An Investigation into the Stochastic Patterns of Gambling Consumption. Desmond Lam, University of Macau Dick Mizerski, University of Western Australia

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1 An Investigation into the Stochastic Patterns of Gambling Consumption Desmond Lam, University of Macau Dick Mizerski, University of Western Australia Abstract The gambling industry is a big business worldwide. Research on gambling behaviour has mostly centred on cognitive- and affect-based theories. In this study, totally stochastic patterns of consumption were assumed. It was hypothesized that gambling behaviour for any game followed a predictable pattern that could be modelled at both the product and the category level. An empirical study using the 1999 Australia Productivity Commission survey dataset supports the existence of widespread stochastic gambling patterns. The implications for public policy makers, and marketers of gambling products, are discussed. Introduction The global gambling industry is the largest segment of the entertainment category. Gambling has become the leading leisure activity in many countries. In Australia, the gambling industry accounts for an estimated 1.5 per cent of its GDP, and employs over 100,000 people (Productivity Commission, 1999). While the gambling market has the highest penetration and purchase frequency among consumption goods (Mizerski and Miller, 2003), little research has fully addressed the explanations for gambling behaviour. To date, the majority of research on gambling purchases has been from a psychological point of view, focusing on cognitive and affective factors. This study suggests that one major unexplored causal factor in gambling consumption is the habitual and stochastic nature or repeat behaviour. A model of this pattern of gambling behaviour is discussed, and empirical illustrations of its fit to a wide variety of gambling products used to demonstrate its viability. Current Theories in Gambling Gambling has been formally defined as staking money on uncertain events driven by chance (Productivity Commission 1999, p. 6). It embraces the essence of risk taking in order to gain some value (Abbott and Volberg, 2000; Bernstein, 1996). The vast majority of research on gambling has examined the motives underlying problem and pathological gambling from sociological, psychological, and social leisure perspectives (Tse et al., 2005). The various hypothesized motives of gambling have generally fall into three groups; economic, symbolic, and hedonic. These explanations of gambling behaviour have most often focused on the cognitive and affect perspectives of gambling consumption. The most popular explanations for gambling purchases are cognitive-based (c.f. Wagenaar, 1988; Rogers, 1998; Oh and Hsu, 2001). In the cognition paradigm, behaviour can be modified through communication and trial that changes perceptions, beliefs, attitudes, and behavioural intention (East, 1997). Researchers using cognitive-based paradigm to explain gambling behaviour typically assume that gamblers are driven by faulty or flawed reasoning. Another explanation for gambling behaviour is an affective-based theory. Previous researchers have also argued that gambling is driven by experiential aspects of consumption (Holbrook and Hirschman 1982) or through affective elements such as emotion, moods and hedonic reinforcements (Zajonc and Markus,

2 1982). For example, Titz, Andrus, and Miller (2001) found that casino players reported that they derived hedonic pleasure from gambling. However, cognitive- and affective-based studies on consumers responses to marketing activity have provided little assistance in guiding changes in gambling behaviour. One possible reason for finding little effect of marketing pro or anti promotion messages on gambling behaviour is that many gambling products have reached maturity. Their purchase becomes largely habitual, so that little affects these rather-stable gambling product markets. As such, the purchase of some gambling products may reflect an underlying stochastic pattern often observed in many consumer and industrial markets that have frequent purchases with multiple brands (Ehrenberg, 1972; East, 1997). If gambling consumption is stochastic in nature, then one may find some predictable behavioural patterns. In the past few years, a few researchers have started to investigate lotto and online gambling behaviour through the perspective that the Negative Binomial Distribution (NBD) represents the influence of habitual behaviour in a population. These studies found consistent patterns of gambling in their populations, that past gambling behaviour matches the NBD pattern (Mizerski et al., 1998), and past gambling behaviour or habit guides most future gambling behaviour (Jolley, Mizerski and Olaru, 2006). These recent findings further suggest predictable patterns in purchase behaviour and loyalty for individual gambling products on an aggregate market level. Predictable Purchase Patterns and the Stochastic Preference Models When one considers consumers in a product market in the aggregate, many markets follow simple empirical laws (Ehrenberg, 1971). This means it is common to find regularity (Ehrenberg, 1995; East, 1997) in their frequency of purchasing (Ehrenberg, 1972; Ehrenberg, 1988), and that their pattern of purchase reflects the Pareto 80/20 Principle (Anschuetz, 1997). According to Ehrenberg (1988), consumers behavioural tendencies in repeat purchase, given stable market conditions, can be modelled as a stochastic process, without including any cognitive factors. In fact, models that analyse patterns of behaviour are often known as stochastic preference models (Morrison and Schmittlein, 1988; Wagner and Taudes, 1986). These models are often very accurate in explaining past use and predicting future choice based on observed or reported behaviour over a specific period of time. One of the simplest and most widely reported stochastic models that usually provide a close representation of observed consumer buying patterns is the Negative Binominal Distribution (NBD) model. The NBD model provides a probability density function that is based solely on the penetration of the market (i.e. percent of the population purchasing), the average frequency of those that purchase, and the time period over which the purchase is reported. In general terms, the NBD model is best applied to study purchase behaviour for a total product category, or a single brand. Despite the ability to explain and predict market phenomenon, the NBD model does not require the inputs of any marketing (e.g. pricing or promotion expenditures) or attitudinal (e.g. perceptions, beliefs or intentions) variables (cf. Morrison and Schmittlein, 1988). A more advanced version of the NBD stochastic model, which is one of the best-known empirical generalization models in marketing (Uncles, Ehrenberg and Hammond, 1995), is the Dirichlet model. The model integrates several earlier regularities and stochastic models such as the NBD and Beta-Binominal models. It requires more variables than the NBD model. Beside the

3 penetration rate and average purchase frequency of the category, the Dirichlet requires the relative market share of brands/products within that category. Both the NBD and the Dirichlet models have been applied to a wide range of goods and services (Uncles, Ehrenberg and Hammond, 1995), and have demonstrated the existence of stable buying propensities in steady conditions (Morrison and Schmittlein, 1988). Their primary application has been made to situations where frequent choices were made and in a relatively stable environment. These conditions roughly approximate stable mature product categories, arguably the situation in most product markets (cf. East, 1997). However, both models appear rather robust and may be useful in applications for categories in the growth or decline stages (Uncles, Ehrenberg and Hammond, 1995). Kau et al. (1998), in an effort to analyse brand loyalty for packaged goods in Japan, applied the Dirichlet model to Japanese panel data for 5 product categories. They found that in virtually all categories studied, the Dirichlet predictions closely fit the observed data. A similar study of Chinese panel data for select products found the purchases were very close to NBD and Dirichlet predicted values (Kwok, 2006). Despite their documented predictive abilities, stochastic models have not been previously applied to the study of a broad range of gambling behaviour. If the NBD and Dirichlet fit the behavioural gambling data, it suggests that there is a normal and expected pattern of gambling where a minority of gamblers account for most of the gambling. This would happen irrespective of most marketing efforts except for distribution (cf. Ehrenberg, 1972). The ability to break these consumption patterns in a group of buyers is relatively rare for most consumer package goods (Ehrenberg, Hammond and Goodhardt, 1994). Applying past findings in consumer package goods to gambling would tend to suggest more behavioural explanations for continued gambling. This would require a rethinking of the how to modify gambling behaviour, and the often assumed link between regular and problem gambling (cf. Productivity Commission, 1999). For example, it may be that the usage patterns reflected in gambling products are no different from non-gambling items such as toilet paper and toothpaste, and reflect the predictable pattern of use. In this case, pathological patterns would be expected to show significant differences from NBD expected patterns in either penetration of the population or the amount of purchase. If gambling behaviour does follow a predictable pattern, then contrary to findings from previous gambling studies (i.e. McDaniel and Zuckerman, 2003), the role of demographics, psychographics and cognition would be minimal. There is substantial empirical evidence to suggest that gambling behaviour does reflect a stochastic pattern of behaviour, and that this pattern reflects the effects of habit, not cognition in gambling behaviour. Research Methodology In an effort to explore the range of games played and their potential stochastic nature of gambling behaviour, and to provide sufficient external validity, information collected from the Australian Productivity Commission survey was used. The Productivity Commission s National Gambling survey is the largest national survey on gambling patterns and behaviour to be carried out in Australia. It was implemented as a telephone survey, and sampled the 18+ years old adult population. In order to ensure a representativeness of the sample, it was stratified by area, age and gender. There were more than 10,600 final respondents to the survey in total but only 8,554 of them (81%) gambled within the last 12 months. A range of legal gambling products were examined in this study and included lotto, instant (scratchies),

4 electronic and video gaming machines, wagering on horseracing, keno, casino table games, wagering on sports, and bingo. At the product/game level, the data on aggregate penetration and average frequency of play/purchase in the population were input into and NBD model in order to derive an expected distribution of play of the game. This distribution was then compared with the observed distribution using simple correlation. The required data were then entered into the Dirichlet model to derive an expected distribution of play/purchase of games at the category level. The Dirichlet distribution was then compared against the observed distribution with the chi-square test. Results Table 1: Observed Distribution versus NBD-Derived (Expected) Distribution of use of Buyers ^ - p < Country Product Sample Size Correlation (r) ^ Lotto 6, Instant 4, Australia Productivity Commission Electronic Gaming Machine 3, Horse 2, Keno 1, TableGames Sports Bingo The standardized regression coefficient results are shown in Table 1. Although the expected and observed are not identical, the distributions are similar (i.e. correlations are highly significant) for all gambling products in the Australian sample (all at p<.005). The finding supports the hypothesis that there is a strong stochastic element in gambling behaviour at the game/ brand level. The observed data was then compared to the Dirichlet pattern to see if it could explain gambling behaviour on a category level; as if the category was gambling and the games were brands in the category. The results on estimated penetration and average purchase frequency are shown in the Table 2. No significant (p>.05) differences between the distribution of observed and Dirichlet-estimated values were found. Table 2: Observed versus Dirichlet-Derived (Expected) Purchases Per Buyer of Share of Category Penetration No. Australia the Product Requirements O T O T O T 1 Lotto 75% 85% % 56% 2 Instant 54% 48% % 35% 3 EGM 44% 34% % 32% 4 Horse/Track 28% 26% % 30% 5 Keno 18% 13% % 28% 6 TableGames 9% 3% % 26% 7 Sports 7% 7% % 27% 8 Bingo 6% 9% % 27% 9 Private 5% 5% % 26% 10 Others 1% 1% % 26% Average Product 25% 23% % 31% Correlation, r % Variance Explained, r

5 Average Absolute 4.20% % Deviation (T-O) O Observed, T Theoretical (Dirichlet-derived) On the whole, the Dirichlet model was able to explain the penetration and purchase frequency of games at the category level. There were, however, differences for a few individual games. Nevertheless, the results point to a stochastic pattern of gambling behaviour that can be predicted by the NBD/Dirichlet distribution. Any deviations may imply a number of things such as an unusually successful game, unusually high or low problem gambling at that product level, a niche or unsuccessful product. Discussion and Implications The findings in this study are only preliminary and must be evaluated in light of the sampling method employed to capture regular gamblers or non-pathological gamblers. Moreover, the measures that were used had a different purpose from their use in this paper. Different phrasing of the questions, metrics of the response scales, and additional questions on different areas of demographics, psychographics or cognitive processes may yet yield better results. Gambling in other countries may not experience the repeat purchase patterns reflected in Australia, although Lam (2005) did find similar results for 5 countries gambling on several games. Nonetheless, any extrapolation must be done with caution. Furthermore, the support for the stochastic patterns does not rule out other explanations and theoretical paradigms (cf. East, 1997) of gambling purchase. Given these limitations, these Australian survey respondents reported gambling behaviour largely appeared to closely follow to those predicted by the NBD and Dirichlet models. Critics of gambling often blame marketing activities such as advertising and promotions for initiating and boosting gambling purchase levels (Karcher, 1989), often to vulnerable ethnic segments and underage players (Selinger, 1993; cf. Davidson, 1996; Productivity Commission, 1999). However, Mizerski et al. (1998) showed that gambling purchase and advertising recall were not associated. Furthermore, Heiens (1993) reported little if any advertising effects in his analysis of their effects on a mature Colorado lotto six years into its lifecycle. It appears that there is a lack of empirical justification for the critics fear of gambling marketing efforts once the category matures. The fit of the NBD and Dirichlet models may suggest a strong and predictable basis for gambling that is primarily dependent upon past purchase. Some would refer to this as a habit-driven purchase (East, 1997; Ouellette and Wood, 1998). The findings also suggest that advertising to discourage gambling would be rather ineffective in gaining real changes beyond that forecast by the NBD/Dirichlet patterns. Past research on other products suggest that promotion for gambling, or not to gamble, needs to significantly reposition the reason to buy/not buy the gambling product (East, 1997, Jolley et al., 2006). The link between amounts of individual gambling and problem gambling may require further review given the current finding of NBD/Dirichlet patterns in purchase. Any suggestions that heavy purchase of gambling products is a risk factor (cf. Productivity Commission, 1999) which lead to problem or pathological gambling need to account for this expected pattern. Perhaps significant deviations from the NBD/Dirichlet can provide diagnostics of this group of buyers. Benchmarking with stochastic models is how it is presently used in marketing research (Ehrenberg, 1997) and future research may show how it can be applied in the gambling area as well.

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