08554572 0.07669617 
##          8          9         10         11         12 
## 0.07964602 0.06784661 0.08259587 0.05309735 0.06489676

monthpopulation_prop <- c(0.08,0.08,0.09,0.08,0.08,0.08,0.09,0.08,0.09,0.09,0.08,0.08)
monthchi<-chisq.test(table(team$BirthMonth), p = monthpopulation_prop)
monthchi

## 
##  Chi-squared test for given probabilities
## 
## data:  table(team$BirthMonth)
## X-squared = 24.553, df = 11, p-value = 0.01059

monthchi$observed

## 
##  1  2  3  4  5  6  7  8  9 10 11 12 
## 46 28 38 33 21 29 26 27 23 28 18 22

monthchi$expected

##     1     2     3     4     5     6     7     8     9    10    11    12 
## 27.12 27.12 30.51 27.12 27.12 27.12 30.51 27.12 30.51 30.51 27.12 27.12

Discussion

The RAE has been found across several sports from the 1980s to 2020, but there is limited resarch in professionall football in Australia. This study sought to find whether or not there was statistically significant evidence to support rejecting the null hypothesis that the RARE was not present and that population would follow a normal birth distribution.

Birth Quartile A Chi-square goodness of fit test was used to determine whether the distribution of professional footballers in Australia followed the normal birth quartile distribution of 25% Q1, 25% Q2, 25% Q3 and 25% Q4. The test was statistically significant, χ2 = 13.012, df=3, p<0.01 This suggests that the distribution of of professional footballers in Australia do not follow the the normal birth quartile distribution.

Birth Month A Chi-square goodness of fit test was used to determine whether the distribution of professional footballers in Australia followed the normal birth month distribution of 8% Jan, 8% Feb, 9% Mar, 8% Apr, 8% May, 8% Jun, 9% Jul, 8% Aug, 9% Sep, 9% Oct, 8% Nov, 8% Dec. The test was statistically significant, χ2 = 24.553, df=11, p<0.01 This suggests that the distribution of of professional footballers in Australia do not follow the the normal birth month distribution.

These results support similar studies throughout professional football in europe (Kelly et al. 2019; Romann & Fuchslocher, 2013; Salinero et al. 2018).

An interesting observation was seen in the distribution by position which identifies that the GK position appears to have a normal distrubtion, whilst the CDM position is heavily skewed to the right. Further investigation should be made into whether there are different methods of talent identification and youth development pathways for these positions to seek to explain the difference.

Additionally we note that whils the frequency distribution of players skews tot he right, highlighting the RAE, this does no occur for the distribution of Minutes Played. So whilst professional footballers born in the first three months of the year may have an advantage in being identified as talented athletes and selected in a teams squad, this does not neccesarily occur in playing selection for games and further investigation across other competitions and sports may provide insights into whether or not the RAE occurs in playing minutes or only in squad selction.