An Econometric Evaluation of Racial Biases in the Premier League

Racism in Football – Will We Ever Kick it Out?

Abstract

Racism and discrimination have unfortunately played a major role in football, essentially since the creation of the sport due to social, political, and economic reasons. Although racism is not as prevalent as it was before the 21^st century, there are still issues with the subject that exist to this very day. Various types of discrimination occur within the sport and despite attempts from the FA alongside institutions such as FARE and Kick It Out, the issue and the effect it has on many players, does not look like disappearing anytime soon. Therefore, the aim of this essay will be to introduce and analyse the different types of discrimination that occur within British football, with the assistance of literature reviews and critical evidence, and delve deeper into the problem at hand using a fixed effects linear regression model. This model will investigate whether racial bias is at play when it comes to disciplinary sanctions given out by referees.  I will be analysing the phenomenon of racism as an issue in football, with a specific focus on British football and its biggest competition, the Premier League, with my hypothesis stating that: Darker skinned players are more likely to be booked than lighter-skinned players, which was proved to be false. The results found show no considerable evidence that referees exhibit racial bias against any form of skin tone, with this conclusion seen as a credit to training and anti-racism institutions.

Table of Contents

Click to expand Table of Contents

Section 1: Introduction

Section 2: Literature Review

2.1 – Discrimination in Monetary Terms

2.2 – Discrimination in Playing Opportunities

2.3 – Referee Biases

Section 3: Data

3.1 – Collection of Data

3.2 – Summary Statistics

3.3 – Initial Findings

Section 4: Econometric Methodology

5.1 – Regression Model

5.2 – Hypotheses

Section 5: Empirical Results

5.1 – General Analysis

5.2 – Position Analysis

5.3 – Skin tone Analysis

Conclusion

References

1. Introduction

The primary purpose of the following paper is to introduce and analyse the topic of racial biases within a high-profile team sport worldwide, and in this context, test for the presence of racial discrimination in the application of disciplinary sanctions in British football and the Premier League. Regarding other pieces of work, this specific type of issue has been the subject of only two other studies to date in the context of a professional team sport, with Price and Wolfers (2010) providing an application to professional basketball in the US and Witt and Reilly (2011) providing research on the Premier League.  With a focus on player, referee and game-specific fixed effects, the authors differ in their concluding findings. Price and Wolfers find “more personal fouls are called against players of a particular racial group when the games are officiated by opposite compared to own-race refereeing crews”, thus displaying clear racial biases. On the other hand, Reilly and Witt conclude that there is “no evidence of unfair treatment of players from racial minority groups in the accumulation of disciplinary cards”. With differing outcomes shown, it will be intriguing to see my findings and how they compare to the work done prior to mine.

In an attempt to evaluate the relationship, if one is found, between racial discrimination and disciplinary sanctions, we first have to break down the topic through existing studies on racial discrimination within British football. This will be done throughout the section “Literature Review” which has been split up into 3 sub-sections. The first section entails me analysing discrimination in monetary terms, with both wages and the valuation of players based solely on their race to be discussed. Naturally following, the lack of playing opportunities or rather opportunities in their primary position is researched in the third section. Finally, we come to the fourth section in which we introduce the inspiration behind the essay and the reasons why this was chosen. A proposition of racial bias in referees come to fruition and biases that referees may already exhibit outside racial terms are introduced and deliberated upon.

With previous studies reviewed, we next move on to introducing our model. This model will aim to question and analyse the relationship between racial bias and disciplinary sanctions in the English Premier League and evaluate whether or not this correlation truly exists. In order to investigate this proposed relationship, the model consists of a framework that uses a rich dataset on players for all games played in the Premier League between the 3 seasons of 2014/2015 and 2016/17, the most recent full seasons completed to date. The key emphasis in this model will be the correlation between the skin tone of a player and the number of disciplinary sanctions served over a playing season as measured by the accumulation of yellow and red cards. Becker’s (2010) Economics of Discrimination was intriguing in terms of the analysis as he uses for a similar model to mine and provided an alternative theoretical framework in the sense that Premier League referees, who during this time were all white, could exhibit on average a taste for discrimination against opposite race (or non-white) players. However, I would prefer to interpret refereeing decisions as subject to the potential influence of unintended or implicit discrimination, rather than a deeper issue, due to the training they receive on a weekly basis and the benefit of the doubt is given to them due to the pressure they are placed under every game. Summary statistics collected from my preliminary model are then analysed and initial findings are discussed upon the subject.

The following section details the econometric methodology. The structured body of the empirical model has been inspired by work written by Reilly & Witt (2011) on the same topic. Differences in our bodies of work lie with a richer dataset from myself, beginning with the 2014/15 season whereas Reilly and Witt took their data from the Premier League season of 2003/04. I also opted to include the number of red cards a player received to get a more accurate representation of disciplinary sanctions. Variables such as Position and Games Played were included in my model whereas Witt and Reilly chose to include Age and Native Language spoken. Finally, the most distinct change comes from the dependent variable tested against. Both pieces of work tested for the racial bias of course with our hypotheses remaining similar, however, my main independent variable was the shade of their skin whereas their variable was the race of a player. Asian, Black, White and Mixed Race were the categories chosen for the authors mentioned and I elected for 5 distinct categories of Very Light, Light, Mixed, Dark and Very Dark.

Concluding remarks will follow the econometric methodology and empirical results have been discussed. One of my expectations prior to the experiment taking place will have to do with the disciplinary sanctions recorded. I will be expecting the total amount of cards to be higher in comparison to a previous study done on the same topic purely down to how the culture of the game has changed.  Yellow cards are usually awarded to players who exhibit actions of ‘foul play’, whether that be a single violent challenge or an accumulation of softer tackles, but there can also be acts by players that will warrant a straight yellow/red card, regardless of their skin tone. Professional fouls e.g. intentionally stopping a fast break, taking off your shirt during a celebration, time wasting, and dissent are all actions that are given bookings, per the rules of the law.  With these occurring regularly throughout a game and have no bearing on the racial bias from the referee, there is no doubt these would influence my findings. Red cards on the other hand are less regularly given out, as they are awarded for more serious offences e.g. violent conduct, or if a player receives two yellow cards. These evaluations and more will be summarised in the conclusion and whether racial bias plays a part in determining disciplinary sanctions will indefinitely be found during this essay.

2. Literature Review

Now of course, extreme forms of racism have died down in recent times, mainly due to the efforts and genuine attempts by authorities such as Kick It Out and FARE, and also with the abolition of the colour ban in worldwide sports, occurring in the mid-21^st century.  Despite this, there are still extensive amounts of evidence prevalent today that exhibit racial discriminatory practices in modern times. Becker (2010) found various forms of discrimination within sports which included the following topics: Inequality in compensation, inequality in hiring standards and inequality of positions (both playing and managerial). With this in mind, current literature on various types of discrimination that have occurred in British football, and more notably the Premier League, will now be reviewed.

2.2 – Discrimination in Monetary Terms

The theme of racial discrimination in monetary terms in England has attracted limited research, mainly due to the restrictions on access to salary data to the common researcher. However, an exception comes with the work of Szymanski (2000) who was able to indirectly examine racial salary discrimination through the exploitation of wage bill information. The information was taken from a panel of 39 clubs that had played in the English 1^st Division between the 1978/79 season and the 1992/93 season (became Premier League in 1992/93 season). This test assumes all teams were operating on or within their own production frontiers, with the labour market for players being highly competitive. Szymanski found that clubs with an above average proportion of black players tended to perform, on average and with other things being equal, at a higher level in relation to their wages. Although at first, this does suggest that owners are allowing lighter-skinned players to underperform without any monetary repercussions in comparison to their darker peers, Szymanski also found no evidence of consumer or fan-based discrimination, which could also mean that this wage bill was just put down to smart business from each of the club’s management.

Continuing on from this and the theme of discrimination in monetary terms, Reilly and Witt (1995) and Medcalfe (2008) provide studies in using transfer fees that clubs pay for their players, concluding that there is no racial discrimination regarding the price of a player once their overall talent and skillset has been taken into consideration. However, there is a widely held perception that British players are over-valued compared to foreign players. Even though the Premier League is increasingly global in its appeal to audiences and players worldwide, the requirement that eight out of the club’s 25-man first-team squad must have spent at least three years at an English or Welsh academy before their 21st birthday adds an artificial hike to the cost of those players, with the demand for ‘home-grown’ players at a continuous high (Foster, 2016). Players such as John Stones, Jordan Pickford, and Michael Keane all fit the criteria and have since been bought for a combined fee of £107.5 million from clubs looking to meet the home-grown rule. Contrastingly, players that were purchased from foreign clubs such as Riyad Mahrez, Ngolo Kante and Eden Hazard (all of whom have gone on to win the PFA Player of the Year Award for the last 3 years) combine for a transfer fee of only £38.4 million, with each of their individual expected transfer fees increasing exponentially since arriving in the Premier League (SkySports, 2018). Although clubs might just have a British preference in order to match their required home-grown quota, there is clear evidence that British players that are coming into the Premier League are regarded as more valuable compared to their foreign peers, giving them a perceived advantage based on race rather than footballing talent.

2.3 – Discrimination in Playing Opportunities

There has also been a case made in various literature for how discrimination can play a role in the labour market that is football. Dr. John Mills was the most prominent researcher on the topic, with his study in 2018 finding that skin tone in English football continues to have a significant impact on which positions footballers play on the pitch.  This research was unique in the sense that a 20-point rating scale was used opposed to the usual binary form of classifying skin tone (generally either black or white) and was collated, reviewed and ratified by around 1,300 researchers. His research found that footballers of a darker skin tone are more likely to occupy peripheral positions traditionally associated with athleticism and strength while teammates of a lighter skin tone are more likely to fill central positions conventionally considered to need organisational skills and creativity (Mills et al., 2018). Is there a racial dimension to this problem or is it simply lazy coaching from above?

Additionally, Goddard and Wilson (2008) conducted a study based on the potential effect that a player’s race can have on his labour market transition probabilities. These probabilities are calculated with the dependent of variables of divisional transition, initial status, and retention, using a three-equation model. They concluded with the findings of hiring discrimination against black players, with these players having higher retention probabilities even though they tend to be employed by teams of a higher status divisionally. This means black athletes need to perform at a higher than average level in comparison to their white equals, suggesting discrimination in the hiring labour market. The work of Goddard and Wilson (2008) also seems to suggest that there are stereotypes within Western culture around black athletes being more naturally athletic, whilst white athletes tending to be more creative and intelligent, which has also been reflected in certain media outlets and pundits within the sport when referring to the work of black players.

Another approach used to investigate this topic came in the work of Bachan, Reilly and Witt (2014), where they explored the correlation between racial composition and match outcomes for the French and English national teams. This was done using match-specific variables which included the make-up of the first 11 of the respective teams. Although no solid evidence was found to suggest that racial biases played a part in the team’s performances, there were still areas of concern. Reports stated that a former English coach was given instructions to make sure the national team was predominantly made up of white players, with the French following suit in openly questioning the choice of black players in the national side, totally disregarding talent and choosing race instead (Bachan et al, 2014). Even national players fall victim to racial profiling, with countries unwilling to go down the avenue of the ‘typical black player’ even if the talent is there, thus affecting their playing opportunities severely.

2.5 – Referee Biases

With stereotypical racism seen to be prevalent throughout the history of British football, I would now like to introduce the inspiration behind my proposed econometric model, with alleged racial biases from referees to be analysed.

Looking at the behaviour of referees in generally, Dawson and other researchers (2007) found that across the period of 1996 to 2003 in the Premier League, referees were inclined to award more disciplinary points (yellow/red cards) to the away team rather than the home team (Dawson et al., 2007). Although this may be the case, analysis done by Reilly and Witt (2011) found that, compared to referees that officiate in the premier tiers of football in Italy, Germany & Spain, English referees are much more professional in terms of their bias.  They are continuously subject to a high degree of scrutiny, whether that comes from social media in today’s day and age, or from the Video Assistant Referee (VAR) which has just recently come into fruition.  In addition to this, Premier League referees are monitored by a match assessor who gives them grades on their performances which is discussed during a compulsory meeting every 2 weeks (PGMOL, 2018). Referees are generally required to make decisions within the second, so there can be some form of tolerance when permitting bias upon them. However, this leniency would not excuse a more sinister form of bias-motivated by race. Although this is a serious accusation, all Premier League referees working today are drawn from the white ethnic group, making the proposition more likely to occur, even unintentionally. Payne (2006) took this study on using laboratory evidence and concluded on the theme of ‘weapon bias’ – the idea that an individual’s tendency to unknowingly make stereotypical decisions will increase with the need to make decisions rapidly, which is the case 99% of the time for referees, especially in high leverage moments (Payne, 2006).

Another form of potential referee bias was conducted in the study done by Reilly and Witt (2013). Tests for home biases were undertaken using player/match level data, with the measured bias coming in the form of the strictest sanction, the red card. Although evidence was found for home biases in the Premier League, this did not occur through this form of disciplinary actions, but rather smaller factors that would not have a major effect on the game e.g. fouls given.  Further studies took place by Reilly and Witt in 2016, with the use of both random effect and player-specific models and a non-panel pooled logit model, to test for potential biases in the number of bookings given to the away team. Credit to refereeing training and the employees themselves, as next to no evidence was found to suggest referees were succumbing to pressure from external factors (Reilly & Witt, 2016).  As the measure of social pressure in this experiment was the fans in attendance, especially in the Premier League, the fact that referees are not swayed to make decisions that would have a major effect on the game to favour the home team, should be recognised and praised.

The prospect of racial bias in regards to referees in the Premier League intrigued me the most during my research, with the effect that a yellow card can have on the overall result of the game often underrated. A booking, especially one given to an integral member of the team, could change the game plan of said player, perhaps rendering them unable to make a tackle with the knowledge that he may be cautioned for the second time. Sanctions could also have implications for a player’s wage rate if a club’s pay structure is related to disciplinary actions. Both of these factors and many more would put clubs with a large number of darker skinned players at a distinct disadvantage and if there is a racial bias shown in referees, especially in a high-profile league like the Premier League, this type of behaviour could result in extreme backlash from fans, players and organisations alike worldwide. All in all, this research prompted me to delve deeper into this proposed form of discrimination through a unique and detailed dataset and interrogate whether or not there is a relationship between race and disciplinary sanctions, which will now be discussed in the following section.

3. Data

After introducing, discussing and analysing various forms of racial discrimination in British football, I would like to research whether or not these effects could ‘trickle down’ to the referees involved in the game, as they play a vital role in the game of football which often gets overlooked. With significant evidence pointing to discrimination, stereotypes and racial bias in other forms of the game, could it also be found in refereeing decisions concerning darker players? In this model, I will be investigating whether or not darker players or more likely to get booked/penalised for fouls, with aggressive stereotypes playing a part.

3.1 – Collection of Data

All the data that has been used to create this econometric model was provided by the Premier League’s official website and the following statistics were taken for each player found in this database: Number of yellow cards, Number of red cards, Age, Fouls committed, Games played and their playing position. I was also able to extract their skin tone through this website, and the racial classification of these players was based on the review of colour photographs found both on the official Premier League website and the player’s respective club website (Premier League, 2018). Players were classified solely on the shade of their skin rather than their background as this an experiment that is purely trying to investigate whether or not there is racial bias, therefore making the data used validly. These players were divided into 5 distinct groups based on their skin tone, which are as follows: ‘Very Light’, ‘Light’, ‘Mixed’, ‘Dark’ and ‘Very Dark’.

I have also chosen this classification as skin colour/tone would be the first thing that a referee would see when dealing with a player and if racial bias were to be found, referees would stereotype based on their first impression, which in this case would be their skin colour alone. Even though the Premier League is a league based in Britain, I still opted to classify players by skin tone specifically, therefore separating Black British and White British players, however this may be a route to go for in a further study of the topic as there may be a bias towards home-grown players regardless of their complexion. White British players often fell into the category of ‘Very Light’ whereas White European players made up the majority of the ‘Light’ group but also featured in the former group mentioned significantly. Black British, Black European, and Black African players featured across the categories of ‘Mixed’, ‘Dark’ and Very Dark’, with those of Asian descent all featuring in the ‘Very Light’ category.

A time-varying covariate has also been constructed in the form of the age variable. Players at or over the age of 33 at the beginning of the respective season have been defined as ‘veterans’ as seen in Table 1. This variable gives us an idea of how age affects your overall play when it comes to receiving sanctions. At their ages, their footballing experience gained could give them the edge when it comes to avoiding a sanction as they know how the referee tends to act during particular situations. However, these ‘veterans’ could also see their performances declining, resulting in steps missed and late tackles, often resulting in an influx of yellow cards.

Players represent the unit of observation in this experiment and are taken from the 22 clubs that featured over the 3-season period of 2014/15, 2015/16 and 2016/17 that this dataset covers. These clubs include: Arsenal, Aston Villa, Bournemouth, Burnley, Chelsea, Crystal Palace, Everton, Hull City, Leicester City, Liverpool, Manchester City, Manchester United, Newcastle United, Norwich City, Queens Park Rangers, Southampton, Stoke City, Sunderland, Swansea City, Tottenham, Watford & West Ham. All first-team players that had made at least one appearance for a Premier League club listed above between the seasons of 2014/2015 to 2016/2017 were eligible for this experiment. Fixed effect dummy variables for the 22 clubs also feature in this analysis, with the inclusion of these variables ensuring control for the differing club cultures, as clubs with a more aggressive style of play are more likely to be given a greater number of bookings. This panel is comprised of 1,605 observations carried out on 1,012 players, with close to 37% of players remaining in the Premier League for multiple seasons during this 3-year period.

3.2 – Summary Statistics

Table 1 (can be seen on Page 18) provides a description of both the variables used in the model and some specific summary statistics found using the data taken from the players. Standard deviation is represented by the numbers in parentheses found underneath their respective values. In order to incorporate both forms of disciplinary sanctions into this model, I have taken yellow cards to the equal one card and red cards to equal two. For example, if a player has received 5 yellow cards and 1 red card over the course of a season, his total card count will be set at 7. I have done this as although red cards are rare in comparison to yellow cards, I wanted to take into account all forms of punishment received by players and consequently given out by referees.

The average number of cards received per player across all seasons was 2.64, with the seasons holding the largest and fewest number of issued cards being 2014/15 and 2015/16, with an average of 2.82 cards and 2.32 cards respectively. The average foul count was just under 16 committed, with the 2015/16 season again showing signs of leniency from referees throughout this season, with dataset low average of 14.7 fouls committed per player. The average player in the sample also played around 19 games per season across the dataset used. ‘Veteran’ players only accounted for 8% of the data, a testament to how tough the demands of the Premier League are, with most of these players operating as goalkeepers and defenders. As expected, the distribution of players in terms of their playing position is concentrated between midfielders and defenders, with these 2 positions combining to account for over 72% of the sample size. Additionally, the skin tone “Very Light” was the largest player skin tone throughout the dataset, with just over half of the players falling under this category. This again was expected as the majority of players in the English Premier League are home-grown British players. Out of the 1605 observations collected in the database, almost 29% did not receive a yellow or red card throughout the 3 seasons.  This statistic will have major implications for the model, which will be discussed in the section “Econometric Methodology”. Relevant notes for the table are as follows: Summary Statistics represent the means of the relevant variables, numbers found in parentheses represent the standard deviation.

Table 1: Variable Descriptions and Summary Statistics

VARIABLE	Variable Description	Summary Statistics
Cards	The total number of yellow and red cards received by a player in a given season.	2.6430 (2.7746)
Fouls	The total number of fouls committed by a player in a given season.	15.8417 (14.7429)
Season 2014/15	= 1 if observation relates to the 2014/15 Premier League, = 0 otherwise.	0.3308
Season 2015/16	= 1 if observation relates to the 2015/16 Premier League, = 0 otherwise.	0.3427
Season 2016/17	= 1 if observation relates to the 2016/17 Premier League, = 0 otherwise.	0.3265
Games Played ‘Veteran’ Player	The number of games played by the player in a given season. = 1 if the player is 33 or over years of age at the start of a given season.	19.555 0.0804
Goalkeeper	= 1 if the player is a goalkeeper, = 0 otherwise.	0.0847
Defender	= 1 if the player is a defender, = 0 otherwise.	0.3265
Midfielder	= 1 if the player is a midfielder, = 0 otherwise.	0.3963
Forward	= 1 if the player is a forward, = 0 otherwise.	0.1925
Very Light	= 1 if the player is Very Light, = 0 otherwise.	0.5047
Light	= 1 if the player is Light, = 0 otherwise.	0.1421
Mixed	= 1 if the player is Mixed, = 0 otherwise.	0.1230
Dark	= 1 if the player is Dark, = 0 otherwise.	0.0579
Very Dark	= 1 if the player is Very Dark, = 0 otherwise.	0.1657

This data will now be for a preliminary exercise, with the differences in both fouls committed and cards received in comparison to their skin tone to be examined.  Due to the nature of this model, we will first allocate players to either a “white” or a “non-white” category, for the purpose of this initial experiment. As we are researching potential racial bias in a predominately white league, I felt that placing players into these two distinct groups, to begin with, would be interesting. Essentially, the two skin tones of “Very Light” and “Light” will fall into the former category and “Mixed”, “Dark” and Very Dark” will fall under the latter. This will be done with a set of parametric (T-Test) and non-parametric tests (Mann-Whitney U-Test) in order to determine if there are any significant differences statistically across these 2 groups. Both types of tests were used to assess any statistical differences between the population means for the t-test and the population median for the Mann-Whitney U-Test.  Where the standard t-test results may lack in applying for attributes, the non-parametric Mann-Whitney is able to apply for both variables and attributes, giving us a more reliable set of results. Having both types of statistical tests available also allows us to account for if there was no information about the population with regards to the non-parametric test, although this would not be a problem in our framework, with the number of observations and players known. Our parametric test also assumes that variables are measured on either a ratio or interval level, with both fouls committed and the total number of cards, falling under the latter category (Surbhi, 2016.) The results found for the aforementioned categories are reported in Tables 2 and 3 respectively.

Table 2: Fouls Committed

Season	Average Foul Count for Darker Players	Average Foul Counts for Lighter Players	T-Test	Mann-Whitney U-Test	Sample Size
2014/15	17.18	15.78	1.006 (0.315)	1.053 (0.294)	531
2015/16	15.98	14.09	1.510 (0.132)	2.170 (0.030)	550
2016/17	17.35	16.10	0.906 (0.365)	0.693 (0.490)	524
All Seasons	16.83	15.32	2.698 (0.007)	2.586 (0.009)	1605

Table 3: Cards Received

Season	Average Cards for Darker Players	Average Cards for Lighter Players	T-Test	Mann-Whitney U-Test	Sample Size
2014/15	2.46	3.03	-2.14 (0.033)	-1.99 (0.047)	531
2015/16	2.09	2.45	-1.63 (0.105)	-1.75 (0.080)	550
2016/17	2.44	2.98	-2.01 (0.045)	-2.45 (0.143)	524
All Seasons	2.33	2.82	-2.23 (0.026)	-2.14 (0.032)	1605

3.3 – Initial Findings

The data shown above will now be used to analyse and examine any differences that may have been found, concerning both fouls committed, and cards received across the two distinct skin groups. During this introductory exercise, I have used a set of both parametric and non-parametric tests in order to determine if any statistical differences lie at a 5% level. Dealing with fouls committed first, the point estimate for the foul count was greater with darker players across all seasons on average, with the data also being statistically significant at the 5% level. On the other hand, the point estimate for the total cards received was higher for the lighter group, was significant across all seasons on average, and was only not significant during the 2015/16 season at the 5% level.  Therefore, the results from this preliminary exercise show that lighter skinned players are penalised less than darker skinned players are, however, darker players do receive fewer cards on average. These initial results are interesting, to begin with; however, the differences in card count especially might not be accurate with these simple tests. A key characteristic that would affect the outcome of the total amount of sanctions that a player might receive would be his position. Naturally, goalkeepers are less likely to find themselves in a position to commit a foul and thus receive a booking, in comparison to a midfielder or a defender. Additional factors such as the club the player plays for, the age of players and even the number of derbies a player participates in, have not yet been considered. Because of this, a more thorough analysis of this topic requires the use of a more advanced econometric test, which will be done in the next section.

4. Econometric Methodology

Assuming omitted factors from the previous experiment such as Position and Games Played vary across participants, we will be able to account for these factors using a standard linear regression. This allows for a relationship between covariates and fixed effects to be seen, but there is no necessity for a parametric distribution to be specified. All observations will be used in this model but players who do not feature for more than one season make no obvious contribution to the within-group variation, therefore making no difference to the estimates of the included covariates. Fixed effects for all players are attainable in this framework, however, which is very useful given the role of the time-invariant factor of race (any given season) (Reilly & Witt, 2011).

4.1 – Regression Model

A total of 5 variables were used in the linear regression ran through the STATA software in order to establish any correlation with the following variables and the total number of cards received: Skin tone, Games Played, Position, Seasons and Fouls committed. The independent variables of Skin tone and Position variables are expected to have the biggest effect on the number of total cards received, with Skin tone forming the foundation of my hypothesis and Position naturally affecting my results. This leaves me with the formula for my linear panel regression as follows:

CARDS_i = β₀ + β₁SKINTONE_i + β₂FOULS_i + β₃GAMES_i + β₄POSITION_i + β₅VETERAN_i +€_i

where CARDS is the total number of cards received (yellow and red), FOULS are the number of fouls committed by a player and GAMES are the total amount of games a player has appeared in, in a given season i which is also present for all other variables. There are a few variables that have not been taken into account due to the inability to quantify them in a regression, although they might have a minor effect on the number of cards a player receives e.g. club culture, nature of the player. These are incorporated into the error term, €_i. The variables SKINTONEand POSITION represent ordinal and nominal data respectively and are each represented by their own dummy variables as seen in Table 1. Likewise, VETERAN is a dummy variable equal to 1 if the player is over 33 years old, and 0 if otherwise, which again can be seen in Table 1.

With the nature of the linear regression, I could encounter some drawbacks using a linear panel method as the dependent variable is assumed to be continuous rather than ordinally discrete. As I am dealing with count data throughout this model, a Poisson model will also be run in order to offset this problem. Unlike the linear panel model, this model will not include players that have received zero yellow cards in their appearances, as they would make no contribution to the conditional maximum likelihood function. The estimation of these models with fixed effects can occur using either a conditional maximum likelihood estimator or an unconditional estimator. The conditional procedure is conditioned on the sum of the counts for the individual over time, giving us an easier estimation process (Reilly & Witt, 2011). Also, with the econometric software of STATA that I have used, there will be no biases included due to the problem of ‘incidental parameters’. This allows my estimation of the method and use of software to leave me with both valid and reliable results.

4.2 – Hypotheses

With the main question of this model being whether or not darker skinned players are more likely to be booked than lighter skinned players, we now also have to introduce our hypothesis in formula form, which can be written as:

H₀:β₁ ≤ 0

H₁:β₁ > 0

This shows both our null hypothesis in H₀, stating the slope of the regression line is less than or equal to zero and our alternative hypothesis in H₁, stating the slope of the regression line is greater than zero. The alternative hypothesis represents our initial question, if there is a positive correlation between a darker skin tone and the likelihood of a player receiving a disciplinary sanction, with the null hypothesis naturally stating the opposite. In our results, if our coefficients for the categories Mixed, Dark and Very Dark are greater than zero (assuming results are also found to be significant at the 5% level), we can conclude there is a relationship between skin tone and bookings within this model, by rejecting the null hypothesis and accepting the alternative hypothesis. The conclusion of our overall hypothesis should really only hold if the opposite instance is present for the Light and Very Light categories. Essentially, if the coefficients for the two categories are also positive, we cannot differentiate between the two race categories, as they have the same correlation in terms of bookings. Further evaluations of our results will be discussed in the following section, “Empirical Results”.

5. Empirical Results

With the foundation of the regression introduced and explained, we are now able to use the above mentioned to find our empirical results. The estimated model provides a deep exploration into our hypothesis, with variables such as Position played, and Games Played used in this experiment that would have a direct effect on the hypothesis of whether skin tone affects the referee’s decisions when it comes to disciplinary sanctions. Time dummies are included in the framework (relevant seasons) in order to account for any potential altercations in refereeing policy over time in the Premier League. For example, the rule that players will receive bookings for simulation/diving was only implemented in 2017 which would affect our dataset and the potential outcome of the results in comparison to seasons prior. The main catalyst for disciplinary sanctions is expected to be the number of fouls committed due to obvious reasons, and this variable will also feature in the empirical specification, with the linear and poisson model exhibiting 1605 and 1142 fixed effects respectively, specific to each observation found across all 3 seasons. Further analysis of the empirical results calculated using the regression found in Table 4 will be discussed in the next section. Relevant notes for the table are as follows: ***, **, * represent statistical significance at the 1%, 5% and 10% level respectively and – represents the base group of estimation and these variables have been omitted in the regression. The number of club controls within the database is set at 21, with one club omitted as the base club.

Table 4: Fixed Effects Model for Cards Received

VARIABLES	Linear	Poisson
Constant	0.1714 (0.114)	0.0483 (0.826)
Season 2014/15	–	–
Season 2015/16	-0.3016*** (0.006)	-0.3041** (0.025)
Season 2016/17	-0.0776 (0.483)	-0.0859 (0.520)
Fouls	0.1221*** (0.0039)	0.1249*** (0.002)
Games Played   ‘Veteran’ Player	0.0340** (0.0428) -0.0438* (0.0373)	0.1306*** (0.0022) -0.0198** (0.0169)
Forward	–	–
Midfielder	1.1858** (0.014)	1.0231** (0.021)
Defender	1.2345** (0.033)	1.5656*** (0.006)
Goalkeeper	-1.3233*** (0.0027)	1.3778** (0.018)
Very Light	–	–
Light	0.4346** (0.029)	0.4165 (0.160)
Mixed	-0.4778** (0.021)	-0.3466* (0.050)
Dark	-0.4999* (0.088)	-0.6513*** (0.008)
Very Dark	-0.5019** (0.010)	-0.7590*** (0.001)
Club Controls Included	Yes	Yes
Sample Size	1605	1142
R2	0.5812	0.5081

5.1 – General Analysis

With the results shown above, we can deduce various findings. When looking at the number of cards given out by referees as the seasons go, there is evidence of leniency within the Premier League. On average, the total amount of cards received by players has decreased by around 0.19 cards, with the largest decrease coming in the 2015/16 season at 0.3 cards per game, which was also found to be significant at the 1% level. However, leniency in cards received does not correlate with leniency in fouls given as evidenced with an increase in fouls, although relatively small, at roughly 0.1, with the commission of an extra foul increasing the card count on average (and ceteris paribus) by the same value. This was anticipated prior to the regression and unsurprisingly, this variable accounted for over 50% of the variation in total cards received also. Being a ‘veteran’ player was deemed to decrease the total amount of cards, although only minimally at the 5% level, suggesting experience does outweigh a natural decline in overall athleticism, but only marginally.

Analysing the data, the average number of cards received per player was at 2.64 across all seasons, with both models revealing evidence of a positive skewness, which can be seen in Figures 1 and 2 below. This number is much higher compared to the study undertook with data in 2003/04 to 2007/2008 in which only 1.82 cards were given out on average (Reilly & Witt, 2011). This is most likely due to there being stricter rules implemented in order to protect players rather than underlying racial factors. There have also been bookings given out to players due to simulation (diving) or professional fouls (intentional fouls done to stop a fast break). Both actions are straight yellow cards which would obviously affect the data and would have nothing to do with stereotypes or racial biases.

Figure 1: Kernel Density Plot for Linear Panel Model Fixed Effects

Figure 2: Kernel Density Plot for Poisson Model Fixed Effects

5.2 – Position Analysis

Position wise, the results show that the field position of a player has a statistical influence on the variable of cards received. On average (and ceteris paribus), goalkeepers receive around one less booking in comparison to forwards, with this data found to be significant at the 1% level. This result makes sense considering goalkeepers are rarely called into action in which they must commit a foul compared to forwards who are usually tasked with pressurising opposing defenders and committing ‘professional’ fouls, to slow down play, which warrants a straight yellow card per the rulebook. However, when goalkeepers are committing fouls they are usually the last man, meaning these fouls are more likely to lead to straight red cards, thus affecting the card count substantially for the goalkeeper position. Additionally, goalkeepers are the main culprits when it comes to receiving ‘professional bookings’ for time wasting. Goalkeepers tasked with taking goal kicks use this as the perfect opportunity to time waste unfairly to gain the desired result. As a result of this, referees often give out straight bookings as a signal to the keeper to hurry up, on top of adding on additional time.

One result that stood out to me was the reversal of the coefficient for goalkeepers, with a negative correlation between cards and goalkeepers found with the linear model but a positive correlation found with the linear data. With goalkeepers rarely pulled up for bookings to begin with, eliminating goalkeepers with no bookings would have given us a small sample size with a high tendency to receive bookings, thus skewing the data. In terms of midfielders and defenders, these two positions are statistically more likely to receive one more card compared to forwards, which was expected. Defenders just edge out midfielders when it comes to receiving sanctions, which are again found to be significant at the 1% level and was also expected prior to the experiment taking place. Overall, there is shown to be a clear variation in total cards when it comes to a player’s primary position, with approximately 90% of the variation in the fixed effects model down to a player’s different position.

5.3 – Skin tone Analysis

From the preliminary exercise that took place initially, there did appear to be a racial undertone to the decisions of the referees in terms of disciplinary sanctions. Players with a darker skin tone were penalised more often than their lighter-skinned peers, although they were also booked less often as well in comparison. In this model however, there is no evidence of racial bias towards darker skinned players in this panel when controlling for match performance affecting variables and a variety of other club controls.  With negative coefficients for Mixed, Dark and Very Dark players ranging from around -0.5 to -0.75 for both linear and poisson data, we can see that the slope of the regression line does satisfy the condition for the null hypothesis at the 5% level. This means we cannot reject the null hypothesis and fail to accept the alternative hypothesis, giving us a conclusion of no racial bias being exhibited towards darker players in terms of disciplinary sanctions.

In fact, the evidence claims at a 5% significance level that mixed race, dark and very dark players are receiving around a half fewer bookings compared to very light players, and light players are getting booked at a rate of 50% more often, on average and ceteris paribus, with the trend continuing on through our poisson model. Our regression coefficients also show a correlation to where you are more likely to receive a booking if you are a lighter player, with numbers decreasing across the range of skin tones, for both the linear and poisson data.  Although there could be a case made that using the significant evidence found (other factors still have to be taken into account), referees are carrying themselves in a more lenient manner with players outside their skin tone (as all referees in this database would be classified as very light), we can conclude with our original hypothesis being false. There is no evidence on the basis of both the linear and poisson model, that darker skinned players are a victim of racial bias and therefore are not more likely to receive disciplinary sanctions compared to their lighter-skinned counterparts.

Conclusion

This paper has introduced and analysed various forms of racial discrimination that have been displayed throughout British football and mainly the Premier League. With studies on the topic done prior to mine, a hypothesis was formed and tested to examine whether or not racial biases play a factor when referees give out sanctions to players, namely darker skinned players. The key research question was answered using an econometric model analysing a fixed effects panel model. The evidence gained from this model gave a strong indication that there is no distinct correlation between darker skinned players and an unfair treatment when it comes to bookings, with there even being evidence of a greater leniency when it comes to referees with darker skinned players.

With referees (who in this sample were all white) displaying no evidence of a racial bias towards non-white players and thus their own race, this could be taken extremely positively on both anti-racism institutions and training that these referees receive. In his own study, Dr. Witt took from referees being cleared of any form of racial bias that “This may also reflect the fact that referee behaviour is heavily informed by the anti-racist initiatives that have characterised the professional game in England over the last decade or more” (GetSurrey, 2013). Anti-racism institutions such as Kick It Out and FARE could have played a part in referee behaviour when it comes to this issue, as these movements would be responsible for referees becoming more racially sensitive and aware over time, thus explaining the outcome observed from our model.

In terms of future research that may be done on this agenda, additional variables that were not used in this framework, or are hard to quantify in a sense, have to be held accountable for. Variables such as the effects of league position, the culture of a club, fixtures played home or away, the number of derby games and crowd attendance could all potentially have a significant effect on sanction outcomes. Factors like this would allow for the club, referee and game effects to be controlled which would provide us with more accurate and perhaps more insightful findings into disciplinary outcomes and whether or not these would have a significant effect on the racial bias as well, remains to be seen.

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