Master Thesis
University of Groningen
MSc Business Administration – Specialization Finance Author: Vladimir Milchev (s2189569)
Supervisor: Prof. Dr Auke Plantinga
JERSEY ADVERTISING AND THE
IMPORTANCE OF TEAM RESULTS -
EVIDENCE FROM THE ENGLISH
PREMIER LEAGUE
Abstract:
Contents
I. Introduction ...3
II. Literature Review...4
2.1 Traditional treatment of corporate finance decisions ...4
2.2 Behavioral treatment of corporate finance decisions ...9
2.3 Empirical evidence in support of psychological pitfalls ...10
2.4 Hypothesis ...13
III. Methodology and Data ...14
3.1 Football Clubs...14
3.2 Abnormal Returns...16
3.3 Performance Measurement ...17
3.4 Variables List...21
IV. Regression Analysis and Discussion ...24
4.1 Integrity Tests ...24
4.2 Regression Models ...25
4.3 Auxiliary Regression Models ...28
V. Limitations ...33
VI. Conclusion...34
VII. Appendix ...35
I. Introduction
A great majority of sources on the internet rank football as the most popular sport in the world today (Topendsports.com, Spotonlists.com, Mostpopularsports.net). The number of fans of this sport ranges between three and three and a half billion people which is literally half of the population on the planet. The FIFA World Cup is ranked as the number one sports event along with the Olympic Games. There can be no doubt of the significance football has not just as a source of entertainment but also as an economic factor. The numerous fans are also potential consumers of goods and services related to sport and the popularity of the major football events contributes greatly to the GDP of the host-countries during or after their respective years as can be seen in Table 1 below.
Table 1. World Cup Host Countries (1998-2014), by GDP and percentage of change after hosting
Country/Host year GDP Year Prior to Hosting GDP Year Hosted (% of change)
GDP Year After Hosting (% of change) Brazil 2014 2.25 2.24 (-0.44%) N/A South Africa 2010 284.2* 365.2* (28.5%) 403.9* (10.6%) Germany 2006 2.85 2.99 (4.91%) 3.43 (14.72%) Japan 2002 4.16 3.98 (-4.33%) 4.3 (8.04%) South Korea 2002 533.1* 609* (4.9%) 680.5* (11.74%) France 1998 1.4 1.51 (7.86%) 1.5 (-0.66%)
Note: GDP in US Trillions of Dollars (Source: World Bank). A (*) signifies GDP in Billions of US Dollars
One specific issue that, to my knowledge, lacks research is the relationship between stock returns of official sponsor companies and the performances of the sponsored teams. Such a connection should exist as when a company sponsors a football team it advertises itself to the viewers of the team’s games – the football fans. If a team wins matches and performs well more viewers will watch the team’s games and thus the advertisement will reach a larger audience. This in turn is expected to influence positively the returns of the sponsor.
The remainder of the paper will be organized as follows: in section two I will look at traditional and behavioral corporate finance literature to find grounds for the hypothesis of the paper; in section three I will explain my methodology by describing the data collection and the data set; in section four I will discuss the regression analysis; in section five possible limitations of this research will be analyzed and section six concludes the paper.
II. Literature Review
2.1 Traditional treatment of corporate finance decisions
The traditional view of how the market functions and how firms increase their value contradicts the hypothesis of this paper. Firms raise capital by issuing debt or equity, borrowing from financial institutions or utilizing their operating cash flows. They then use these new funds to undertake new projects, to invest in research and development, to acquire or merge with other companies, enhance their inventories or pay dividends. All these activities can either be value creating or value destroying and if they do create value then this increases the stock price of the given company.
In traditional theory, in order to estimate whether a certain decision is value creating or not managers perform a discounted cash flow analysis. Since all of the activities mentioned above involve a certain amount of risk, the discounted cash flow analysis aims to evaluate the risk/return relationship and provide grounds for the managers’ decisions. If the present value of a given project is predicted by the DCF analysis to be at least equal to the required investment then traditional theory says that the firm should undertake the project because it would be value creating. Then the investors, who are the actual owners of a company, would learn about this NPV project through the media and would assign greater value to the stocks of that given company which simply means that the price of these stocks would increase (Shefrin 2007).
Exactly how accurate and how prompt would the undertaking of the new project be reflected in the stock price of the company depends on the market efficiency. This is the main claim of the so called efficient market hypothesis or EMH. Usually there are three types of EMH which are considered by economists – the weak-form, the semistrong-form and the strong-form hypothesis (Fama 1969).
already incorporated in the stock price of that company. This implies that applying trend analysis is pointless because past stock performance data is easily accessible and practically costless and if it contained valuable information about the future performance of the company it would already have been reflected in the stock prices.
The semi-strong form hypothesis claims that all publicly available information regarding a company and its prospects must already be included in the stock price of that firm. Because this information is publicly available, the semi- strong EMH asserts that investors have immediately included it in their valuation of the company and that the stock prices have adjusted accordingly.
Finally, the strong-form hypothesis further expands the amount of information reflected in stock prices to also include insider information. There is little doubt that managers and board members of a given firm do in fact possess information which puts them a step ahead of the market. This advantage provides an opportunity for illegal trading activities and much of the functions of the Securities and Exchange Commission in the US are directed toward the elimination of such practices and a strengthening of the plausibility of the strong-form EMH (Fama 1969).
So what does traditional theory say about the relationship between stock price returns of sponsor companies and the performance of their sponsored teams? First of all I need to clarify a few key notions. The stock price by itself represents the desirability of investors to hold the stock of a given company. If these stocks produce abnormal returns it means that at least the strong-form EMH is incapable of fully explaining the factors which influence a certain stock’s price. Second, I have to make a clarification about the nature of sponsoring. The word sponsoring can be easily substituted by the term advertising. Essentially that is what the nature of sponsoring is – a company pays a certain amount of money or provides certain goods and services so that it can be advertised by the sports’ team or event it sponsors. The question now becomes whether advertising creates value.
(2004) elaborate further that advertising should create firm value because it would influence future cash flows by its contribution to future sales. Thus future earnings, which capture future cash flows, would serve as a good estimate for the future benefits of investing in advertising. We already know that the semi- strong and strong-form EMH predict that future earnings are publicly accessible and known and should be reflected in the stock price of a company so advertising as an investment should not produce abnormal returns. However, the topic of this paper is slightly different. It is not just advertising per se that matters but also the efficiency of the advertising firm which in this case would be an English football team.
Table 2. Champions League Winners (as of 2012)
Position Team Titles Year
1 Real Madrid 9 1956, 1957, 1958, 1959, 1960, 1966, 1998, 2000, 2002 2 Milan 7 1963, 1969, 1989, 1990, 1994, 2003, 2007 3 Liverpool 5 1977, 1978, 1981, 1984, 2005 4 Bayern Munich 4 1974, 1975, 1976, 2001 5 Barcelona 4 1992, 2006, 2009, 2011 6 Ajax 4 1971, 1972, 1973, 1995 7 Internazionale 3 1964, 1965, 2010 8 Manchester United 3 1968, 1999, 2008 9 Benfica 2 1961, 1962 10 Juventus 2 1985, 1996 11 Nottingham Forest 2 1979, 1980 12 Porto 2 1987, 2004 13 Celtic 1 1967 14 Hamburg 1 1983 15 Steaua Bucuresti 1 1986 16 Marseille 1 1993 17 Chelsea 1 2012 18 Feyenoord 1 1970 19 Aston Villa 1 1982 20 PSV 1 1988
21 Red Star Belgrade 1 1991
22 Borussia Dortmund 1 1997
Source: Uefa.com
the largest fan-base are also top performers which proves my claim that performance and popularity go hand in hand.
What does this mean for the hypothesis of the paper? First of all I agree that there is a significant difference between a television channel and a football team when it comes to advertising. I claim that it is more probable for a television company to increase its ratings than for a football club to do so. My reasoning is that it is much easier to start a new type of show or program which could turn out to be sensational than to do something sensational as a football team. This is because football is more static. Think about who the top teams were twenty or thirty years ago and compare them to those now and you will realize that most of the members of the top ten list today were in the same list three decades ago (see Table 1,Appendix Tables 4,5). On the other hand, we have seen not only shows or channels but whole media groups come and go numerous times in every country over that same period. This assumption is difficult to prove and should be considered with caution but I believe that the logical reasoning behind it is sufficient for the purpose of this paper. What I wish to achieve by assuming this is to highlight the difficulty for a football team to perform abnormally well. If you are already at the top no matter what you do you will most likely not surprise anyone. Football experts and analysts around the world confirm this notion with their forecasts. Coefficients for matches and football tournaments always place the better team overall as the most probable winner which means that outcomes are to some extent predictable and, of course, if we look at the winners of popular leagues and tournaments we would very rarely see major deviations from forecasts.
2.2 Behavioral treatment of corporate finance decisions
Behavioral corporate finance deals with the possibilities for irrational behavior by all agents comprising the market. These possibilities are called psychological pitfalls of traditional corporate finance theory and are often the only possible explanations for certain economic phenomena. These pitfalls include biases, heuristics and framing effects which often result in irrational decisions not only by managers but across the general population (Shefrin 2007).
It is important to note that traditional corporate finance theory predicts that both managers and investors should perform analysis in order to determine the value of their investments. If there is a positive relationship between the abnormal returns of a sponsor company and the performance of the team it advertizes in this implies irrational behavior since traditional theory predicts that such a relationship cannot exist. The psychological pitfalls studied by behavioral analysts can explain such behavior. The pitfalls which could support and explain the hypothesis of this paper are availability, excessive optimism and affect.
Availability is a psychological heuristic which causes market agents to invest in projects or companies which are readily available just because of the easy access without actually performing any future earnings analysis (Shefrin 2007). This heuristic could be one explanation in support of this paper’s hypothesis. It could be that sponsors of major teams exhibit abnormal stock returns because of the strength of the signal they send by engaging in the sponsorship. This explanation however says little about the impact of the performance of the team and is thus of second importance.
Excessive optimism is a psychological bias which occurs when investors or managers overestimate how frequently they will experience favorable outcomes and underestimate the occurrence frequency of unfavorable outcomes (Shefrin 2007). Excessive optimism can be caused by mood changes such as football matches’ results, for which further evidence is provided later on. What is more, misestimating the risk involved in a project could lead to greater risk taking and subsequent adverse outcomes. In the case of football teams’ sponsors excessive optimism due to result-related mood changes could cause investors to artificially inflate the market value of the sponsors’ stocks which would sooner or later backfire and result in unexpected losses.
heuristic, mood changes brought about by excellent or poor team performance could explain positive or negative abnormal stock returns of the sponsor company. Although this psychological explanation is subject to much criticism and controversy, the amount of empirical evidence that corroborates its significance not just in relation to sports but to the economy as a whole increases. In fact, a recent study has shown that the majority of CEOs consider factors such as ‘gut feelings’, ‘manager confidence’ and ‘manager reputation’ as important and determining in the decision making process which leaves the question of what they actually rely on when making their decisions (Graham, Harvey, Puri 2009).
2.3 Empirical evidence in support of psychological pitfalls
Hirshleifer and Shumway (2003) examine the relation between whether a day is sunny and stock returns that day at 26 stock exchanges internationally from 1982-97. They find that sunshine is highly significantly correlated with daily stock returns. After controlling for sunshine, other weather conditions such as rain and snow are unrelated to returns. While the weather effect does not represent a risk-free arbitrage opportunity, they also discover that it is possible to improve the Sharpe ratio of the market portfolio, though somewhat modestly, by trading on the weather, even when there are transactions costs. These results are difficult to reconcile with fully rational price-setting. Furthermore the authors claim that these results are not the result of data mining and that their findings imply that investors can benefit from becoming aware of their moods, in order to avoid emotion-based errors in their judgments and trades.
Frieder and Subrahmanyam (2004) examine what happens to financial markets when the mood of a large group of traders might affect the market before, during, or after a religious or cultural occasion. Using U.S. equity returns for a two-day window on either side of the two festive occasions they studied, St. Patrick's Day and Rosh Hashanah, they find strong anticipatory return effects of the two holidays. They propose that optimism and/or increased investor confidence (and consequently decreased risk aversion) accompany these festive occasions, which is seen through enhanced buying of risky assets and a concomitant run-up in prices. Volume drops on Rosh Hashanah and Yom Kippur, which highlights the notion that nonfinancial opportunity costs are important.
how much they were willing to pay for lottery tickets and insurance. One control group received a gift of candy which was used as a mood stimulus and members of that group were willing to pay more both for the lottery tickets and for the insurance policies. A third experiment was conducted to determine whether this test could signify a greater willingness to spend in general after a mood improvement but the test did not result in a significant relationship. Thus the authors conclude that mood improvements change the risk- averseness of agents. A further study was conducted on the number of lottery ticket sales in Central Ohio which showed that on a day following a victory by the Ohio State University football team, sales tend to be greater than on days following a defeat.
Kamstra, Kramer, and Levi (2003) test for the impact of seasonal affective disorder (SAD) in the seasonal time-variation of stock market returns. SAD is a documented medical condition whereby many people slip into depression due to the shortness of the days in autumn and winter. Experimental research in psychology and economics shows that depression further leads to heightened risk aversion. Building on these connections (between the length of day, depression and risk aversion), the authors provide evidence that stock market returns vary seasonally with the length of the day. They call this result the SAD effect. Using data from several stock exchanges and controlling for market seasonal effects as well as other environmental factors, stock returns are shown to be significantly related to the amount of daylight in autumn and winter. Furthermore, the patterns at different latitudes and in both hemispheres provide evidence of a relationship between seasonal depression and seasonal variation in stock returns: markets situated in a higher latitude show more pronounced SAD effects, while the results in the Southern Hemisphere are six months out of phase, as are the seasons. Their final conclusion is that the SAD’s effect on economic magnitude is large.
information. Instead, they believe that the effect stems from the impact of sports results on investor mood.
Renneboog and Van Brabant (2000) investigate how a football club’s performance affects its stock price. Consistent with the hypothesis of this paper, they find a significant positive relationship between the stock price of a listed football club and the results it produces. Furthermore, the effect of a loss on the stock prices was found to be greater than that of a win, consistent with behavioral corporate finance theory which predicts that people on average value a ten-dollar loss as much as a twenty-five-dollar gain (Shefrin 2007). The effect of the game results was further estimated to fade away within 5 trading days, which is the average amount of time between domestic games.
Bell, Brooks, Mathews and Sutcliffe (2009) confirm the results of this study by also considering the impact of match results on the stock returns of English football clubs. Their main finding is that, while match results affect the share price, these effects are modest compared with the changes in club stock prices caused by other variables. As a result, the proportion of the variation in share prices explained by match results is very small. The market index mostly has a significant positive effect on returns, as the CAPM predicts, although for every 1% rise in the index, the share price rises by only about 0.1%. Furthermore, points surprises, or surprising results, have a positive influence on returns.
In a study very similar to what this paper aims to achieve, Hanke and Kirchler (2010) find a statistically significant impact of football results (at an individual game level) of the seven most important football nations at European and World Championships on the stock prices of jersey sponsors. The general trend which they ascertained is that the more important a match and the more unexpected its result was, the higher was the effect on the sponsor’s stock price. This find also confirms my earlier claim that the predictability of a team’s performance is important when evaluating the value of the sponsorship and is line with the strong and semistrong EMH – whenever there is an unexpected result, there should be an abnormal return. However, the authors did also acquire results which are not entirely compatible with the EMH hypotheses: the fact that victories in general generate positive abnormal returns and losses result in negative abnormal returns.
market returns and vice versa implying a positive relationship. Furthermore, just like in the last paper I mentioned the impact of more important games was found to be much greater than the impact of less important games such as friendly matches.
Finally, Palomino, Renneboog and Zhang (2009) also examine the effects of game outcomes on the stock prices of football clubs listed on the London Stock Exchange. They, however, use two pieces of information – game results as well as game predictions obtained by examining betting odds. Their results show that the stock market reacts strongly to news about game results, generating significant abnormal returns and trading volumes. Abnormal returns for the winning teams do not reflect rational expectations but are high due to overreactions induced by investor sentiment. They do not find the same results for losing teams and find no significant impact of the release of new betting information even though betting odds are a fairly good predictor of game outcomes. The authors conclude that investors tend to ignore certain information such as games’ forecasts and that investors’ mood is predicted to have an impact on the stock price reactions of game outcomes especially when a team is expected to win.
2.4 Hypothesis
To summarize, the traditional theory or the EMH predicts that a relation between football clubs’ performance and the returns of their sponsors’ stocks should exist only if the market is at best weakly efficient. However, weak efficiency is difficult to support. After all, investors use a variety of models when making their decisions and those models are not based solely on historical data which is widely accepted as a poor predictor. Hence, if the stock returns/team performance relationship exists behavioral theories would gain credibility. Since there is a multitude of evidence showing that behavioral corporate finance theory often fills in gaps which traditional theory cannot, I will base my hypothesis on the former and try to either prove or disprove it using the data and methodology that is described in the next section.
III. Methodology and Data
To test for a possible relation between stock price returns and team performance, I calculate abnormal returns of the companies who sponsor major English clubs in the period from 1992 until 2012. I chose this starting year because that is when the English Premier League was established as it is known today – Barclays Premier League (BPL), named after its major sponsor Barclays. After 1992 the leading clubs in England sought to capitalize on the increased worldwide popularity of the English First Division by breaking away from “The Football League” and thus found the BPL. The newly found competition sold televising rights to more countries and further increased its tremendous fan base. “Since [1992] the number of countries televising English football has quadrupled” (Observer 2002). This huge increase implies a greater value of any type of marketing activities within the BPL and changes the setting for the companies who are considering whether or not to have their logos on a major team’s jersey.
Coincidentally, 1992 was also the year when the most popular club tournament in the world, the Champions League, also changed its format and obtained its current name. Here is what the official Champions League website writes about the change: “The major turning point in the evolution of the competition came in the 1992/93 season when the UEFA Champions League, involving a group stage in addition to the traditional knockout elements, was officially inaugurated after a pilot round robin during the previous season (Champions League Official Website).” This change increased the number of teams participating in the tournament and made more room for stronger teams who were not able to win their domestic leagues to also play internationally. This significantly increased the tournament’s popularity and number of viewers which translates into a better advertising opportunity for all sponsors. For the chosen period the following game outcomes are observed: 2,864 wins (49%), 1,415 draws (24%), and 1,582 losses (27%) or 5,861 observations in total.
3.1 Football Clubs
name is on the jersey during each match. Every one of the top teams has numerous sponsors and partners. Liverpool, for example, has eighteen (Liverpool FC Official Website). However, there are very few, if any at all, supporters of the team who would be able to list more than two.
3.2 Abnormal Returns
I calculated abnormal returns using the equation:
ARit = Rit – E(Rit |Xt ), (1)
where AR, R and E are the abnormal, actual and expected returns for firm i’s stocks at time t. I have obtained the actual return R from Thompson’s Datastream. I collected closing daily stock prices for each publicly listed sponsor. I ignore observations when the sponsor is missing from the database or not publicly listed. I calculated continuously compounded returns:
Ln(Pt ) – Ln(Pt-1 ), (2)
where Pt is the price of the given stock at day t. At this point it is important to note that
the actual match day is t-1. So the abnormal return is obtained by using ‘tomorrow’s’ stock price of the sponsor. The reason is that matches are very often played when the stock exchanges are closed. So, technically, the market would not have had time to react to news from the football fields. Since I already provided empirical evidence for the importance of investor mood both in general and when it comes to sport, a similar reasoning can be applied for the purpose of this research: namely that the abnormal returns caused by investors’ emotions should be greatest immediately after the mood-changing event and should then gradually wane until the market adjusts (see Beaver, 1968; Patell and Wolfson, 1979).
The expected stock return, however, should be estimated using one of the known models. The most common models for the expected stock return are the constant mean return model and the market model. The expected stock return is assumed to be constant in the mean return model. Since this assumption is not very realistic, I will use the market model. With the help of statistical packages I will estimate a regression model and use that to obtain abnormal returns. The market model assumes that security return is a linear function of the market portfolio return. Therefore, I can run the following regression:
Rit = αi + βi Rmt + εit, (3)
Here Rit is the company’s stock return and the independent variable is simply the market
OLS regressions regressing past company stock returns on past market index returns. I chose to take values from five years in the past in order to increase the predicting power of the model. Using just one year might not be enough and might produce biased results because we would have subsequent years’ events influencing each other (Alexander and Chervany, 1980). This would also hold true for five years but the effect will be much less severe. More than five years would be very difficult to accomplish because companies might not have stock price observations for that many years prior to 1992 or prior to the start of their sponsorship which would mean they would have to be dropped from the model. The ten teams I have selected to research have had about fifty sponsors from January 1992 until December 2012. That makes five sponsors per team or four years per sponsor, on average. Second, I chose the MSCI index as my market returns estimator. I think that it is a suitable index first because it holds a large proportion of the publicly listed companies in each country and second because it offers index returns in all nine countries (China, US, UK, Denmark, Malaysia, South Korea, Japan, Germany and Singapore) whose stock exchanges list at least one of EPL top ten teams’ sponsors.
Now that I have clarified these issues let us look back at the OLS regressions for estimating alpha and beta. I will run a regression consisting of five-year market returns and five-year sponsor returns for each year in the observation period and for each country. So, for example, if I estimate Carlsberg’s returns for 1997, I regress its returns from 1992 until the end of 1996 on the MSCI returns for Denmark over the same period. For the next year’s estimations I do the same but I will replace 1992 values with 1997 ones. Analogously, I obtain alphas and betas for each sponsor. Finally, with the help of these constants, I obtain the expected return for the desired current year (in the example above that would be ’97 and ’98) by substituting the alphas and betas into equation (3) and plugging in the MSCI values for that same year. Once I have the expected returns for each observation day it is a matter of simple substitution of the expected and realized returns into equation (1) in order to receive the abnormal or excess returns.
3.3 Performance Measurement
necessary. Using the other website I check the correctness of the first website’s data. An additional goal would be to see whether relegations and promotions also have an impact on the sponsors’ stock returns. Logically, if there is a relationship between performance and stock returns, relegations should have a strong negative effect and promotions a strong positive one.
the research done by Bell (2009) who found that the importance of the game affects the football clubs’ stock prices, I will multiply the points for a victory or loss in a derby match or a match in a late stage of a tournament, meaning semi-final or final, by 1.5.
Table 3. Summary statistics of game outcomes and points awarded as per before mentioned point distribution system
Team Wins Draws Losses Total points Total points with derbies multiplied by 1.5
Newcastle 458 240 303 1679.67 1720.50 Sunderland 366 224 354 -100.17 -125.58 Manchester Utd 712 232 185 5692.17 5942.26 Manchester City 410 237 335 898.17 857.42 Arsenal 622 276 231 4340.00 4413.75 Chelsea 595 262 238 3975.50 4103.58 Aston Villa 381 267 307 1389.50 1431.42 Everton 346 243 334 781.33 759.92 Tottenham 412 241 333 1258.67 1237.75 Liverpool 560 258 268 3360.67 3432.66
attendance in all tournaments I am looking at for the 2011/2012 season. As you can see, ranked from top to bottom the tournaments are listed in exactly the same fashion as they are in Sportingintelligence’s ranking table. Just for reference I have also included Manchester United, Arsenal and Chelsea’s home attendances in the specific tournaments. Manchester’s average attendance should provide the best estimation of a tournament’s importance since United have the largest stadium and thus the largest sensitivity to the significance of each game. The close resemblance with the tournament averages is obvious and confirms the weights I have assigned to each competition. However, you can see that Chelsea’s average attendances (which are about half those of United) are, first of all, very close to each other and second, do not mimic the overall averages’ pattern. This is not surprising because Chelsea is, as we have already seen, one of the top ten most supported teams but it has a very small stadium compared to the other top teams. This means that the stadium is more likely to fill up and is less sensitive to the weight of a given game. That is why it is important to look not just at teams’ average attendances but the overall tournament turnout which ranks the five tournaments in the exact same fashion as I have.
The top ten English teams’ results represented by the points I will assign to each game outcome constitute the main independent variable in my model. Nevertheless, if I wish to include the results of all teams and the returns of all sponsors’ stocks into one model I need to somehow match the data so that the regression would make sense. I have decided to do this using each game as an observation point as opposed to using a whole day and all the games played in it. That way each abnormal return of a team’s sponsor will have its team’s points for the current game.
emotions and I would expect them to have the strongest effect on investors as well (again assuming that the hypothesis of this paper is true).
3.4 Variables List
Following is a list of all variables I have used in all the different regression models, which will be discussed in the next section, and a detailed description how they were constructed.
“Abnormalreturns” – The dependent variable. It shows the abnormal returns of each company for the respective day. The method of computation was shown earlier. An important note that should be made here is that for ease of calculation I deleted some stock price observations in certain years before I calculated the abnormal returns. The reason for this is that I wanted to make each year have the same amount of observations: some years had 260, some 261 and some 262. That is why I removed respectively the last or the two last observations of June for the years that had more than 260 stock price observations. I chose June because there are no games played in midsummer months and the removal of these values would not influence the regression results. It does, however, influence the slope coefficients and the intercepts of the predictor past-five-year regressions according to which the abnormal returns are calculated. Nonetheless, this effect is very small and should not impact the overall results of the research but is something that should be noted. “Score” – The main independent variable. It shows the amount of points earned by the top ten teams during a current observation day. The points were assigned according to the importance of the tournament in which the games were played. The weights of the tournaments and respectively the values of the wins are shown in Table 6 in the appendix. Draws earn 1/3 the amount of points for a victory and losses earn the negative value of the amount for a victory. If the game is considered to be a derby or is either a semi-final or a final of a tournament the respective points were multiplied by 1.5. Determining whether or not a game was a derby was done according to the listing of English derbies and rivalries on footballderbies.com website. A table with all English derbies listed in that website can be found in the appendix (Table 14). An additional note: matches from Super cups and the Community Shield matches were excluded because they are a 1-match tournament and would distort the data.
variables is used in regression scenarios for robustness check of the main model.
“Regularpts” – A replacement variable for “score”. It assigns the same values to each game outcome as the points given in real-life football (three points for a win, zero for a loss and one for a draw) without taking into consideration the importance of the game.
“Negativelosses” – A replacement variable for “score”. Basically it is the same variable as “ regularpts” but instead of a zero it assigns -3 to each loss.
“Zerodraws” - A replacement variable for “score”. It assigns the same values for wins and draws as “score” but replaces the points for a loss with a zero.
“Wins” – The amount of points earned by the top ten teams from victories during a current observation day according to the points system. Assigns a zero to both draws and losses.
“Losses” - The amount of points earned by the top ten teams from losses during a current observation day according to the points system. Assigns a zero to both draws and wins. “Draws” - The amount of points earned by the top ten teams from draws during a current observation day according to the points system. Assigns a zero to both wins and losses. “Hire” – A dummy variable equal to 1 if a new manager was hired. Data for this variable was obtained, again, from footballdatabase.eu. Hiring or sacking other staff members was not incorporated in the variable as this news is hard to obtain and very few people are interested in it so it does not make any sense to include it. To avoid disturbing the main independent variable by assigning zeros, the observations for “hire” were matched with the observations of the points by placing the 1 on the first match day of the new manager. Also, managers are very often hired or sacked during the summer months when no matches are played. During those months fans are less likely to track the current events in their favorite teams’ locker rooms. Of course, a lot of them do but the impression of the new manager is strongest on his debut out on the field and that is why I chose to mark that observation day as the day a manager was hired.
“Sack” – A dummy variable equal to one if the current manager was sacked. This dummy variable is constructed in the same way as “hire”.
“Buy” – A dummy variable equal to 1 if a new player was purchased. Data for this variable was obtained, again, from footballdatabase.eu. In the same fashion as the dummies for managers, the 1 was marked in the first match day after the transfer was completed.
is marked on the first match day after the transfer was completed.
“Trophy” – A dummy variable equal to 1 if a trophy was won. Data for this variable was obtained from worldfootball.net.
“Sponsor” – A dummy variable equal to 1 if the team has changed its main sponsor. Data for this variable was obtained from the website historicalkits.co.uk. The site records English clubs’ kits since the teams’ foundation. The sponsors are almost always changed between seasons so I mark the first match day of the new season as the day when the sponsors changed. After all, that is also the first day when most fans see the new jerseys. The website also mentions the specific month when a sponsor was changed if that happened mid-season. Luckily, the final dataset does not include such sponsor changes so a team’s first match of the season with a new sponsor is the only case when the sponsor dummy variable has a value of 1.
“Relegation” – A dummy variable equal to 1 if a team was relegated. Data for this dummy was collected by examining the football club’s games. Because a club knows if it is relegated or promoted before the new season starts, this dummy variable receives a one on the last match day of the season prior to relegation.
“Promotion” – A dummy variable equal to 1 if a team was promoted. Data for this dummy was collected by examining the football club’s games. Because a club knows if it is relegated or promoted before the new season starts, this dummy variable receives a one on the last match day of the season prior to promotion.
“Companyid” – A variable which assigns a discrete number value to each sponsor company’s observations. The total number of sponsors participating in the model is 26 so each company has its own number from 1 to 26.
IV. Regression Analysis and Discussion
An important thing to note about the model is that it has, in fact, only two actual variables – the dependent variable, which represents the abnormal returns, and the variable which shows the number of points a team has won on a given match day. All other variables in the model are dummies which control for certain external events which might either influence performance, as in the case with buying or selling players, or influence the general public’s perception of the team and their emotions towards it, which could happen when the team wins a cup or is promoted to a higher division.
4.1 Integrity Tests
4.2 Regression Models
The first regression model I constructed is simply a regular OLS regression of the type: ARit = αi + β1 *score + β2 *hire + β3 *sack + β4 *buy + β5 *sell +β6 *trophy + β7 *sponsor +
β8 *relegation + β9 *promotion + Σi n=10 βn *Companyit, (4)
where ‘company’ represents the dummy variables marking the abnormal returns’ observations of each sponsor company. The company dummies attempt to make the regression pooled and capture firm-specific effects. Using statistical tools I tested the model for autocorrelation, heteroskedasticity and multicolinearity. The results of these tests and the tests themselves can be found in the appendix in Table 11. The only statistically significant problem that the model displays is heteroskedasticity – a problem which is often present when a series of daily stock returns is examined. To fix this issue I chose to simply re-run the regression models with robust standard errors. Although this method might be simplistic and some might argue that it does not fully correct the problem the results of the regression will show that in this case this simple solution would be sufficient.
The results of the corrected regression, unfortunately for behaviorists, are just about as insignificant as they can get. First of all, the R-squared of the model is only just over two percent signaling a very weak explanatory power of the model. Second, all variables but one company dummy have produced highly insignificant results. The only dummy that shows significance in this model is the dummy representing the abnormal returns of NTL. This is strange for a couple of reasons. First, this company is the only firm from the list of
26 sponsors that has sponsored two teams in the research period – Newcastle and Aston Villa – and it was their sponsor simultaneously during the 2000/2001 and 2001/2002 seasons. Second, the coefficient of the variable is negative meaning that the better the teams performed the lower were NTL’s abnormal returns. This find is at first glance nonsensical and could be due to data mining or in other words – coincidence.
ownership of the clubs live television and radio rights. In line with this new project, NTL also competed for the right to broadcast EPL matches but the deal collapsed due to disagreement on the final terms. The company’s next project was a joint venture with the Football League to create an internet portal for all the teams it includes, which means all 72 English teams of the three divisions lower than the Premier Division. Together with the six teams which NTL partially owned, that resulted in a total of 78 football club websites for which the company had to pay rights fees. Eventually, that deal also fell through as NTL could not pay its installments (Guardian 2002). Although a long shot, these unsuccessful deals could provide an alternative explanation for NTL’s significant negative coefficient of abnormal returns. These deals were both made in 2000 when NTL became the sponsor of Newcastle and Aston Villa. It is possible that shareholders saw the troubles NTL had to pay for its broadcasting rights and knew that if the EPL teams performed well then NTL would have to pay more. This argument is not unsubstantiated as it just so turns out that the first three seasons of the new century were very successful for Newcastle – they managed to finish in top positions and in two of the years they even qualified for the Champions League. Aston Villa did not share the same success as Newcastle but it did have its moments – it won the Intertoto Cup which also gave it a place in the UEFA Cup. This means that the sponsorship would now cost NTL more and investors could have seen this as a potential threat that NTL might not be able to meet its financial obligations and this could have produced the lower abnormal returns. More likely, however, is the explanation that this is all just due to coincidence – both of these teams simply performed well while NTL was already experiencing difficulties with its inability to cover the rights fees.
and value of the coefficient for the performance measurement variable. Since the hypothesis of this paper is that there is a positive correlation between performance and stock returns, the sign of the independent variable “score” alone is enough to force a rejection of that hypothesis. The fact that this negative correlation is insignificant is actually logical because such a relationship would not make sense: it can sometimes happen, as in the case with Newcastle and Aston Villa, but this occurrence would be an exception and should not be observed overall. Furthermore, after applying the robust standard errors to the regression the significance of the relationship between performance and stock returns actually decreases further, which combined with the fact that it is an inverse relationship gives me grounds to claim that this method of heteroscedasticity correction was appropriate and that the model’s output is in no way
biased.
Another important note that should be made for this model is that the multicollinearity test showed VIF values higher than 10 for two dummy variables – Carlsberg and Samsung. Since these are dummies the fact that they exhibit multicollinearity should not be worrying. Also, these two variables are among the top company dummies in terms of number of observations: Carslberg, the company that has the highest VIF value, is also by far the dummy with the most observations which are close to a thousand out of the total 5,861 and Samsung has over four-hundred. Having this in mind it is not surprising that the test has produced such results. However, for the sake of being thorough I also re-ran the model using robust standard errors and excluded these two dummies. The new multicollinearity test shows that the model is now OK but the significance of the variables and their coefficients remain almost unchanged. The only difference now is that another company dummy – the one for Sega – is shown to be statistically significant but again with a negative coefficient which implies that there are other forces at play and that the performance of Arsenal, the team it sponsors, is not the cause of this inverse relationship. The results of the multicollinearity tests can be found in Tables 12 and 13 in the appendix and the outputs of both models can be found in Table 10 in the appendix.
Nevertheless, these slight disturbances should not be ignored. That is the reason why I chose to also do a panel regression holding firm effects fixed. For the purpose of this regression I created an additional variable called ‘companyid’ which assigns a different number from one to twenty-six to each company’s abnormal return observations. In other words this is basically an
identifier variable upon which the statistical package will test the interdependence of the other variables. Expectedly, the results from the regression, which can be seen in Table 10 in the appendix, are pretty similar to the OLS regression’s results. The coefficients of all variables remain almost unchanged and their signs are the same. Curiously, the signs of the coefficients in either of the regression models for promotion and relegation are both positive and those for the transfers of players are both negative which is counterintuitive and contributes to the overall picture of a lack in significant explanatory power of the model. The only noticeable differences in the panel regression are that now the p-value of the ‘score’ variable has decreased a little (but still remains far from significant) and that the R-squared of the model has decreased to almost zero. Overall, this regression confirms the results of the previous one and verifies that sponsor stock returns are not related to the performance of the teams sponsored.
4.3 Auxiliary Regression Models
Despite this uniformity among the results I still did several more different regressions in order to corroborate the findings with more certainty. The first such, let us call it supplementary, regression was to test the direct relationship between the performance and returns variables in a model which excludes all dummies. After all, it could be that the addition of the complementary variables somehow distorts the results. A simple test for a direct relationship would shed more light on the propriety of expanding the model and on the integrity of the results so far. This test I conducted in three different manners: first, I used the variables as they were in the main model – using the earlier described points system and the abnormal returns; second, I substituted the points I assigned with regular points as they are in real-life football; finally, for the third test I substituted the zero values of losses in the second test with a -3 to account for the fact that losses should have a negative effect on sponsor returns as is claimed by the hypothesis of this paper. In terms of significance, the first test produces the worst results of any regression I ran. The p-value of the independent variable is over 0.8 and the R-squared of this model is smaller than 0.0001 which is why it is shown as a 0. The coefficient of the variable is s t i l l
negative but is the least negative one of all coefficients for this variable in the other models. To me this translated into a sign that the points system I used was indeed more appropriate than using just the regular points a club receives after each match. My logic is this: if there is indeed no relationship of any sort between stock returns and performance (between
any two variables for that matter), ideally we should see p-values close to 1, R-squared values close to zero and coefficients close to zero; or, in other words, a model with absolutely no explanatory power. Rationally, the first direct relation test produced the results which are closest to this perfectly bad scenario.
The other two models produced slightly increased R-squared values (0.0001 in both cases to be specific), much higher coefficient values in terms of absolute value and lower p-values. Usually this would be a move in the right direction but my argument is that this would be true only if the models actually improved already significant variables and if their coefficient was not contrary to common sense – there simply cannot be an inverse relationship between returns and performance because it would be contrary to both theory and logic. I believe that what we have here is rather a slight decrease of a very serious insignificance due to an introduced confusion in the model by ignoring the importance of the games which is a proxy for the number of viewers. And the number of viewers, as I have already argued, is what this research is essentially about: the more people watch the greater the probability of an influence on the sponsors’ stock returns. What is more, the same movement in the values of the regression output is noticed between the two tests when using normal match points and when substituting the zero points for a loss with a negative three. The negative loss points model shows higher p-values and an almost three times smaller coefficient of the dependent variable. Looking at these two regressions alone and ignoring the first one would also suffice to confirm my logic. Surely if a win had a positive impact on stock returns then a loss should have a negative one. We know from behavioral empirical studies that people actually value losses about 2.5 times more than they value gains. It is true that those studies focus on personal wins and losses but I think it would be reasonable to assume that it would also hold true when watching your favorite team play – the disappointment from a defeat in an important game is higher and lasts longer than the ecstatic feelings which a victory gives. Hence, it is more than rational to expect the model with negative values for defeats to have greater explanatory power and be generally healthier than the one who assigns a zero to every loss. What we actually see from the results is that the trend is kept – from the best, in my opinion model, which weighs games according to their importance, through the model which simply administers the negative impact of lost games to the one that uses match points directly as they are allotted in the real world the p-values of the performance variable fall, the R-squared rises slightly and the slope coefficient increases in magnitude several times.
they move towards the worst of the three? The answer is simply that in this case the healthiest model is the one with the worst statistical outputs, as paradoxical as that may sound. The reason for that is that there is simply no relation between these two variables. There is no direct relationship, there is no inverse relationship, these events are simply not related. And how can a model show this fact? By producing the worst possible output. Just like when a model showing significant relationships between certain variables is made worse by adding unrelated ones, so is a model showing no relation at all made a little less bad when it is distorted but nevertheless remains statistically insignificant. In statistical language this explanation would sound like this: in essence there is a ‘battle’ going on between the null hypothesis and the alternative hypothesis. This research is specified in such a manner that the null hypothesis is that there is no relationship between the variables. When the model shows significance, or low p-values, it means that the alternative hypothesis that a relationship exists wins. With the decrease of the p-values we can reject the null hypothesis with greater confidence with makes the alternative hypothesis stronger. On the other hand, the opposite effect would mean that the null hypothesis becomes stronger and it is strongest when the p-values are highest. Since the sign of the slope coefficient is itself suggesting that there is no relationship it should not be surprising that the statistically weakest specification of the model is actually the best one – that is when the null hypothesis is strongest. That is why I believe that this is not a paradox at all but, rather, yet another confirmation of the initial results of the complete model. As a final testament to this claim is the result of the performed omitted variables check on the complete model which shows that the model suffers from omitted variables with a 99.99% probability. The movements of the abnormal returns are simply not explained by the variables provided.
true but wins and draws produce opposite results. So the problem with the previous models was not how losses were measured but, again, simply the fact that the outcomes of the games do not exhibit a significant relation to the changes in abnormal returns. And when I measured losses differently what probably happened was that their coefficient also became negative because they now had less negative values of -3 and 0. In comparison, their average value when measured according to the points system described earlier is -9.3.
So why is it that performance and stock returns show a negative correlation albeit insignificant? The fact of the matter is that these teams simply performed well during the twenty years measured but the same does not hold true for their sponsors. The teams won almost 49 percent of the time while they lost only about 27 percent of the time. The points collected from victories exceed those deducted by losses in absolute value by almost 11 000. Apart from that these teams also won 69 trophies, both domestic and international, from 1992 until the end of season 2011/2012. The sponsors’ abnormal returns, on the other hand, are on average negative. This alone shows an absence of any sort of a correlation between the two and is further corroborated by the results of all the models described.
But what if it was not losses but draws that were improperly specified? Someone might say that, yes, losses should have a negative impact but ask why draws should have a positive one. Why not zero influence? It is arguable whether draws should have no influence or a slightly positive one – sometimes a draw can win a title or could win progression to the next phase of a tournament. But I have decided to take this note into account and also re-run the regression with an independent variable assigning zeros to all draws instead of their previously assigned values. The results do not change anything – the coefficient is still negative, the R-squared close to zero and the p-value of the variable far above the significance levels.
the same results on the tests for heteroskedasticity, multicollinearity, autocorrelation and unit roots. The only statistically significant problem in all of them is heteroskdasticity and that is why every regression, be it with or without dummies, is ran using robust standard errors.
The final model which I analyzed as an ultimate check to the hypothesis of this paper incorporates only the observations for Liverpool while their sponsor was Carlsberg. The reason I wish to do this is because their contract was the longest shirt sponsorship in English football history (Bleacherreport.com) and because Liverpool is still ranked as the most successful English team ever. Thus, I essentially have the extreme form of my own experiment – the best performing team with the longest sponsorship. The rationalization why this is the extreme form of the experiment goes back to the previous discussion of how a team’s performance is related to its popularity and how the size of a team’s fan base matters for the sponsor who wishes to advertize. In this case we can also add another point: time should also be a factor of a sponsor’s success because as time progresses fans become accustomed to seeing the sponsor’s logo on their favorite club’s jersey and they associate it more closely with that club. Sometimes even the goods which the sponsor sells or produces become part of the whole football experience. This was, and I would say that it still is, the case with Liverpool and Carlsberg. Fans started drinking that beer simply because it was on the team’s shirts and it became a sort of ritual which became so influential that even though the company is still a team sponsor, the fact that it is not on the jersey appears to be unsettling some of the club’s supporters (Worldsoccertalk 2009). In other words, while Carlsberg’s logo was on the Liverpool FC jersey, we would have every reason to believe that the team’s performance would influence the sponsor’s stock returns – LFC are the top-ranked English team, they have had the longest sponsorship in English history and the sponsor’s products go hand in hand with a good football experience. In every possible way this is a unique case and is as close as you can get to the perfect setting for establishing a connection between stock returns and sport games’ outcomes.
One result, though, needs further attention. The LFC model shows that the hiring of a new manager has had a significantly negative influence on Carlsberg’s stock returns. This result, however, should be interpreted with caution for several reasons. Firstly, in four of the six cases the new managers started off with a win. Secondly, there is no significantly negative reaction to the sacking of a manager. If fans dislike the new manager this could probably mean that they wanted the old manager to stay but the coefficient on the sack variable is positive even if very small. Thirdly, there are only six observations for this dummy variable during the researched period. This finding can easily be the result of coincidence. Also, Liverpool’s managers were changed largely because the board of directors, and the fans for that matter, aspired greatly to see LFC as the winner of the Barclay’s Premier League. This has yet not transpired and despite the fact that the club won eight other trophies its managers were sacked mainly because of the board’s frustration at how the club performed in the BPL. Thus, we should expect a positive reaction to the hiring of a new manager. Of course, the opposite might also hold true if the fans actually liked their old managers despite the poor-league performances and it was only the board of directors who were unhappy. Whatever the case, this dummy’s significance should not be taken as a definite verdict for the reasons enumerated above and because it was not present in the complete model where the dummy had more observations. In other words, it could be a coincidence, it could be a phenomenon only valid for Liverpool, it could be due to lack of observations and it does not mean that we can expect that a manager’s debut would result in negative abnormal returns for the team’s sponsors.
V. Limitations
In terms of data there are almost no limitations to the topic of this research. Almost all data is publicly available and easily accessible. It would have been best if information on injuries could have been gathered and added to the regressions but unfortunately such data was impossible to obtain or was incomplete. Injuries of key players influence a team’s performance and could be used as possible signals from investors. Of course, it is doubtful that this information would have significantly changed the main findings of this paper since factors which should have had a much greater effect on abnormal stock returns actually turned out to be insignificant.
factors which are much more important to investors when analyzing the stock markets than sports results. This means that if a relationship did exist it would be very weak and the influence of sports results would be very small. As a result, a sudden change in any major economic factor would bring about much more significant changes in abnormal returns which would easily overshadow those of the teams’ performances. For the conclusion of this paper to hold true in absolute, the research needs to be conducted in a setting where there are no serious economic shocks. This is obviously not true for the past few years. Such a stable environment is actually impossible to exist since the global economy is very dynamic and the companies which sponsor major teams are from different countries which makes it even harder to assume stability.
Second, it is difficult to determine the proper way to analyze such a weak relationship. I have chosen to search for a next-day effect but there are other possibilities as well. Some of the papers cited above which have researched similar topics have used event studies using an interval of a few days around the event (the match in this case). There are grounds for both methods but there are also flaws. A large event interval would mean that the probabilities of other factors influencing the stock returns increases. Also, sometimes games are played within just a couple of days and the effects of their outcomes would become blurred. On the other hand, most domestic league games are played over the weekends and very often on Saturdays. This is a problem when the relationship is analyzed using only a one-day interval as I have. The claim of behavioral literature is that investors act on their emotions and if their favorite team has won on Saturday there is plenty of time for their emotions to cool-off by the time the stock market opens.
Thus you see how arguments can be drawn against both alternatives for evaluating the effect football results have on sponsors’ stock returns. Because of that, and because of the fact that the relationship is by nature very indirect, any conclusion on the matter should be considered with caution no matter how believable it looks.
VI. Conclusion
performance of the teams they sponsor. I use data on football matches of the top ten English teams and their sponsors’ stock returns in the period from 1992 until 2012. The results of the analysis, however, show strong support to the contrary – such a connection does not exist. The performance of the sponsored teams is not an event significant enough to affect the returns of their sponsors, which are, after all, major multinational companies. These results are robust to many different specifications of how performance should be measured. This seems to provide evidence in support of the traditional theory and its efficient market hypothesis and to contradict results of a few similar papers which favor the behavioral explanations.
VII. Appendix
Table 4. Champions League Winners (as of 20 years ago)
Position Team Titles Year
1 Real Madrid 6 1956, 1957, 1958, 1959, 1960, 1966 2 Milan 4 1963, 1969, 1989, 1990 3 Liverpool 4 1977, 1978, 1981, 1990 4 Bayern Munich 3 1974, 1975, 1976 5 Ajax 3 1971, 1972, 1973 6 Internazionale 2 1964, 1965 7 Benfica 2 1961, 1962 8 Nottingham Forest 2 1979, 1980 9 Barcelona 1 1992 10 Manchester United 1 1968 11 Juventus 1 1985 12 Porto 1 1987 13 Celtic 1 1967 14 Hamburg 1 1983 15 Steaua Bucuresti 1 1986 16 Feyenoord 1 1970 17 Aston Villa 1 1982 18 PSV 1 1988
19 Red Star Belgrade 1 1991
20 Marseille 0
21 Chelsea 0
22 Borussia Dortmund 0
Table 5. Champions League Winners (as of 30 years ago)
Position Team Titles Year
1 Real Madrid 6 1956, 1957, 1958, 1959, 1960, 1966 2 Liverpool 3 1977, 1978, 1981 3 Bayern Munich 3 1974, 1975, 1976 4 Ajax 3 1971, 1972, 1973 5 Milan 2 1963, 1969 6 Internazionale 2 1964, 1965 7 Benfica 2 1961, 1962 8 Nottingham Forest 2 1979, 1980 9 Manchester United 1 1968 10 Celtic 1 1967 11 Feyenoord 1 1970
12 Red Star Belgrade 0
Table 6. English clubs ranked by number of trophies score system by Sportsintelligence.com
Rank Club League
Table 7. Top ten private firms in the US
Rank Company State Industry Revenue ($bil)
1 Cargill MN Food, Drink & Tobacco 109.6
2 Koch Industries KS Multicompany 100.0
3 Mars VA Food, Drink & Tobacco 30.0
4 PricewaterhouseCoopers NY Business Services & Supplies 29.2
5 Bechtel CA Construction 27.9
6 Publix Super Markets FL Food Markets 25.1
7 Love’s Travel Stops & Country stores OK Convenience Stores and Gas 24.4
8 Ernst & Young NY Business Services & Supplies 22.9
9 C&S Wholesale Grocers NH Food, Drink & Tobacco 20.4
10 US Foods IL Food, Drink & Tobacco 18.9
Average: 53.3
Table 8. Top ten public firms in the US
Rank Company Sales Profits Assets Market Value
1 JP Morgan Chase 108.2 21.3 2,359.1 191.4 2 General Electric 147.4 13.6 685.3 243.7 3 Exxon Mobil 420.7 44.9 333.8 400.4 4 Berkshire Hathaway 162.5 14.8 427.5 252.8 5 Wells Fargo 91.2 18.9 1,423 201.3 6 Chevron 222.6 26.2 233 232.5 7 Wal-Mart Stores 469.2 17 203.1 242.5 8 Apple 164.7 41.7 196.1 416.6 9 Citigroup 90.7 7.5 1,864.7 143.6 10 AT&T 127.4 7.3 272.3 200.1 Average: 212.6 21.3 799.8 252.5
Table 9. Average attendances
League Cup FA Cup EPL Europa League CL Average Attendance
12,280 16,188 34,601 21,704 41,930 Overall
52,624 N/A 75,387 63,297 74,278 Man United (home)
54,398 59,817 60,000 N/A 59,785 Arsenal (home)
Table 10. Regressions results
Model R squared Variable Coefficient P-value
OLS regression, robust 0.0231 Score -0.0000 0.741
Model R squared Variable Coefficient P-value
Model R squared Variable Coefficient P-value
OLS regression, normal standard errors 0.0231 Score -0.0000 0.644
