TV-audience, uncertainty of outcome
and change in viewership during
half-time
Evidence from the Dutch Eredivisie
Sybren Negenman, s2163705
Abstract
This paper looks into the relationship between TV-audience and the uncertainty of outcome hypothesis in the Dutch football league. The model used in this paper predicts that fans prefer matches with a clear favourite and an underdog. The findings of this paper are in line with the majority of previous studies. In addition, this paper presents a new approach by looking at the change in viewers at half-time and match uncertainty. Results show that the measure for uncertainty at half-time has no effect on the change in viewers. However, goal difference at half-time has a significant effect on change in
viewership.
Keywords: uncertainty of outcome hypothesis, loss aversion, TV-audience, football, Dutch league
Supervisor: Professor R. H. Koning University of Groningen
1
Introduction
In 2016, the KNVB, the Dutch football association, asked Chris Woerts, a marketeer and commercial director at Feyenoord and Sunderland, to come up with an idea to make the Dutch Eredivisie more attractive for the public. One of the arguments he made was to reduce the number of teams to 16 to increase competitive balance and this would increase viewership and attendance. However, this only holds when the public cares about competitive balance.
Sports is full of uncertainty. The winner of a match, the score of every match and league standings at the end of the season are all uncertain. The thing that makes sports interesting is that there is always uncertainty about the outcome no matter which teams are playing. The consumer does not know the outcome of the match before the match has started.
Rottenberg (1956) was one of the first to come up with the idea that the demand for sports matches depends on the uncertainty of the outcome of that match. He looked at the uncertainty of league standings. In his paper, the uncertainty of outcome hypothesis (UOH) states that demand for a game depends on the uncertainty of the outcome of that game. Rottenberg (1956) argues that ”The tighter a competition, the larger the demand” in other words, the demand of individuals increases when the level of the teams are close to each other. Neale (1964) agrees with the idea that uncertainty leads to interesting matches in sports. He argues that more changes in league standings increases the demand. In addition, he extends the UOH by adding a paradox. The so-called Louis-Schmelling paradox describes the situation of a monopolist in the market i.e. a dominant and wealthy team that buys all the talent in the league. The results is that the competitive balance in the league is disrupted. Other teams are not able to compete with the ’monopolist’ team in the league. According to the UOH, this disruption in competitive balance results in lower demand. In their chase to become the best of every team, they still need competition to increase demand.
a model by Card and Dahl (2009). The uncertainty of outcome hypothesis predicts that demand is highest for matches where the outcome is most uncertain however when the UOH does not emerge from the model, individuals prefer upsets. Upsets are matches where there is little uncertainty about the outcome of the match and the team with the much lower probability of winning actually wins. For the ease of simplicity I assume that an upset occurs when the team with the lower probability of winning, wins the game. The degree of the upset depends on the difference of the winning probabilities of both teams involved. The model by Coates et al. (2014) can identify whether or not individuals are more interested in watching games where the outcome is uncertain or prefer watching games where the outcome is more certain.
Previous research has applied this model to different sports and different leagues. In this paper, I will use the model by Coates et al. (2014) to help identify whether or not television demand in the Dutch Eredivisie follows the uncertainty of outcome hypothesis. I will look at the decision to watch matches as well as a dynamic framework in which individuals are allowed to change channels during half-time. This leads to the following two research questions:
1: Does TV-audience in the Dutch Eredivisie follow the UOH?
2: Do fans, after they know the half-time results, keep watching the game or do they switch to games where the outcome is more uncertain?
In the next section of this paper I will explain the theoretical model from Coates et al. (2014). After that I will discuss previous research that has been done regarding the UOH and the main findings. After that I will come up with an econometric model and state the hypothesis. Next, I will discuss the data I will be using to test my hypothesis. In the last two sections I will present the results and draw conclusions.
2
Theoretic model
to watch a game contains an element of risk. Kahneman and Tversky (1979) modelled decision making under risk and is known as prospect theory. Prospect theory helps with decision making that involves risk. It states that individuals do not make decision based on the final outcome but on the potential gains or losses and that reference points are important when making decisions when risk is involved. Before the match begins, the individual does not know the outcome of the game. The reference point reflects the fans’ expectations beforehand about the outcome of the game and makes decisions with respect to this point.
Without reference points, consumer theory implies that individuals gain ”consumption utility” from watching a game, they gain utility from a win (UW) and utility from a loss (UL), where the utility from a win is larger than the utility from a loss, UW > UL. Let p be the probability of the home team winning, then:
E[U ] = pUW + (1 − p)UL (1) The expected utility is increasing in p. This implies that the expected utility is highest for matches where there is a clear favourite, high probability of winning the game. Under the assumption that fans of either team want to see their team win, the total demand for the match where the home team is expected to win increases with fans that support the home team. I assume that home team is the team the fan is supporting and away team is the team that the home team is playing. The opposite is true when the probability of the away team winning is greatest. This is not in line with the UOH, which predicts that demand is highest for matches where teams’ performances are equal to each other i.e. probability of winning, p in equation 1, is equal to 0.5. Accoring to equation 1, expected utility is higher for values of p > 0.5.
Coates et al. (2014) extended the model by including a reference point. Koszegi and Rabin (2006) extended the model by not only allowing for ”consumption utility” but also utility that is derived from the actual outcome and some reference point, ”gain-loss utility”. The reference point is different for every game and every individual.
draw is a possibility also used the model proposed by Coates et al. (2014).
Following Koszegi and Rabin (2006), I assume that the reference point is the fans’ expectation about the final results of the match. The reference point of the fan is given by E(y = 1) = 1 × pr+ 0 × (1 − pr) = pr. For any fan, the reference point is equal to the expected win probability of their team before the game has begun. Experiencing a win results in ”consumption utility” (UW) and ”gain-loss utility” conditional on the reference point (pr) of the fan. Deviation from the reference point results in ”gain-loss utility”. The utility from a win of the home team is given by
UW + α(y − pr) = UW + α(1 − pr)
Where α is assumed to be the marginal impact of a deviation from the reference point. I also assume that α > 0. The equation shows that an unexpected win results in higher utility than an expected win. The deviation from the reference point with an unexpected win is greater and results in higher ”gain-loss utility” compared to the ”gain-loss utility” from an expected win.
For a home loss, a fan gets utility from consumption (UL) and utility from a deviation from the reference point. Let β be the marginal impact of a deviation from the reference point. I assume that β > 0. The utility from a loss of the home team is given by
UL+ β(y − pr) = UL+ β(0 − pr)
This equation shows that an expected loss generates more utility than an unexpected loss. The deviation from the reference point with an unexpected loss is greater and results in lower ”gain-loss utility” compared to the ”gain-loss utility” from an expected loss.
Figure 11 shows the previous statements regarding the outcome of a match, the ref-erence point and utility in a graphical representation. It can be seen that the utility of winning is always higher than the utility of losing, UW > UL. For a win for the home team, the utility is highest in the case where the home team unexpectedly wins the match, pr = 0. The home team upsets the away team. The utility is lowest for a home team that wins the match given that the probability of the home team winning the match is 1, pr = 1. The home team is expected to win the match and indeed wins the match. For the home team that loses the match, utility is highest in the case where the probability of the home team winning the match is 0 i.e. the home team is expected to lose the match. The
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utility of a loss for the home team is lowest in the case where the home team is expected to win the match but unexpectedly loses the match. The away team pulls off the upset.
Figure 1: Game outcomes, Reference points, and Utility
Now assume that the probability of the home team winning the game is equal to the reference point of the fans, the objective probability of the home team winning the game, p = pr. The decision to watch a game is based on the expected utility the fan receives. The expected utility is the probability of a home win times the utility from a home win plus the probability of a home loss times the utility from a home loss.
E[U ] = p[UW + α(1 − p)] + (1 − p)[UL+ β(0 − p)] (2) Rearraging terms
A special case of this model is that of the pure fan. This is a fan that has no preference for either team winning the game. He does not support either team. A pure fan of the game receives the same utility from a win and a loss, UW = UL, and ”gain-loss utility” is irrelevant. The decision for the pure fan to watch a game is assumed to not depend on the probability of the home team winning the game and the uncertainty of the outcome. Coates et al. (2014) assume that the portion of pure fans is very small. I will also assume that this portion is very small and therefore can be ignored.
2.1
The uncertainty of outcome hypothesis
Figure 2: UOH, expected Utility and viewers
The uncertainty of outcome hypothesis predicts a concave relationship between the prob-ability of the home team winning and the expected utility of watching, as can be seen in figure 22. Coates et al. (2014) call this the ”Classical UOH”. The maximum expected utility is reached at pmax, which lies in the interval [0.5, 1). According to Rottenberg(1956) pmax is around 0.55. Fans will attend the game when the expected utility from viewing the game is higher than the reservation utility, E[U ] > v. Looking at figure 2, fans will watch the game when p0 < p < p1. In addition, as the outcome of games become more
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uncertain, the probability of the home team winning gets closer to pmax. At values of p closer to pmax there are more people for which E[U ] > v. The expected utility function of equation 3 holds when (β − α) < 0 and [(UW − UL) − (β − α)] > 0. The first condition, (β − α) < 0 states that an unexpected win should result in a higher marginal utility than an unexpected loss. The second condition states [(UW − UL) − (β − α)] > 0, the utility from a win is higher than a loss. Given that (β − α) < 0 holds and [(UW > UL), the second condition also holds.
The value for pmaxcan be found by taking the first derivative of equation 3 with respect to p and set it equal to 0. This gives for pmax
pmax = 1 2 −
UW − UL 2(β − α) (β − α) < 0 implies that pmax≥ 1
2. The classical UOH also requires that p max
< 1, this is equivalent to UW − UL< α − β. This relationship entails that fans prefer more uncertain games over games where their team is expected to win.
2.2
Loss aversion
Figure 3: Loss aversion, expected Utility and viewers
certain. For loss aversion, fans prefer games where the outcome is more certain. Fans attend games where the probability of a home win is large or when the probability of a loss is large and they hope for a potential upset. Losing results in a larger decrease in utility than the results of a win on the increase in utility. In equation 3 this would relate to β > α, the marginal impact of a negative deviation from to the reference point is larger than the marginal impact of a positive deviation from the reference point. The results is a convex utility function as can be seen in figure 33.
To help explain figure 3 it is easier to rearrange equation 2, this gives
E[U ] = [pUW + (1 − p)UL] + (α − β)p(1 − p) (4) The consumption utility is given by [pUW + (1 − p)UL] and the ”gain-loss utlity” is given by (α − β)p(1 − p). Hence, consumption utility is increasing in the probability of the home team winning. The ”gain-loss utility” is decreasing in p until p = 12, this can be seen by taking the first and second derivative of (α − β)p(1 − p) with respect to p. The first and second order derivative are given by
∂(α − β)p(1 − p)
∂p = (α − β)(1 − 2p) ∂2(α − β)p(1 − p)
∂p2 = −2(α − β)
The first derivative is smaller than 0 for p < 12 since β > α and the first derivative is greater or equal to 0 for p ≥ 0. The minimum is reached at pmin = 12−UW−UL
2(β−α) . As can be seen in
figure 3, for p < pmin the negative effect of the ”gain-loss utility” dominates the positive effect of utility from consumption. For p > pmin the positive effect of consumption utility dominates the negative effect from ”gain-loss utility”. The graph is decreasing for values below pmin and increasing after pmin. Hence, fans who are loss averse and have reference-dependent preferences receive more utility from games where the home team is expected to win or expected to lose than games with more uncertainty. Some fans are more excited about seeing unexpected results than matches where the outcome is uncertain. This is supported by Osborne (2012) who states that fans of the game like to watch the more favoured team to lose and that the low-probability of winning creates excitement in its own right.
Again, same as with the UOH, fans will watch the game when the expected utility of watching the game is larger than some reservation utility, E[U ] > v. Loss aversion can be
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identified when the reservation utility, v, is low enough that when p rises there is a decline in demand for that game. When the reservation utility is larger than the utility gained from a loss, the probability of the home team winning (p1 in figure 3) could be very large.
Hence, for fans who are loss averse and have a high reference point, the probability of the home team winning has to be very high.
2.3
Dynamic model
The data I have allows me to look at the difference between first and second half viewers. There are two types of fans that could be watching the game. A fan that watches the game for either team that is playing or a fan that loves the game itself. Both type of fans can either prefer games where the outcome is uncertain or games where the outcome is more certain and the fan is either loss averse or hopes for an upset. A fan that supports either team that is playing, will most likely watch the entire game despite the score at half-time. They support their team no matter the score. When their team is winning they will watch the second half and when their team is losing they will likely watch the second half hoping they will come back.
Some fans however might switch to a simultaneous game where the expected outcome follows their preferences. Fans can switch to simultaneous games at zero cost. Simul-taneous games are games that have overlap with other games. At half-time he or she re-evaluates the available choices. In the case where the UOH holds, a fan that watches a game where at half-time the outcome of the game is almost certain, he or she will switch to a game where the expected outcome is more uncertain.
I will use the theoretical model proposed by Coates et al. (2014) as a theoretical foundation for the change in viewership during half-time. I assume that the second half of the game is a new game. I make this assumption so I can use the theory developed by Coates et al. (2014). In their model they state that fans decide to watch a certain game based on the expected utility and a reference point. The reference point is based on the probability of the fan’s team winning the game. The probability of the home team winning before the match begins is noted as p.
after the first half is noted as p2nd. For ease of simplicity I assume that only goals affect the probability of winning and hence reference points.
Like the non-dynamic model I will distinguish between UOH and loss aversion. Change in viewership during half-time is best explained with the graphs by Coates et al. (2014). I will start with the UOH depicted in figure 2. When the score is equal during half-time p = p2nd, the win probability of the home team remains the same. In this case, fans that are watching the game keep watching the game. It is possible that there are additional fans tuning in based on their preferences and p2nd. For pmax < p2nd < p, we are on the right side of pmax. The probability of the home team winning decreases after the first half. The outcome of the match becomes more uncertain and hence E[U ] increases. In this case, viewership during half-time is likely to increase. For pmax < p < p2nd, the probability of the home team winning increases after the first half. Hence, the home team has scored at least one goal more than the away team. The outcome of the match becomes more certain and E[U ] decreases. Viewership during half-time is likely to decrease. For p2nd < p < pmax, we are on the left side of pmax. The probability of the home team winning decreases after the first half. The away team has scored at least one goal more than the home team. The outcome of the match becomes more certain and E[U ] decreases. In this case viewership during half-time is also likely to decrease. For p < p2nd < pmax, the probability of the home team winning increases and the match becomes more uncertain. The outcome of the match becomes more uncertain and E[U ] increases. During half-time viewership is likely to increase. In the case where p = pmax, a change in the probability of the home team winning results in a decrease of E[U ]. The match will become more certain and hence viewership during half-time decreases.
p2nd< p < pmin, we are on the left side of pmin. The probability of the home team winning the game decreases after the first half. The game becomes more certain and fans of the home team are hoping for an upset in the second half. The expected utility increases in this case and viewership during half-time is likely to increase. For p < p2nd < pmin, the probability of the home team winning the game increases after the first half. The outcome of the match becomes more uncertain in this case and E[U ] decreases. Viewership during half-time is likely to decrease. In the case where p = pmin, a change in the probability of the home team winning increases the certainty of the outcome, increases E[U ] and hence increases viewership during half-time.
3
Results previous studies on UOH
In this section I will discuss previous studies on the uncertainty of outcome hypothesis. A lot of research has been done on the relationship between demand and the uncertainty of outcome. In this section I will summarize some papers that examine the UOH and demand in national football leagues. All these papers work with the same model described above, all use a proxy for outcome uncertainty as independent variable and TV viewership or stadium attendance as dependent variable. Table 1 summarizes the results of some of the studies regarding attendance or TV-audience and the UOH.
Table 1: Previous studies in Football on attendance or viewership and the UOH
Author(s)
Football league
Uncertainty measure Result
Benz et al. (2009)
German tier 1 2001-2004
Betting odds, f(win%)
UOH
Buraimo and Simmons (2008)
English tier 1 2000-2006
Betting odds
Loss aversion
Buraimo and Simmons (2009)
Spanish tier 1 2003-2007
Betting odds
Loss aversion
Buraimo (2014)
English tier 1-5 2006-2012
Betting odds
Loss aversion
Forrest and Simmons (2002)
English tier 2-4 1997-1998
Betting odds
UOH
Forrest et al. (2005)
English tier 2-4 1997-1998
Betting odds
UOH
Martins and Cr´
o (2018)
Portugese tier 1 2010-2015 Betting odds
Loss aversion
Falter et al. (2008)
French tier 1 1996-2000
f(points)
-Czarnitzki and Stadtmann (2002) German tier 1 1996-1997
Betting odds
-Peel and Thomas (1992)
English tier 1-4 1986-1987
Betting odds
Loss aversion
Peel and Thomas (1988)
English tier 1-4 1981-1982
Betting odds
Win preferred over loss
Forrest and Simmons (2002) adopt a similar model as Peel and Thomas (1988, 1992) and also use betting odds. However, they fear that the betting odds are subjected to biases. They suspect that betting odds set by the bookmakers depend on the support for both teams. They deal with these biases by correcting the betting odds for differences in mean attendance. The probability of a home win for example is the odds by the bookmakers of a home win plus the difference in mean attendance level of the previous season for the home and away team. They find that fans are more attracted to competitive matches. In Forrest et al. (2005), they examined the same hypothesis as in Forrest and Simmons (2002) however they use television viewers and the matches that the broadcasters choose to broadcast. They find that both the viewers as the broadcasters favour matches that are more competitive.
Czarnitzki and Stadtmann (2002) look at the uncertainty of outcome hypothesis and attendance in the top tier league in Germany. They also use betting odds as a measure for the probability of the home team winning. Besides the uncertainty of the outcome as a determinant for attendance they also include reputation of the club, loyalty of fans and the performance of the team. They find that uncertainty about the outcome plays only a minor part in attendance. Reputation and loyalty of fans appear to be more important for attendance. In contrast to the studies mentioned before, they argued that stadium attendance is right-censored due to the maximum capacity of every stadium and hence Tobit is preferred over OLS to estimate the parameters of interest.
Falter et al. (2008) look at consumer demand for domestic football games after that country has won the world cup. In their model they include their own measure of un-certainty between two teams. Their measure for unun-certainty contains points of the home team, points of the away team and home team advantage. However, in their study they find that this measure of uncertainty is insignificant in determining stadium attendance after controlling for a World Cup victory effect, the stage of the competition, team char-acteristics, match characteristics and team fixed effects.
at data from the highest Spanish league and instead of a Tobit model they use a Prais-Winsten panel regression model. The Prais-Prais-Winsten model allows the error terms to be correlated across panels. In both papers they find significant evidence that fans are loss averse. However, Buraimo and Simmons (2009) find also evidence that the UOH holds in the case when the dependent variable is TV viewership instead of stadium attendance. Buraimo (2014) extended the research by looking at the top 5 leagues in England. For the top tier league he used a Tobit model and a panel data model with fixed effects for the lower leagues. In all cases he found evidence of loss aversion.
Benz et al. (2009) examine the demand and uncertainty of outcome in the highest league in Germany. Their method differs from the other papers because they use a quan-tile regression method in stead of OLS or Tobit model. They believe that a consumer’s utility from a home team win is increasing in the number of spectators. The home team win probability has a greater influence for higher attendance numbers. For the uncertainty of outcome they use several measures. They use betting odds, relative league standings of both teams, a comparison between the points of both teams and home team advan-tage. They find evidence of the UOH. However, they argue that a team’s reputation is more important that outcome uncertainty which supports the findings of Czarnitzki and Stadtmann (2002).
Martins and Cr´o (2018) looked at five seasons in the top league of Portugal. In their paper they looked at TV viewership as measure for demand. They suspect that this vari-able is subject to endogeneity problems since the most popular matches are broadcasted. They estimate a two-stage Tobit model to deal with the problem of endogeneity. They find evidence that the classical UOH is not important and fans prefer games where the home team’s probability of winning is larger than the probability of winning for the away team. In addition, the away team has a reputation of playing qualitative football or perceived sporting success.
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Econometric model
In this section, both a non-dynamic model as a dynamic model will be discussed. To test the hypothesis stated below, I will use a fixed effects panel data model. Fixed effects is used since this accounts for instance for team’s reputation and fanbase.
4.1
Non-dynamic model
Assume that every person who watches a game has an expected utility that exceeds the utility they receive from not watching the game, otherwise they will not be watching. For the econometric model I will use the model by Coates et al. (2014). The econometric model is based on equation 3. This equation can be simplified to
E[U ] = θp + γp2+ λ (5)
This equation makes it possible to explain audience with an econometric model. TV-audience depends on the expected utility and a reservation utility. The econometric model used in this paper is given by
log(viewers)ijt = λ + θpijt + γp2ijt + µXijt + Dt + Di + Dj + ijt (6)
Where viewers is some measure for viewership of a game between team i and team j at time t. The parameter p is a measure of the probability the home team wins. Where Xijt include home and away team ranks, goals scored and conceded of both teams and pre-match points of both teams. It includes a dummy variable that is 1 when the match is a derby and 0 otherwise. Derby matches bring something special to teams, they play with more passion. Also included is a dummy for the temperature. The dummy variable is 1 when the outside temperature is 20 degrees or warmer and 0 otherwise. I assume here that when it is warmer than 20 degrees outside, people are less likely to stay indoors and watch TV and rather do outside activities. The model includes also time-period fixed effects, Dt. Think about games that occur during holidays or during the weekend. Viewership of these games might negatively be affected because people are on holiday or positively because people have no work obligations. Di and Dj are fixed effects for the home and away team.
H1 Loss aversion: γ > 0 implies that β > α.
H1a γ > 0 and θ < 0 implies β > α and UW− UL< β − α. The marginal consumer gets more utility from a home win than a home loss and has loss aversion. The marginal impact of loss aversion is larger than the difference in utility between a home win and a home loss.
H1b γ > 0 and θ > 0 implies UW − UL > β − α > 0. The marginal consumer gets more utility from a home win than a home loss and has loss aversion. The marginal impact of loss aversion is smaller than the difference in utility between a home win and a home loss.
H2 γ = 0 and θ > 0 implies β − α = 0 and UW− UL > 0. This suggests that the marginal consumer does not have reference-dependent preferences. The utility gained from a home win is larger than the utility from a home loss.
H3 γ < 0 and θ > 0 implies β − α < 0 ≤ UW − UL. This is in line with the UOH. The consumer prefers games that are more uncertain and gets more utility from an unexpected win relative to an unexpected loss.
4.2
Dynamic model
Based on the theory, change in viewership depends on the change in the probability of the home team winning the game. In other words, it depends on the rate of uncertainty about the outcome of the match. Fans are able to keep watching the game they are watching or they can switch to a simultaneous game. In addition, they are also able to switch to a different channel or turn the TV off.
To deal with the problem of fans switching to different channels, dummy variables are included for other sporting events that are on TV at that moment. The assumption that is being made here is that fans that are watching football matches are also interested in seeing other sporting events besides football. In addition, the assumption is that not only are they interested in other sporting events, other sporting events are the only thing they are interested in besides football. Dummy variables are included for cycling and skating. These sporting events are broadcasted on national television and available to every individual.
In addition to keep watching TV there is also the possibility of turning off their tele-vision. It is difficult to measure when fans turn their TV off. To control for fans turning their TV off the temperature is included in the model. This is again a dummy when it is warmer than 20 degrees outside assuming that when it is hotter than 20 degrees, people are enjoying the outside.
Besides the above mentioned options for fans, team specific fixed effects, variables that account for the attractiveness of the match and time-period fixed effects are included for the same reasons as with the non-dynamic model. To estimate the effect of the uncertainty of outcome on the change in viewers of the first and second half I use the following model: ∆(viewers)ijt = λ + β1g1ijt + β2g2ijt + µXijt + Dt + Di + Dj + ijt (7) This model is based on equation 6. When the change in viewers is positive, than there are persons who turned their TV on during half-time or persons have switched to this match during half-time from another program. When the change in viewers is negative, than persons have either switched their TV off or they switched to a different channel. In the above equation, g1ijt is the measure of uncertainty of the game that the fan is
watching, g2ijt is the maximum measure of uncertainty from the simultaneous games. Xijt are the variables that account for the attractiveness of the match. In addition, dummies are included for cycling and skating events that are also broadcasted on TV during the football game. Time dummies are included to account for opportunity costs during holiday months or during months where relegation and title matches are important. In addition, yearly dummies measure how change in viewers has changed over time, more or less alternative programs available (Paul and Weibach 2007).
When fans are loss averse, an increase in the rate of uncertainty has a negative effect on the change in viewers during half-time.
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Data
To estimate the parameters of equations 6 and 7, I use data4 from the Eredivisie over five seasons. The dataset contains information on first and second half viewers for ev-ery game in the Eredivisie during those seasons. These games are broadcasted by FOX Sports. During that period, fans can watch individual games for a one time fee or buy a subscription for a monthly fee. With a monthly subscription fans can watch every game that is broadcasted during that month. In addition, the dataset contains betting odds for multiple large betting sites, temperature of the three closest weather stations, goals scored at half-time, as well as the time dummies for day and month the game was played on. Data on rank of both teams, goals scored and conceded is widely available on the internet, I make use of the site www.voetbal.com.
For the number of viewers in equation 6 I take the total number of viewers, they decided to watch the match based on the expected utility and a reference point. The variable is transformed by taking the logarithm of total viewers to look at percentages. For the number of viewers in equation 7 I take the difference between first and second half viewers. Since teams differ in the total number of fans, teams with more fans, will also attract more viewers. For the 2014-2015 season, data on first and second half viewers is not available. However, since FOX Sports only has 3 channels in the Netherlands it is difficult to broadcast every game where there are for instance 5 games played at the same time. Hence, I do not have viewership data on every single game in the Eredivisie that has been played during these 5 seasons. I exclude games where there are no number of viewers from the sample. The number of viewers is measured in thousands of viewers. Note that from the season 2013/2014 onwards, viewing numbers are no longer measured in one digit after the comma.
For the probability of the home team winning, I use an average of betting odds from different betting sources. Betting odds reflect the current status of both team as well as incorporates home team advantage. Betting markets are assumed to be efficient. To
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account for bookmakers margin (overround), I transform the betting odds using the mul-tiplicative method proposed by Clarke et al. (2017). The mulmul-tiplicative method is the most used method because of the simplicity. The probability of home team i winning is given by pi = 1 xiw 1 xiw + 1 xid + 1 xil
Where xiw, xid and xil are the betting odds for a win, draw and loss respectively for home team i. This method only accounts for the bookmakers margin, not for the long-shot bias where long-shots tend to be overbet and favourites are underbet. It is possible to account for this bias according to Clarke et al. (2017) however, this measure requires data I do not have. Hence, I will use the multiplicative method.
A measure is created for the rate of uncertainty of the game during half-time. For simplicity and the available data I will use the half-time score in order to define a measure for the rate of uncertainty.
Rate of uncertainty = |fh− fa| fh+ fa
The rate of uncertainty of a match depends on the half-time score. Matches where the scoreline is equal are more uncertain than matches where one team has scored more goals. The rate of uncertainty is defined over the interval [0, 1]. When the result at half-time is a draw, the rate of uncertainty is equal to 0. When either team has scored more goals that the other team, the measure increases. Drawback to this approach is that this measure does not differentiate between 1 − 0 and 5 − 0 for instance. Both scores will receive a rate of uncertainty equal to 1. In the conclusion a different measure is proposed that differentiates between these two scores.
Derbies are matches where two teams are relatively close to each other geographically and winning this match is important for the fans regardless of form and standings of both teams. Matches that are considered to be derbies in the dataset are the matches between FC Groningen and SC Heerenveen ”The derby of the north”, matches between FC Twente and Heracles Almelo ”The derby of Twente”. In addition I will also include the matches between Feyenoord and Ajax, ”De Klassieker”. Technically this is not a derby however this is seen as the biggest match in the Eredivisie between two historically great clubs. After the 2009 season, ”De Klassieker” is played without away fans.
be more interested to watch quality of play. Goals scored and conceded and total points by both teams before the match starts are also included as control variables. For the first game of the season this data is not available, therefore these observations are excluded from the dataset.
Time dummies are included to control for possible leisure or work-related activities during the week or weekend, or holiday season of the year. Also during a season, fans might lose interest because of the final standings and there is no tension about ranking. Including a season dummy allows to control for any economic shocks. It also captures changes in possible subscription fees by FOX Sports.
Data on temperature comes from the three closest weather stations to the stadium and is measured in degrees Celsius. This will give me the temperature on the day the match is played. When the weather outside is delightful and the sun is shining, people might be less willing to stay indoors and watch a football game.
Included are also dummy variables for other sporting events. Sporting events that are included are skating and cycling. These variables capture individuals’ interest for other sporting events. These sporting events are broadcasted without subscription fees and are accessible to everyone.
Table 2: Descriptive statistics
Variable Obs Mean SD Min Max
Table 2 reports descriptive statistics of key variables. First of all notice that the maximum number of viewers for a single match is almost 1.2 million. This is the match on the final day of the league between Ajax and Twente where the winner would be crowned champion. This is a single outlier and excluded from the sample. The minimum value of a change in viewers was attained at the match between PSV and Ajax on the 18th of September 2011. The half-time score of that game was 1-1. The maximum value of a change in viewers was attained at the match between Ajax and Heerenveen on the 27th of October 2010. The half-time score of that game was also 1-1. Both games are regular games at the beginning of the season. The match where the goal difference at half-time equalled 5 was the match between PSV and Groningen on the 27th of March 2013, at the end of the season. This is not a major outlier since there are several games where the goal difference at half-time equals 4. The match where the total number of goals scored at half-time equalled 6 was the match between Vitesse and ADO Den Haag on the 3rd of October 2014. Again this is no major outlier since there are several games that had 5 total goals scored at half-time. Finally, for the pre-match points of home and away team there is a negative minimum value. At the beginning of a season every team starts with 0 points and accumulates points throughout the season. However, in the 2014/2015 season FC Twente got 6 points deducted at the start of the season due to not achieving financial targets set by the KNVB.
6
Results
6.1
Non-dynamic model
The estimates of the coefficients for three fixed effects models are reported in table 3. All three models include day, month and season dummies as well as team fixed effects. See equation 6.
coefficient estimate corresponding to the probability of the home team winning squared is positive (γ > 0). According to the hypotheses developed by Coates et al. (2014), hypoth-esis H1a is satisfied. In this model, the UOH does not hold. Individuals are loss averse or are hoping for a potential upset.
In model 2 several control variables are added. Total goals scored pre-match for the home and away team and total goals conceded pre-match for both teams. The goals scored are insignificant for both teams however, goals conceded for the away team is negative and significant at the 5% level. An increase of 1 goal conceded for the away team results in a 0.6% decrease in total number of viewers, ceteris paribus. Fans of the away team dislike it when their team concedes a lot of goals and this decreases the total number of viewers. The signs of the home team winning probability and probability squared are unaffected by the addition of these control variables. Both variables remain significant however the home team winning probability becomes significant at the 90% level and home team winning probability squared becomes significant at the 95% level. Hypothesis H1a is satisfied for this model. Fans are loss averse.
In model 3, more control variables for performance are added as well as a dummy for derby matches and a dummy for temperature at the day of the match. The sign and the significance of probability and squared probability of the home team winning remain unchanged. However, goals conceded by the away team is no longer significant. The dummy variable for temperature is significant at the 95% level. The local weather temperature has a negative effect on TV-audience. When the temperature is above 20 degrees Celsius, the TV-audience decreases by 18.8%, ceteris paribus. When it is nice weather outside, people are inclined to watch less tv indoors and perhaps enjoy the nice weather outside. H1a is satisfied for this model. Fans are loss averse.
Table 3: Results non-dynamic model
Dependent variable: Log(viewers)
Model 1 Model 2 Model 3 Coefficient Coefficient Coefficient
Home win prob −1.140∗∗ −1.014∗ −1.059∗
(0.568) (0.587) (0.608)
Home win prob2 1.035∗ 1.120∗∗ 1.161∗∗
(0.541) (0.541) (0.542)
Home goals scored −0.001 −0.007
(0.003) (0.004)
Home goals conceded −0.004 0.001
(0.003) (0.005)
Away goals scored 0.003 −0.002
(0.003) (0.005)
Away goals conceded (−0.006)** −0.003
(0.003) (0.004)
Pre-match points Home 0.004
(0.007)
Pre-match points Away 0.005
(0.007)
Home team rank −0.011
(0.007)
Away team rank −0.007
(0.007) Derby −0.065 (0.128) Temperature −0.188∗∗ (0.083) Observations 1352 1352 1352
Day, Month, Season dummies Yes Yes Yes
Team specific fixed effects Yes Yes Yes
R2 0.431 0.434 0.440
6.2
Dynamic model
The estimates of the coefficients in equation 7 are presented in table 4. The coefficients are estimated using a panel data model with team fixed effects and time period fixed effects. The variables of interest are the rate of uncertainty at half-time and the maximum rate of uncertainty of simultaneous games. For model 1 I find that both variables are negative, however they are insignificant. This implies that the change at half-time is not due to the rate of uncertainty about the outcome at half-time. There is no evidence of the fact that fans prefer matches where the outcome is more uncertain over matches where the outcome is more certain.
The rate of uncertainty at half-time and the maximum rate of uncertainty of simulta-neous games remain insignificant in model 2. I included variables that account for total goals scored in the first half and the difference in goals scored between both teams after the first half. The goal difference between both teams has a negative effect on the change in viewers. The effect is significant at the 90% level. When the goal difference has increased by 1 after the first half, the difference between first and second half viewers decreases on average by approximately 12 thousand, ceteris paribus. This implies that the probability of winning has increased after the first half, p < p2nd. The results from the non-dynamic model show that fans are loss averse. Combining this with the theory discussed in section 2, we are left of pmin in figure 3. An increase in the probability of either team, reduces the expected utility from watching the game and hence viewership decreases on average.
Including different measures for a team’s performance and quality as robustness checks does not change significance levels of both measures for uncertainty. The difference in goals scored at half-time is no longer significant.
Table 4: Results dynamic model
Dependent variable: Change in viewers first and second half
Model 1 Model 2 Model 3 Coefficient Coefficient Coefficient
Match uncertainty half-time −2.559 14.209 16.165
(6.279) (10.692) (10.565) Max uncertainty half-time other games −0.557 −1.364 −1.496
(6.778) (6.698) (6.697)
Goals scored half-time −0.181 −0.353
(3.755) (3.706)
Goal difference at half-time −11.965∗ −11.541∗
(7.098) (6.977)
Rank team Home 0.921
(1.221)
Rank team Away 0.789
(1.245) Cycling 24.592∗∗ (11.931) Skating 8.494 (10.717) Temperature 21.331 (13.252) Observations 761 761 761
Day, Month, Season dummies Yes Yes Yes
Team specific fixed effects Yes Yes Yes
R2 0.154 0.161 0.206
7
Conclusion
In this paper I used the model by Coates et al. (2014) and the theoretical background they came up with to examine the relationship between TV-audience and the uncertainty of outcome hypothesis.
Using data from TV-audience for the Dutch Eredivisie, I found no evidence in favour of the uncertainty of outcome hypothesis. The results from this paper are in line with what most other researchers also found. Individuals prefer football matches where the probability of one team winning is high and there is a possibility of a potential upset. When the temperature is above 20 degrees Celsius, there is a significant drop in total viewership. The measure for the rate of uncertainty has no significant effect on the change in viewership during half-time. However, goal difference at half-time has a significant and negative effect on the change in viewership during half-time. This implies that uncertainty does have some effect on the change in viewership during half-time.
Future research can make a distinction between TV-viewers that subscribed to FOX Sports for a month or ordered a single game. People that only bought a single match do not have the ability to switch to different games. People who subscribe to FOX Sports for a month are most likely fans of a particular team that want to watch every game their team is playing in. Using a different measure to calculate the probability of the home team winning. Instead of using the multiplicative method which does not account for the long-shot bias, use the more advanced methods that account for this bias. Finally, based on the goal difference at half-time having a significant effect on the change in viewership at half-time, the measure proposed in this paper regarding the rate of uncertainty should be closer looked at. The rate of uncertainty measure proposed in this paper was found to have no significant effect on the change in viewership.
Since we now the attack strength of a team, we can predict the goals scored by this team. First we divide the attack strength of a team by the seasons’ average home goals scored. Next, we divide the defensive strength of the away playing team by the season’s average of away goals conceded. We now know the average goals scored at home for the home playing team and the average goals conceded away for the away playing team. Multiply these numbers with the season’s average goals scored at home games and we get the average number of goals the home playing team will score against the away playing team. Using a similar approach, we can also calculate the average number of goals the away playing team will score.
Using the Poisson distribution where x are the different event occurrences, in this case the goals scored. And the expected event occurrences are the likelihood of both teams scoring. This will result in probabilities for both teams of scoring 0,1,2,3,4 etc. goals. Since the scores at half-time are known. Using the poisson distribution and the calculated probabilities of scoring x goals, it is possible to calculate the probability of a draw. When the half-time score is for instance 2-0, we calculate the probability of the away team scoring 2 goals. This probability can be used as a measure for uncertainty. The higher this probability, the higher the measure of uncertainty is.
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