The fallacy of online gambling companies; between retention and rehabilitation

The fallacy of online gambling companies; between

retention and rehabilitation

Master’s Thesis Econometrics, Operations Research and Actuarial

Studies

The fallacy of online gambling companies; between retention and

rehabilitation

Joris Moossdorff

Abstract

Online gambling is increasing in popularity. Just as regular gambling, this implies that certain people are at risk of addiction. Furthermore, just as any company, there are customers that churn which lowers the firm profits. Online gambling companies have to choose between retaining addicted gamblers resulting in increased profits or letting them go, but doing the right thing in terms of corporate social responsibil-ity. This imposes a delicate issue where firms want to know how to treat different types of customers in an appropriate way. We propose they can do so by monitoring customer behavior with a control chart. This monitors when individuals are at risk of churn or an addiction. We find that control charts are influential in solving this problem and have some predictive power; we obtain a top-decile lift of 12.1% for the churn model and 16.64% for the addiction model. This paper can help in treating online gamblers in a way that suits their interests and that of the gambling company.

Contents

1 Introduction 5

2 Theoretical Background 7

3 Data 10

4 Methods 12

5 Discussion and Conclusion 19

1

Introduction

According to a large study by the RIA1 _{in 2012, 80% of the American people gamble every}

year and approximately 4% have a gambling problem. A subsequent study even showed that 68% of the American youth (14-21 years) gamble at least once a year and 750.000 of these young gamblers can be classified as problem gamblers2_{. Nowadays, online gambling}

is the fastest growing mode of gambling (Gainsbury, 2015). Furthermore, online gambling offers a broader diversity of products compared to offline gambling and is associated with more severe levels of gambling addictions (Castr´en et al., 2013; Odlaug and Chamberlain, 2014). Therefore it can be argued that online gambling facilitates gambling addictions.

These gambling addictions impose an interesting trade off for online gambling compa-nies. This trade off is based on retaining addicted gamblers resulting in increased profits versus refusing gambling addicts which is the right thing to do in terms of corporate social responsibility (CSR) albeit it decreases their profits (Hancock et al., 2008). Despite cor-porate social responsibilities, gambling companies are continuously trying to improve and retain their customer relationships by retention offers (Coussement and De Bock, 2013). A downside of these retention offers then is that there is a small but non negligible amount of addicted gamblers that are targeted by these offers. (Xuan and Shaffer, 2009). Given that gambling addictions are increasingly interpreted as a disease this is a worrying setting (Yau and Potenza, 2015). This highlights the salient trade off for gambling companies; retain or refuse.

In general, retention efforts will result in increased profits for the firm (Ascarza, 2016; Verhoef, 2003). Opposed to this, possible refuse of these addiction prone gamblers, com-bined with possible increasing costs of customer acquisition, can have severe long-term financial consequences (Ascarza et al., 2016). Therefore companies genuinely try to avoid customer attrition by identifying valuable customers who are likely to churn (Ascarza et al., 2016). It is interesting to note that the goal of marketing is to attract new customers by promising superior value and keep and grow current customers by delivering satisfaction (Kotler and Armstrong, 2010). Confronting this goal of marketing with possible reten-tion efforts for addicted gamblers gives a contradicreten-tion; stimulating addicted gamblers to increasing their spending does not result in customer satisfaction in the long run. Fur-thermore, people who identify themselves as problem gamblers are likely to increase their stakes per bet in order to compensate for their losses (Xuan and Shaffer, 2009). So opposed to retention, gambling companies are morally obliged to let addiction prone gamblers go and deliberately decrease their profits as a result of this. This moral obligation is detri-mental to firm profits as problem gamblers contribute a disproportionate high amount to gambling revenue (Hancock et al., 2008).

Gambling companies may decide to stop offering addiction prone gamblers retention deals and rest their case. An ethical issue that arises here is whether gambling companies really fulfill their duties in terms of corporate social responsibility and deliver customer satisfaction by ’ignoring’ addiction prone gamblers. The core of this issue can be described according to customer relationship management (CRM) which is a strategic approach that is concerned with creating improved shareholder value through the development of

appropriate relationships with key customers and customer segments (Payne and Frow, 2005). The question then is, to what extent it is appropriate to maintain a relationship with a gambling addict since it is acknowledged that the negative effects of an addiction go beyond the individual and also harm families, workplaces and communities (Hancock et al., 2008).

Gambling addictions can be viewed from monetary and non monetary motivations (Flack and Morris, 2015). From a monetary point of view it is often argued that the prospect of winning money results in increased gambling behaviour (Wohl et al., 2014). Non monetary motivations are based on psychological aspects like seeking for excitement, escape, self esteem and the problem of controlling ones impulses (Rockloff and Dyer, 2006). In terms of predicting gambling addictions it was found that high-intensity and frequency of gambling and high variability of wager sizes is positively related to people experiencing3 gambling problems (Braverman and Shaffer, 2010). In general there is consent that males are more prone to these drivers of addictions compared to females (Flack and Morris, 2015).

In determining gambling addictions most previous studies were focused on relating de-mographics and/or the amount of times someone gambles to a possible addiction. In order to intervene in time in an arising gambling addiction it is crucial to study longitudinal activities of an online gambler (LaPlante et al., 2008). Furthermore, to really understand when gambling behaviour is escalating longitudinal data is key (Xuan and Shaffer, 2009). The goal of this study is to see when a person starts to exhibit escalating gambling be-haviour making gambling companies able to act upon it. Both when gambling bebe-haviour tends to go to an addiction and when usage rates are too low in order to avoid customer churn. The research question therefore is; To what extent is deviating from ones gambling pattern by exceeding individual gambling boundaries influential in predicting churn or a gambling addiction?

This study will focus on gamblers their spending patterns and deviations in these patterns. A way to model the spending patterns and deviations is via a control chart developed by Shewhart (1931). This method originates from product quality management where it focuses on monitoring a process and detecting when the process starts to exhibit extraordinary behaviour. Crucial in this methodology is to specify when behaviour can be quantified as extraordinary since some degree of variation is natural (Shewhart, 1931). Furthermore, we need to account for this variation together with heterogeneity since indi-vidual consumer behaviour may fluctuate over time (Fader et al., 2005). An illustration of this for our specific setting is that it may occur that a gambler adapts his/her spending pattern along with previous occurred winnings/losses. Note that it may be relevant to relate these winnings and losses to income. Unfortunately the data4 we use do not include such variables.

We find that repeating extraordinary gambling behaviour increases the probability that gamblers will bet irresponsible or churn. Gamblers that continue to lower their bets relative to their regular spending pattern have an increased probability to churn. Furthermore, gamblers that have an increases spending pattern relative to their gambling history are

3_{They closed their own account voluntarily}

4_{For this study we utilize data from the Transparency Project(www.thetransparencyproject.org),}

more likely to incur an RG intervention.

The remainder of this paper is structured as follows. First, relevant theory about the effects of retaining (addicted) gamblers will be discussed. Then the control chart literature will be elaborated on, followed by the data section where we will discuss data characteristics. Finally, the modeling approach will be clarified followed by the results and a discussion.

2

Theoretical Background

Customer retention

Customer churn and customer retention are key metrics in the field of marketing (Braun and Schweidel, 2011). Since the mid-1990s many scientists tried to disentangle the mys-tery why customers leave or stay with a firm. Given that customers are more and more exposed to switching opportunities churn prediction is vital for a company (Holtrop et al., 2017). For the setting of online gambling, customer-firm interaction is mostly done via email, where approximately one out of five retention efforts results5 in increased gambling (Jolley et al., 2013). In general, targeting customers with personalized retention offers can substantially increase the total profit of a retention campaign (Tamaddoni et al., 2017). Furthermore, retaining customers is less expensive than acquiring new customers so firms have a strong incentive to predict possible churners and try to retain them (Gupta et al., 2004; Reinartz and Kumar, 2003). So in general there is consent, both intuitive and aca-demic, that firms should identify high risk churners and try to retain them as a customer. Predicting churn is a valuable approach in terms of CRM for a gambling company (Coussement and De Bock, 2013). In general, the link between current and future gam-bling behaviour is very strong (Jolley et al., 2006). In addition to this, customer inertia and customer habit can be perceived as an important driver of customer behaviour (Wieringa and Verhoef, 2007; Ascarza et al., 2016). Inert customers ’decide’ not to churn but this decision is not based on their usage rate in relation with the attractiveness of other al-ternatives (Wieringa and Verhoef, 2007). Targeting these customers with retention efforts may result in some of them who would not have churned to churn due to the retention effort (Ascarza et al., 2016). The explanation for this is that these retention efforts can disrupt the customer habit to renew by making them realize they are not happy with the current status quo, paradoxically causing churn. In their article Wieringa and Verhoef (2007) claim that 71% of the customers in a dutch energy market sample can be placed in this inertia segment. Furthermore, the dynamics of the online gambling industry are such that customers can not differentiate clearly between firms causing churn prediction to be more challenging (Jolley et al., 2006). Intuitively this lack of differentiation between alternatives can be very similar for the energy market and the online gambling industry. Therefore the analogy of leaving habitual inert gamblers alone may also be applicable to the online gambling industry.

Most scientific effort was aimed at modelling when a customer churns, not why a

cus-5_{An experimental setting showed that one out of five mails, with a price for the most profitable gambler,}

tomer churns (Braun and Schweidel, 2011; Tamaddoni et al., 2017). Whereas in the context of online gambling it is very relevant to study behavioural trajectories prior to ’churning’ (Xuan and Shaffer, 2009)6. Studying behavioural trajectories can show typical types of behaviour prior to churn, helping in the understanding why customer churn occurs. There are two behavioral trajectories that can result in a type of churn. The first is a low cus-tomer usage rate resulting in voluntarily cuscus-tomer churn (Ascarza and Hardie, 2013). The second is an inappropriately high usage rate resulting in customer churn by firm inter-vention7 _{(Braverman et al., 2013). For this study both types of churn are relevant. Note}

that between the boundaries of a too low usage rate and a too high usage rate, there is a framework that can be described by the habitual inert gamblers that do not necessarily need firm attention.

Gambling addictions

In general, a common way to identify a problem gambler is via direct interaction by means of a psychologist or counselor (Hancock et al., 2008). In addition there are plenty established self-report and interview assessment techniques to identify a gambling problem (Hodgins et al., 2011). For the industry of online gambling however, this is not feasible. Therefore, a crucial aspect of this study will be how to classify a gambler at risk of ad-diction. Such an addiction can be defined by the impaired ability to resist the impulse of gambling resulting in disrupted, compromised or damaged social pursuits (Sasso and Kalajdzic, 2006). Despite the possible usefulness of this definition the difference between regular players and addicts is more subtle; problem gamblers are acknowledged to exist, but there are also gamblers who maneuver between stages of problem and non problem gambling (Hancock et al., 2008).

Previous work has already shown that high risk online gamblers can be identified by means of cluster analysis (Dragicevic et al., 2011; Braverman and Shaffer, 2010; LaBrie et al., 2007). The cluster with addiction prone gamblers mostly contains males and young adults (Miller and Claussen, 2001). When explaining why problems gamblers proceed with their gambling activity it is good to note the difference between pathological gam-blers and problem gamgam-blers; where pathological gambling is medically defined as a severe uncontrollable urge to gamble, problem gambling is rather informally defined and gen-erally perceived as a less severe form of gambling disorder (Hodgins et al., 2011). The explanation for pathological gamblers to proceed in gambling is rather blunt; they can not control their impulses. The explanation for problem gamblers is more ambiguous and may therefore be more interesting to study. In explaining problem gambling scientists tend to focus on psychological explanations like the hot-hand fallacy or the gambler’s fallacy. The hot-hand fallacy can be characterized by a person who experiences success with a random event who thinks that (s)he has a greater probability of success in future attempts (Ack-ert and Deaves, 2009). The gambler’s fallacy is based on observing that a random event experiences more (less) frequently than expected resulting in believing that it will occur

6_{In their article the authors only study the behaviour of online gamblers who voluntarily closed their}

account due to gambling problems

7_{Customers are also able to block their own account due to experienced issues with their gambling}

(less) more frequently in the future (Ackert and Deaves, 2009). Given that events occur random, both fallacies are not backed by any statistical foundation.

Ethics and Corporate Social Responsibility.

Customer retention is not the only aspect in the customer relationship that deserves at-tention as the customer relation can be explained from several points of view (Ascarza and Hardie, 2013). In fact, at the heart of CRM lies the concept of customer centricity (Ascarza et al., 2017). Nowadays, many companies are recognizing the need to become more customer-centric in the way they do business (Ascarza and Hardie, 2013). This con-cept was one of the most debated concon-cepts in the field of marketing and furthermore it was argued that the concept is hard to define in a simple comprehensive way. Despite the lack of a univocal straightforward definition the idea of customer centricity is that firms should acknowledge customer heterogeneity and only target customers that are likely to benefit from the offered marketing effort (Lamberti, 2013). In fact predicting churn is the most important thing in churn management programs for customer-centric firms (Holtrop et al., 2017). As previously stated, addiction prone gamblers are not likely to benefit from gambling stimulating marketing efforts and the question is to what extent customer-centric firms should account for this.

The network between customer, firm, legislation and possible health care facilities raises some ambiguity about responsibilities. From a customer focus one may argue to what extent addicted gamblers can be hold accountable for their actions and treated upon; the online gambling setting showed that retention related responses are driven by addicts their habit of gambling and not by customer satisfaction (Jolley et al., 2006). From a firm perspective this imposes a double-edged sword; retain addicted dissatisfied customers or let go of highly profitable customers. This double-edged sword is vital in understanding the possible reluctance of online gambling firms to act in a social responsible way. From a CRM perspective it is generally perceived that dealing well with customer dissatisfaction is strongly associated with more successful retention campaigns (Andrews and Currim, 2003). Given that we stated that not satisfaction, but the habit of gambling, and therefore addiction, is associated with higher retention rates we end up with a certain paradox: gambling firms are likely to retain dissatisfied customers easily. Besides customer and firm responsibilities, legal foundations differ per country and are mostly assessed on very specific cases and therefore tedious to generalize (Hancock et al., 2008).

Given that responsibilities are not established in a well defined framework we can identify two ethics and corporate social responsibility (CSR) dimensions for marketing firms; positive and normative ethics. Whereas positive ethics describes how the company actually behaves in ethical situations, normative ethics prescribes ideal behavior based on

some predefined8 _{framework (Nill, 2015). Since we do not have data on how managers}

actually behave we should rather focus on how they should ideally behave. And, to clarify how they should ideally behave we should state to what extent they are able to behave ideally. Given that online gambling companies posses information like gambling habits, frequencies, visits and losses they do have sufficient knowledge to act upon (Sasso and Kalajdzic, 2006).

So how should firms ideally behave in the context of gambling addictions? The gam-bling literature is only by exception focused on CSR and the duty of the suppliers to emphasize product safety (Hancock et al., 2008). In fact it should be an industry where responsibilities about use and misuse should be crystal clear (Grayson, 2006). The respon-sibilities of online gambling companies generally contain ensuring that they do not make misleading claims, engage in exploitative practices, omit or disguise relevant information, foster excessive gambling, or target inappropriate9 _{subpopulations (Blaszczynski et al.,}

2011). The retention of addicted customers is in agreement with the fostering of excessive gambling and exploitative practices. Furthermore, retention efforts in the online gambling setting is linked to pathological consumption behavior known as problem gambling (Jolley et al., 2013). Therefore10 _{gambling companies are in fact responsible to act in case of}

irresponsible gambling activities. Control charts

In order to determine when gamblers deviate from their regular gambling pattern we need a clear framework presenting appropriate gambling behaviour. This framework should state when individual gambling behaviour is in control and when it is not. Control implies being able to predict, within certain limits how a certain person behaves based on previous observed behaviour (Shewhart, 1931). These limits imply that there is a cutoff point that distinguishes between in control and out of control situations. The initial representation by Shewhart (1931) of these cutoff points resulted in a control chart representing process behaviour over time in relation to the cutoff points. Given that the process is allowed to move within the cutoff points there is some extent of acceptable variation within a process. If the process behaves within (out of) the cutoff points we say the process is in control (out of control). For our study this will mean that we use the data to determine individuals their mean spending behaviour and assess their individual cutoff points. Then based on the cutoff points we can try to determine when a person is at risk of churning (addiction) when their spending gets below (above) the relevant cutoff point.

Despite the goal of Shewhart (1931) being the same compared to ours; determining when the process gets out control, there are some fundamental differences. The original method was used to monitor rather stable processes like machine work. In this study we are dealing with consumer behavior which is by definition heterogeneous (Fader et al., 2005). Furthermore, unlike machine behaviour there may intuitively be a link between previous earnings and the current amount of stake an individual gambles.

3

Data

In this empirical study we used data from the Transparency project measuring online gam-bling behaviour at Bwin11_{. Data consists of daily aggregated usage data and demographics}

combined with customer usage variables at the cross sectional level. The daily aggregates

9_{People with reduced responsibility or at higher risk to get addicted} 10_{Also based on the previous stated negative effects of a gambling addiction}

provide information about the stakes, losses/winnings and amount of bets for 4134 in-dividuals over a time period from 2000 till 2010 yielding a total of 718737 observations. Since individual differ in the amount of bets they placed during the time period we are dealing with an unbalanced panel. The demographics and customer usage data provide information about age, gender mean stakes registration date. Furthermore it consists of data indicating if the customer has experienced a responsible gambling (RG) interven-tion12_{, how often this occurred and when this occurred. About half of individuals in the}

data set experienced at least one RG intervention. The other half, the control panel, did not experience a RG intervention.

Although we know how many interventions each individual incurred we only know when their first and last intervention happened. Thus, if a gambler had n interventions, n > 2, we only know when the first and last intervention took place and not for the interventions in between. Furthermore, many gamblers incurred two interventions on the same date. Thus, it may be that an individual violated multiple company guidelines at the same time. This means that we can not give intuition on what happens after the first intervention, since this date coincides with the first intervention date for many gamblers.

Data points where stakes were missing, equalled 0 or where individuals only appeared 1 time in the data were excluded from the analyses since the goal of the control charts is to monitor stakes over time. This leaves us with a total of 4015 individuals in the data set. Of these individuals 3630 are male and 385 are female. A full description of the main variables in the data is given in table 1 below. This table needs some further explanation; the panel data set initially only consists of the variables id, date, type of gambling13, amount staked in euros , amount lost in euros and amount of bets per day. The data was altered by adding a dummy variable indicating when an RG intervention occurred. The data distinguishes in three types gambling; casino, fixed odds and live betting. Therefore a person can appear three times on the same day in the data, 1 time for each type of gambling. The UBV and LBV variables will be explained in the next chapter.

Table 1

Obs mean sd min max

Mean stakes per individual 4015 263.41 3045.88 0.01 172124.9

Mean log(stakes) per individual 4015 2.985 1.503 -2.34 9.21

Number of times persons appear in the data 4015 178.80 327.15 1 3931

Average amount of bets per person 4015 27.30 85.74 1 1580.63

Average amount lost per person 4015 18.82 56.92 -1418.10 1287.88

Year of birth 3965 1977 9.79 1918 1991

Sum of RG interventions 4015 .63 .76 0 8

Total UBV 4015 192.84 177.13 0 982

Total LBV 4015 185.38 172.95 0 976

12_{This interventions are caused by excessive gambling behaviour}

13_{For example sports betting, casino betting, bingo, fixed odds, live betting and combinations of these}

4

Methods

Serial correlation and normality.

The traditional control chart model has data assumptions; normally distributed data and ob-servations that are independent of each other (Shewhart, 1931). For our study it is very likely that we need to account for serially correlated data. This is due to the notion that gamblers adapt their stakes based on previous gambling results (Xu and Harvey, 2014). We also account for previous winnings or losses since this reflects previous gambling results. Besides serial cor-relation, individual spending is a non negative variable, and therefore not suited for a normal distribution.

In order to account for possible serial correlation we test the effect of the previous stakes and the loss of a gambler at time t on the amount that a gambler stakes at time t + 1. We include a square of the regressor in the model to account for a possible nonlinear effect. A sole linear effect would misspecify the model since this would imply that expected stakes could be ± ∞. Furthermore we include an individual effect; since we are dealing with customer usage data, heterogeneity can not be neglected (Ascarza et al., 2016; McCarthy et al., 2017; Fader and Hardie, 2007; Rust and Verhoef, 2005; Fader and Hardie, 2010; Braun and Schweidel, 2011; Tamaddoni et al., 2017; De Haan et al., 2015). The model for this proposed effect can be written as

yit= αyi,t−1+ γxi,t−1+ φyi,t−12 + θx2i,t−1+ ci+ it,

where yit equals the amount individual i stakes at time t, xit−1 equals the amount individual

i lost at time t − 1, ui is the fixed individual effect, it is the error term for individual i at time t

and where α, γ, φ and θ are the parameters of interest.

In order to determine the correct analysis we first test the assumption that E(ci|zi) = 0,

where zi is the stacked vector of observations for individual i. This can be done by a Hausman

test which showed that E(ci|zi) 6= 0 (χ21 = 19.01, p < 0.01). Thus we proceed by means of fixed

effects estimation. The results of this estimation are shown in table 2 below. Table 2

Turnover

lag Turnover -0.00777 (0.00589) (lag Turnover)2 5.30e-09

(4.69e-09) lag Lost -0.0375

(0.0350) (lag Lost)2 -4.24e-06

(2.32e-06) Constant 382.2***

(2.239)

Observations 714,720 Robust standard errors in parentheses

** p<0.01, * p<0.05

panel setting and acknowledge that fixed effects estimation suffers from the Nickell bias. The within procedure of fixed effects does not account for correlations between yi,t−1and i,t−1

result-ing in this bias that is typically severe in a context with few observations per individual (Nickell, 1981). It can be showed that the probability limit of this bias equals

−σ 2  T2 (T − 1) − T α + αT (1 − α)2 6= 0,

where σ_2 equals the variance of itand T equals the average time an individual exists in the data.

In table 1 we see that T equals 178.80 for our sample. We claim that this is large enough to call the Nickell bias negligible for our model.

The second assumption was normally distributed data. We first look at the mean of stakes for each individual. Log transformation of the stakes showed that this may be log-normally distributed. This distribution is shown in figure 1. To test normality of the log-transformed data a Shapiro-Francia14normality test was performed. This test shows that the log-transformed data is not normally distributed. Testing the skewness and kurtosis shows that the data is skewed (p < 0.01) to the right which can be seen in figure 1.

After checking the distribution of mean individual spending we look at the process we will model with the control charts; the spending of each individual over time. In general, a control chart approach fixes a distribution for the processes that will be modeled. Given that we are dealing with customer usage data we assume that individuals are highly heterogeneous in their spending over time. Furthermore the right graph in figure 2 below shows that individuals that incurred an RG intervention may be characterized by some extreme peeks surrounding this in-tervention. This means that there are different distributions for gamblers that did and did not incur an RG interventions. Based on preceding arguments we do not find it appropriate to fix a distribution for all individuals.

0 .1 .2 .3 Density −5.00 0.00 5.00 10.00 meanlogturnover

Figure 1: Density of log transformed mean stakes with normal density contour

Although the second assumption has not been met this is not necessary a worrying finding. Normality, or an other distribution, is perceived as necessary in control chart theory in order to

draw an artificial sample from this proposed distribution (Shewhart, 1931; Janacek and Meikle, 1997). Then, based on this artificial sample control limits can be formulated. A pre-specified density is then necessary in order to minimize the false alarm rate. That is the rate in which the control charts report that the process is out of control while it is actually not, say a type-I error (Chakraborti, 2000). This rate can be determined by scaling the standard deviation of the process, σ, by a constant, k, and looking at the percentage of observations that fall within the range of σ ± k given the chosen density. This false alarm rate of course hinges on the assumption that the actual data perfectly represents a sample from the chosen distribution.

The goal of our study is slightly different. We want to see when gamblers start to deviate from an appropriate gambling pattern. A crucial difference with the control chart theory in operations management is that we use the control charts as input for our final models. In these final models we will test if ”violations”15 indicated by a control chart can help in predicting churn or addiction. To serve as input in these final models we need to have a reasonable amount of ”violations” determined by the control chart. This is different then the traditional control chart setting since that setting strives to obtain a very low amount of errors in the process. This is illustrated by the following reasoning; a typical control charts strives for a false alarm rate as low as possible. That is, only look at very extreme values for the process, based on the underlying distribution, since some variation in the process is natural (Shewhart, 1931). A common threshold, based on the normal distribution, is to take three standard deviations as cutoff point for ”inappropriate” machine behaviour. This would imply that approximately 1 out of 300 observations would be classified as inappropriate. For our setting that would mean that many individuals would only have 1 or 2 observations that are ”inappropriate” based on the control charts. Given that we use the control charts as input in our following models this is not an appropriate setting.

We want to use the control charts to predict churn and inappropriate behaviour at the same time. Thus we would need more observations that would be classified as inappropriate by the control chart. We claim that the evolution from occasional gambler towards addicted gambler is more gradually compared to the operations setting. Thus, there is no use in having a false alarm rate that is as low as possible. Furthermore, the behaviour that we are measuring is far more dynamic than the behaviour of an operating machine and the immediate effect of an error is less severe compared to the operations setting. For this study it is more interesting to see if a control chart can assist in predicting gambling addictions then to see what the optimal false alarm rate is.

Control Charts.

We proceed by establishing the control chart for each individual. This is done by tracking indi-viduals their gambling behaviour over time and determining their own upper and lower bound. Given that individual gambling behaviour is not suited for the normal distribution the classical control chart based on means may yield inappropriate control charts (Janacek and Meikle, 1997). Therefore we will use a distribution-free method based on medians. This median based control charts have the same format as traditional control charts and have reasonable power (Janacek and Meikle, 1997). We start our model with classifying the lower limit at the 25thpercentile and the upper limit at the 75th percentile. This means that the observations in the lowest quarter of an individuals gambling stakes will be classified as a lower bound violation (LBV). The highest quarter of observations will then be classified as an upper bound violations (UBV).

We choose these bounds such that each individual has a sufficient amount of violations in order to predict churn or a RG intervention. Note that if we would use a similar bound as in

the operations setting that only the lowest (highest) observations would indicate churn (an RG intervention)16. We proceed with the following model for the control charts

CCi(yi) = mi(yi) ± P25(yi)

where subscript i refers to individual i, CCi is the control chart, mi is the median value, yi is

the vector of observations and ±P25 indicates that we add or subtract 25% of the observations

measured from the median. Note that the total time that each individual exists in the data, Ti,

differs per individual given the unbalanced panel setting. These charts give us the boundaries wherein gamblers are ”allowed” to bet. The difference is graphically shown in figure 2, where the left graph corresponds to a control chart of an individual in the data. Observe that both the upper and lower boundary are violated several times.

0 1 2 3 4 Stakes 1.00 87.00 Time logturnover p25 p75 Typical RG intervention 0 50000 100000 150000 Stakes 1.00 1,294.00 Time

Figure 2: Control chart for person 26 (left) and typical RG intervention for person 1275 (right)

To stress the difference between an UBV and an RG intervention a second graph is added, on the right, in figure 2. Herein the gambling pattern of a different individual, who had an RG intervention, is shown over time. The stakes of this individual dramatically increase at the red dot. This is a typical example when an individual incurred an RG intervention. Note that if we would change the percentiles for our upper bound to, for example, 99.3% an UBV would be perfectly correlated with an RG intervention for some individuals. This emphasizes the use of our current, lower, upper bound; we are interested in what happens before an intervention, for example a structural increase of UBV causing an RG intervention in the end.

Testing.

To test our model we use the amount of violations a gambler had at time t. Both types of violations, UBV and LBV, are monotonically increasing over time. Therefore we use the amount of violations that a gambler had over the past thirty bets. To illustrate this we define

ξi,T∗_,j = T∗ X t=1 vi,t,j − T∗−30 X t=1 vi,t,j,

Where vi,t,j is a variable indicating if individual i obtained a violation at time t for violation

type j, note that j = 1, 2 since we have UBV and LBV. Then ξi,T∗_,j is the total amount of

interventions individual i had in the past thirty17 bets at time T∗ for violation type j, with T∗ ∈ [1, Ti]18. The last thirty bets does not necessarily imply the last 30 days since the data

can register multiple bets per day19. Note that ξi,T∗_,j is undefined for T∗ ∈ [1, 30], therefore we

replace these values with ¯ξi,j; the average amount of violation type j for individual i.

The data already consists a variable indicating when a gambler incurred an RG intervention. We still need a proxy variable for churn. To this end we look at the distribution of the amount of days that is between consecutive individual bets. Table 3 below shows that, in general, online gamblers have a rather high intensity of bets. 95% of the bets are done within nine days of the previous bet and the mean amount of days between bets is only 4.17. We start by taking a 95% confidence interval and define churn as ten consecutive inactive days.

Table 3

mean median sd 95% 99% Day difference between bets 4.17 1 31.02 9 64

Now we will test the effect of ξi,T∗_,j on our two dependent variables; churn and RG

interven-tion. We will do this according to the following model specification

zi,t,k= ξ0i,T∗_,jθ_k+ s0_i,tδ_k+ l0_i,tζ_k+ rg0_i,t|k=2ψ + c_i+ _i,t,k

where zi,t,kis a binary variable indicting if event k happened for individual i at time t. The event

refers to either an RG intervention (k = 1) or churn (k = 2). Let si,t and li,t equal the amount

staked and lost for individual i at time t and let rgi,t|k=2 equal an indicator variable indicating if

individual i had an RG intervention at time t. Note that this variable will only be added for the churn model since an RG intervention often comes together with (mandatory) reduced activity for a certain period. Finally we define i,t,k as the error term and θk := (ρk, ωk)0.

Both variables are binary and therefore suited for a logistic regression. A Hausman test again showed that random effects estimation yields inconsistent estimates20. Thus, we proceed with fixed effects logistic regression. This implies that we can only test time varying variables in our model. As specified, we control for the effect that an intervention has on gambling activity for the churn model.

We start with the interpretation of the churn model. The odds ratio’s imply that a coefficient higher than 1 increases the probability of observing a dependent variable by ( ˆβ − 1) ∗ 100%, where ˆβ equals the associated coefficient. A coefficient lower than 1 decreases the probability by ( ˆβ − 1) ∗ 100%. Interpreting the results in table 4 in this way shows that an RG intervention has a positive effect on the probability that a customer churns, ˆβ = 1.792, p < 0.01. This is logical given the way we defined churn in our model and the lack of activity after an RG inter-vention. After controlling for an intervention we find that an increase in the amount of LBV in the previous thirty bets has a significant positive effect on the probability that a customer churns,

ˆ

β = 1.016, p < 0.01. The same holds for the amount of money that a gamblers loses in a bet, ˆ

β = 1.0009, p < 0.01. An opposite effect holds for the UBV and money staked in the previous bet, ˆβ = 0.999, p < 0.01.

17_{Since this is chosen rather arbitrarily we will test if our model is sensitive to this choice as a robustness}

check

18_{The maximum value for time T}

i differs per person given the unbalanced panel 19_{Casino, fixed odds and live betting are registered separately per day}

Table 4 Odds ratio’s

Churn RG intervention #UBV in the last thirty bets .996* 1.078**

(0.0018) (0.0076) #LBV in the last thirty bets 1.016** 0.998

(0.002) (0.0094) Stakedt 0.999** 1.000009** (0.0000) (0.0000) Lostt 1.0009** 1.0000 (0.0000) (0.0000) RG interventiont 1.792** (0.151) LR χ2 994.29** 198.68** Standard errors in parentheses

** p<0.01, * p<0.05

For an RG intervention we find an opposite effect; now the amount of UBV in the previous month has a positive effect on the probability of observing an RG intervention, ˆβ = 1.078, p < 0.01. The same holds for money staked in the previous bet. ˆβ = 1.000009, p < 0.01. We find no effect for the amount of money lost and LBV.

Predictive validity

Now that we tested our models we want to see how our models perform in terms of predic-tion. If we let all regressors for model k equal x0_i,t,k, k = 1, 2 and stack all estimated coefficients for that model in ˆβk we can calculate the fitted values, ˆzi,t,k, according to

ˆ zi,t,k=

exp(x0_i,t,kβˆk)

1 + exp(x0_i,t,kβˆk)

.

Then we sort these fitted values and compare them with the variable indicating churn. To see how our model performs in terms of prediction we look at the top-decile lift. This measure is commonly used in determining the predictive accuracy of a binary scoring model (Neslin et al., 2006). In order to calculate the top-decile lift we first sort our predictions for ˆzi,t,k. The decile

with the highest predictions is then defined as the top decile. We divide the amount of occured events21in this top decile by the total amount of events in the data and express it as a percentage.

Table 5

Churn RG intervention Top-decile lift % 10.38 13.63

Table 5 shows the top-decile lift for churn or an RG intervention. Since we picked look at deciles a naive model would predict 10% correct. Our model predicts 10.38% for churn and 13.63% for RG interventions. So in terms of prediction the churn model is really close to a naive model whereas the RG model has some gain in predictive power.

Robustness checks

After testing and predicting we proceed with some robustness check to see how our model per-forms under different specifications. In the control charts section of this chapter we chose the violation percentiles to equal 25 and 75. We now test our model for the violation percentiles(VP) equal to 10 and 90. Furthermore we defined ξi,T∗_,j as the amount of violations in the previous

thirty bets. We also include robustness checks for this measure and see how the model performs if we change this to twenty and ten bets.

Table 6 Odds ratio’s VP: 10 and 90

#of bets for ξi,T∗_,j 30 30 20 20 10 10

Churn RG Churn RG Churn RG

# UBV 1.004 1.126** 0.997 1.176** 0.968** 1.26** (0.0024) (0.0088) (0.0032) (0.1156) (0.0049) (0.0195) # LBV 1.036** 0.9878 1.058** 0.998 1.126** 1.03 (0.0029) (0.0138) (0.0037) (0.1721) (0.0058) (0.02531) Stakedt 0.999** 1.000009** 0.9999** 1.000008** 0.9999** 1.000008* (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) Lostt 1.0008** 1.0000 1.0008** 1.0000 1.0009** 1.00005 (0.0000) (0.0000) (0.0001) (0.0000) (0.0000) (0.0000) RG interventiont 1.792** 1.716** 1.71** (0.1309) (0.1327) (0.1325) Top-decile lift % 10.42 15.09 10.52 15.51 11.84 16.64 LR χ2 249.02** 1053.62** 1187.91** 270.69** 1527.33** 218.35**

Standard errors in parentheses ** p<0.01, * p<0.05 Table 7 Odds ratio’s VP: 25 and 75

#of bets for ξi,T∗_,j 30 30 20 20 10 10

Churn RG Churn RG Churn RG

# UBV .996* 1.078** 0.991** 1.119** 0.963** 1.176** (0.0018) (0.0076) (0.0023) (0.0099) (0.0035) (0.1599) # LBV 1.016** 0.998 1.029** 1.012 1.062** 1.017 (0.0020) (0.0094) (0.0025) (0.1189) (0.0039) (0.017) Stakedt 0.999** 1.000009** 0.999** 1.000009** 0.999** 1.000009** (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) Lostt 1.0009** 1.0000 1.0008** 1.0000 1.0008** 1.00006 (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) RG interventiont 1.792** 1.706** 1.693** (0.151) (0.1327) (0.1326) Top-decile lift % 10.38 13.63 10.49 15.18 12.10 14.13 LR χ2 _{994.29** 198.68** 1162.34** 233.61** 1590.41** 182.09**}

Standard errors in parentheses ** p<0.01, * p<0.05

ξi,T∗_,j. We observe similar significance levels for all models. In any case we find that an increase

in UBV (LBV) has a positive effect on the probability of observing an RG intervention (churn). The parameters for UBV in the RG models tend to get higher as the amount of days for ξi,T∗_,j

tend to get lower. Given that there are less bets to ’violate’ this is a rather intuitive finding; exceeding the upper bound happens less often and the effect of one violation may therefore be stronger. The same reasoning holds for LBV in the churn model; the effect tends to get stronger when ξi,T∗_,j is measured over less days.

If we look at the top-decile lift we see that model predictions become better for the churn model as ξi,T∗_,j is measured over less days. Furthermore we see that the top-decile lift for the

model with violation percentiles equal to 10 and 90 is better 5 out of 6 times. So in terms of prediction it is better to make violations more strict.

5

Discussion and Conclusion

The goal of study was to see when betting behaviour tends to escalate making gambling companies able to act upon it. Where escalation could be seen from a firm perspective (churn) or a social perspective (RG intervention). In order to answer the research question we wanted to see to what extent deviation from a gambling pattern results in one of these escalation types. In this study we found evidence that the phase wherein a gambler is relative to his/her own gambling pattern has a relation with our two types of escalation.

We find an increased probability of an RG intervention at time t if the amount of upper bound violations increased over the last thirty bets. Furthermore an increase in the amount of lower bound violations in the last thirty bets before time t increases the probability of customer churn at time t. In terms of prediction we find that our model predicts better than a naive model. Although this is a satisfactory finding it is ambiguous how good or bad this prediction rate is. In any case it seems that there are other factors besides boundary violations that drive churn or addiction.

Theoretical implications

So what do these results imply for the academic world? We mentioned the discussion on ”inert” customers by previous literature. If we relate this to our story it seems that when gamblers are frequently gambling within their own boundaries firms should not act upon them since this may cause churn (Ascarza et al., 2016). Of course the way we defined these boundaries implies that gamblers will exceed them regularly. Despite this, our results support the theory that inert cus-tomers should be treated with caution; it may be better to ignore them and focus on cuscus-tomers that are behaving in a way that may cause churn or, for our case, addiction. Furthermore the use of control charts can be implemented in established churn literature to see if there is a possible gain. Finally we propose a longitudinal method to analyze escalating gambling behaviour. This was claimed as necessary in previous literature (Xuan and Shaffer, 2009; LaPlante et al., 2008).

Managerial implications

certain period of time. Note that this means that a one time violation of a boundary is not of the same order of risk compared to the traditional implementation of the control charts. The type of repeating violations suggests which type of firm action is requested. It was found that one out of five retention efforts in the online gambling industry resulted in increased gambling (Jolley et al., 2006). We propose that this retention is not desired for all customers. Based on our method firms can identify customers at risk of churning and target them, which may or may not be more effec-tive than the mentioned one out of five. Furthermore firms can also target individuals that may not benefit from retention efforts from a CSR point of view. Thus, firms have a better overview of the gamblers that are not harmed by retention and can target customers at risk of churning. In sum, we state that monitoring both boundaries can assist in operating as a customer-centric firm.

Policy recommendations

For policy makers we have a developed a method that may assist in detecting and understanding addicted online gamblers. This is necessary since there are no established measures to detect an online gambling addict. The normal procedures for discovering (offline) gambling addicts are techniques like interview assessments (Hodgins et al., 2011). Since this is less feasible for the online setting there should be some data driven approach to identify gambling addicts. This paper gives an idea on how to execute such an approach. As such, we recommend that policy makers should strive for closely monitoring individuals who start to diverge22 from their own gambling pattern in a repeating way.

Limitations and future research

This study has several limitations. The first thing is that we are dealing with an online set-ting. So we can not necessarily say anything about the offline gambling world. Second, we acknowledge that we do not have any measure for income. Although gambling addictions can also be harmful in a psychological way, income may help to determine how much money is in-appropriate to gamble for a person. Furthermore our models are based on individual data over a longer period of time. It may be more challenging to determine gamblers at risk in a shorter period of time. Future research can assist in determining how much time is needed to make reliable inference.

The RG interventions are determined by the gambling company that distributed the data. We do not know how they determine an intervention. Therefore it is hard to control to what extent we are actually predicting a possible addicted gambler. It may be that gamblers already experienced gambling problems before the RG intervention happened or the other way around. Furthermore the data only consisted of the first and last intervention that happened for a person. This means that for an individual with more23than 2 RG interventions we miss the data points in between. If we had this data points we could better see what happens in between interventions, compared to only looking at what happens between the first and last intervention.

It would also be helpful to know why individuals incurred an RG intervention. We assume that it is related to a proposed gambling addiction, however in the Data chapter we mention that some individuals incurred two interventions at the same day. Thus there are different categories of interventions. Finally there is room for improvement in terms of prediction. This means that there are other factors, besides control charts, that influence our dependent variables. Future research could address this for the online gambling setting.

22_{In an upward trend}

6

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