Wisconsin-lottery-sales T Miller 2020-1 PDF

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Wisconsin Lottery Sales It is January 1999, and Wisconsin Lottery administrators have basic questions about the market for lottery tickets. Administrators are concerned about what appears to be a drop in demand for instant lottery tickets. They are also concerned that both online and instant ticket sales could be affected by the opening of new Indian casinos. Who are the Wisconsin Lottery’s customers, and what makes them buy lottery tickets? Wisconsin Lottery sales contribute to State of Wisconsin revenues. Wisconsin Lottery and Department of Revenue administrators want to have accurate ways of predicting these sales. If they knew who their customers were and how to find them, administrators could do a better job selecting new lottery ticket retailers. There are two general classes of lottery games: online and instant. Online lottery tickets, which are sold at selected retail establishments in Wisconsin, require the buyer to pick numbers to be entered at an online lottery terminal. These tickets are sold to individual customers every day of the year. Some tickets are sold for 0.50, 2.00, and 5.00, but the great majority of lottery tickets are sold for 1.00. Odds of winning are extremely low, but jackpots can be huge. Jackpots for the online game PowerBall sometimes exceed 100 million. Instant lottery tickets, also called “scratch tickets,” come in many

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2020 by Research Publishers LLC

Source: Miller, Thomas W. Machine Learning and Intelligence: Data Science Foundations, Implementation, and Applications. Manhattan Beach, Calif.: Research Publishers LLC, in press. Wisconsin State administrators provided data for lottery sales to the case author, Thomas W. Miller. David R. Blough provided geographical measurements for Wisconsin ZIP codes. Edward W. Frees and Thomas W. Miller used the case data to demonstrate time series forecasting methods in “Sales Forecasting with Longitudinal Data Models,” International Journal of Forecasting, 20, pages 99–114, 2004.

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varieties. These have smaller jackpots and better odds of winning than online lottery tickets. The Wisconsin Lottery sells bundles of instant tickets to legitimate for-profit and nonprofit organizations in Wisconsin, and these organizations, in turn, sell individual tickets to consumers. Most online ticket retailers also sell instant lottery tickets. We might assume that, on average, online ticket retailers place orders for instant lottery ticket bundles about once every four weeks. Competing lottery games are offered by the neighboring states of Illinois, Iowa, Michigan, and Minnesota. States sometimes cooperate with one another. In 1998 the popular game PowerBall, for example, derived its large jackpots by pooling ticket sales from eighteen states and the District of Columbia. Substitute or competing gaming products include bingo and slots at Indian casinos in Wisconsin and neighboring states. We identified fourteen Wisconsin casinos operational at the time of the study. We also learned that new casinos were planned for Madison in 1999 and for Milwaukee in 2000. The Potawatomi Nation plan for Milwaukee (ZIP code 53233) included a 256,000 square foot casino complex with 1,000 slot machines. In developing models for lottery sales, we can draw upon observations of people familiar with lottery activities. We can also draw upon intuition and anecdotal evidence. There are a number of hypotheses to consider: Ticket sales are higher shortly after new lottery games are introduced with television or radio advertising. Higher lottery jackpots lead to higher online ticket sales. There may also be some carry-over effect on instant lottery ticket sales. Ticket sales are higher in those areas that are better served by online ticket retailers. That is, higher numbers of retailers should lead to higher sales. Ticket sales are lower in areas served by substitute gaming facilities, such as Indian casinos. Lower income, less educated people buy more lottery tickets per capita than higher income, more educated people. 2

On average, senior citizens buy more lottery tickets than people in other age groups. The thinking here is that senior citizens have more free time to engage in recreational and gaming activities. Ticket sales are higher during the first week of the month because many people get paid or receive government support checks, such as Social Security checks, on the first day of the month. Although we might expect advertising to affect sales, State of Wisconsin law restricts the Wisconsin Lottery from using extensive advertising. The only time that the Wisconsin Lottery is allowed to advertise is when a new lottery game is introduced. New lottery games are usually instant games, and only a small proportion of these games receives television or radio advertising. For example, in the forty-week period for this study, twenty-seven new instant lottery games were introduced. Six of these games received television advertising, and one received radio advertising. We might assume that each new instant lottery game that received advertising received it for one month (for the week of new product launch and for three weeks thereafter). Sales data for the Wisconsin Lottery are like sales data of many organizations. These are hierarchical or panel data, having both crosssectional and time-series organization. For each retail establishment selling online lottery tickets, the State has a record of the number of lottery tickets sold, their cost, and the time of the sale. Retail establishments fall within sales territories or areas. For the Wisconsin Lottery we might think of ZIP codes as sales territories. We organized Wisconsin Lottery sales data by ZIP code and time. We aggregated instant ticket sales across retail establishments within ZIP codes, and we also obtained instant ticket sales within ZIP codes. We used weeks as our unit of aggregation across time. Weeks began on Sundays and ended on Saturdays; we obtained data for 40 consecutive weeks (the weeks ending April 4, 1998 through January 2, 1999). Table 1 provides names and descriptions of the relevant variables. A geographer helped us locate the East-West and North-South coordinates for ZIP code centroids. He explained that ZIP regions are highly irregular polygons, and that the centroid of a ZIP code is at best an approximate center of the ZIP code region. To get coordinates for Wisconsin ZIP code centriods, the geographer used the Wisconsin 3

Transverse Mercator Geo-referencing System, which measures coordinate axes in meters, with the origin set as an arbitrary point in Iowa, southwest of all Wisconsin ZIP codes. Centriod coordinates should not be thought of as centers of population because it is unlikely that population would be evenly distributed across ZIP code regions. We can link lottery sales data and demographic data using ZIP codes. We derived ZIP code demographics from 1990 United States Census data, with revised Census estimates from 1995. We also recorded the centroid of each ZIP code region in East-West and NorthSouth coordinates. Table 2 shows names and descriptions for the ZIP code demographic and location variables. When fitting linear models to the lottery sales data, we should note that some explanatory variables, such as the size of lottery jackpots, vary across time, but are constant across ZIP code locations. Other explanatory variables, such as population, vary across ZIP code locations, but are treated as constant across time for the 40 weeks that we are considering. Still other variables, such as lottery sales response variables, vary across time and location. In fitting models to these data, we need to identify appropriate error structures, noting which variables vary with time and which vary with location. We do not have to make a distinction between sales dollars and sales volume because most lottery tickets are sold for 1.00. Just the same, we need to define appropriate response variables. In testing certain research hypotheses, we may want to use per capita measures rather than original measures. And, given the characteristics of online and instant sales (online being sales to consumers and instant being sales to retailers), we may choose to develop separate models for the online and instant sales responses. Alternatively, we could try to synchronize online and instant sales information by shifting or lagging one sales time-series relative to the other. State of Wisconsin administrators want to predict online and instant ticket sales and to identify future potentially productive online ticket sales locations. In the process of fitting models, we might think about providing meaningful tests of hypotheses about what affects lottery sales. We have sufficient data to fit a variety of models, including time-series, panel, and spatial data models. Where shall we begin? 4

Table 1: Wisconsin Lottery Data Variable zip

Description ZIP code

weekindx

Index for the week of the study (number between 1 and 40)

weekend

End of week date

weekofmo

Index of the week of the month. The week containing the first day of the month is given the index number 1. Subsequent weeks in the month are numbered in sequence.

wjackpot

Wednesday online PowerBall jackpot in millions of dollars

sjackpot

Saturday online PowerBall jackpot in millions of dollars

nads

Number of new instant lottery games receiving either television or radio advertising (assuming a four-week advertising period)

zolsales

Online lottery sales to individual consumers in dollars summed across retail locations

zinsales

Estimated instant lottery sales to for-profit retailers in dollars summed across retail locations

nretail

Number of listed retailers in the ZIP code

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Table 2: Wisconsin ZIP Code Data

Variable

Description

zip

ZIP code

countycd

County code number

county

County name

perperhh

Mean persons per household times 10

mschool

Median years of schooling times 10

mhomeval

Median home value in 100s for owner-occupied homes

prent

Percent of housing that is renter occupied

polder

Percent of population that is 55 and older

mage

Median age of persons in household

mincome

Median household income in 100s

populat

Population

ewlocate

East-West coordinate for the centroid of the ZIP code

nslocate

North-South coordinate for the centroid of the ZIP code

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