Cross Section of Nevada Slot Regions

Applying the aggregated Nevada time series model to the individual regions provides confirmation of the same general findings in the previous post.  We are also able to group regions by qualitative findings.

The following table suggest one possible interpretation using three qualitative groups.

The R^2 value is the amount of variation explained by our linear model.  Accordingly, within each group, I rank by the region’s R^2.  The higher the R^2, the better our model explained the actual data of the region.  The first thing to note is that the grouping is a pretty good indication of average explained variation.  So, what are the characteristics of each group?

Group 1:  All of these regions have characteristics that match the aggregated model.  All show a long run tightening hold of on average between 1 – 2.5 hundredths of a % per month.

Each member of Group 1 has a monthly oscillating pattern that can be described by two months of data. The average holds are pretty tight.  Finally all show a significant loosening in December.

Group 2:  Reno and Elko stand apart as they have on average a looser hold than their Group 1 counterparts, and show no long run change in monthly hold.  Instead of an oscillating pattern, movements in hold tend to reiterate themselves.  The December loosening is milder in these regions.

Group 3:  NSLT and Mesquite are the only regions that show a tightening in December.  This is most likely the result of the bad fit of the model.  With them SSLT shows a long run loosening in hold.  Their various other coefficients do not lead to any obvious interpretation.  The lack of competition in these regions (relative to the bigger gambling destinations) probably leads to different strategies, exposure to shocks and small sample problems.  An ARCH type model looks like it would be a better fit.

Importantly, the regions when analyzed under the aggregated model do not dispute recession hold tightening.  In fact most of the regional models, even Mesquite, show higher than average tightening during that time. Under the lens of the tightening hypothesis, Mesquite’s peculiarities are likely brought on by the recession.

As far as statistical methodology, there are still places I may have tripped.  Efficient estimators of the variance structure should be explored.  Also, since I ran the regressions one at a time, I could run a panel regression for better estimates.

Evidence of Tightening During the Recession

I will show results from the R statistical language that will solidify some observations we can make about aggregate Nevada slot holds over time.  (Again the data covers the years 2004 - 2014 and comes from  http://gaming.unlv.edu/reports/nv_slot_hold.pdf).  Essentially what we want to do is figure out a regular pattern, subtract that and see what remains unexplained.

The blue line above is the average monthly hold in Nevada that I've talked about before.  The orange line is a standard time series estimate which we will take to be our model.  This estimated model “explains” roughly 70% of the variation of the data (as measured by adjusted R^2).  There are a few things we learn about the data in building this model.

First, a model looking backwards only two months works pretty well as far as capturing the oscillating pattern we see in the market overall.  If the data were weekly, I’d expect to see a relevant period of more than 4 but less than 10 weeks.

Second, there is a linear trend over time of increasing tightness: if you were to draw a straight line through the data, it would have an upward slant.

Third, December is a time of loosening: this explains the periodic low points about 12 months apart. 

Removing any of these three factors greatly reduces the explanatory power of the model.  But incorporating all of them into a one equation model gives us a powerful explanatory tool.  It may be a useful prediction tool as well, but that won’t be my focus here.  In the chart below I plot the errors of the model.

A model with no biases would look random and wouldn't have any discernible patterns.  This is mostly the case for our model except for the period corresponding to the recession, during which we see that the model systematically underestimates the tightening of slot machines.  This I think is strong first pass verification that there is something to investigate as far as concerns the dynamics between Players and Casinos during the recession.  Indeed, the "great tightening" was more than business as usual.

In my opinion this model is mostly useful for capturing descriptive qualities of the market and not necessarily useful for determining whether demand or supply side factors are the cause.  To further this line of analysis, I would apply the same form of model to the individual regions, and see if it retains its explanatory power.  The resulting cross section of variation will give us a lot of clues about why the patterns emerge.

After that, the goal will be to use economically fundamental variables, like income, profit and expenditures of the Players and Casinos, to explain a system of equations governing this list of variables as well as hold.

Supply, Demand and Estimation

The Nevada Gaming Control Board in its Gaming Revenue Reports provides monthly hold data for slot machines (http://gaming.nv.gov/index.aspx?page=149). Hold data is the aggregate of what is payed out to Players divided by what they pay to play. From this, the long run trends in holds can be established.  For example consider Dr. David G Schwartz’ claim that holds have tightened by 13.54% between 2004 and 2014 in the following report: http://gaming.unlv.edu/reports/nv_slot_hold.pdf.  

In the above chart I have placed aggregate monthly data versus a linear trend beginning in January of 2004.  It illustrates Schwartz’ claims, but how useful is this data for evaluating hypotheses like a “great contraction” corresponding to the 2007-2010 economic turmoil?  It turns out it is not so obvious how to interpret this kind of data, and the reason is that each month we are observing the intersection of both an aggregate demand and an aggregate supply function.

A rise in hold from one period to the next could for example mean that on average Players have chosen to play tighter games, or could be that other things equal, the Casino has tightened the average return of its machines.  The reality, we should all realize, is we are seeing layers of strategy from both parties.

So what is it that we need?  First steps might involve analyzing the data by region, which reveals that the Casinos and Players differ in their strategies, region to region.  For example, Elko seems to have tightened during the recession, whereas Mesquite seems to have tinkered less than they did prior to the recession.  One single model is unlikely to explain all the data, and each region can be explained by multiple models.

I bet Players, Casino operators and salesmen in the regions could tell me a lot about what happened during this time.  But given the difficulty of finding all of the relevant information, we have to settle for models which, using what information we have, prescribe behaviors to the Players and Casinos.  Given these assumptions, we then see what the data has to say.  Fortunately we will have lots of models to choose from, and each model chosen should teach us something new.

As a start, I would want to know the change in employment (both aggregate and by region) for each month.  We could use it as a predictor for the change in hold, and this would probably be the best way to gauge the effect of a typical Player’s income.  However, in the regions of interest, the Casinos are also major suppliers of jobs, so the employment data will also give partial information about the financials of the Casinos. It stands to reason that a Casino's financial situation determines in part their slot floor strategy. It is up to the researcher then to make assumptions when interpreting the results (in this example determining the effect of employment on hold through supply and demand channels).

Cleaning the data using time series methods is another step I would likely take.  This would filter out noise from seasonal patterns like Casino purchase timings or the Christmas season, and also long run trends.  But even though time series methods help us get a clearer picture, they implicitly make assumptions about the behavior of Players and Casinos.  Really there isn't a way to do the empirical work without making economic assumptions.  To me this means that we must use our training, experience and imaginations to come up with models that have meaningful predictions, and then test them against the data.

Wealth Effects and Social Casino Gaming

In this post, I want to emphasize the importance of wealth effects even for empirical data.  I have used the wealth effect implicitly or explicitly several times already, so I hope to clarify it in the remainder of the post.

Let's begin by thinking about social casino games.  One advantage they offer over land based games is that you can perform experiments by offering slightly different versions of the game to Players in what is essentially real time.

This should be great! Now we can use the basic t-tests that we learn in every intro to statistics course ever taught.  Except very quickly we start to run into some serious problems, too much seems to be statistically significant.  Another problem is that holding the Return to Player fixed, while putting more money in one feature necessarily means taking money out of the other...so which changes drove the results?  To address these kind of behavioral questions we have to turn to theory.

Rather than construct the experiments by forcing the expected value of the Return to Player to be equal, I would try to establish a wealth effect.  What I mean is that say I had a 95% Return to Player game.  What would be the major behavioral results of giving them the exact same game at 96%, 97%, 98%...? We can learn this by changing how much the Player pays to play the game. This has the advantage of affecting all features of the game equally.

The simplest result would be Players realizing they are getting an x% premium, which induces them to play y% more spins.  But I might expect that some segment of Players are betting below the maximum, playing less expensive games, or even avoiding volatile games altogether. (Bear in mind that the current Social Casino Player has on average less of a taste for volatility than does a Vegas gambler.) For these "corner solution" Players, after giving them a premium we might even see them play less total spins but shift towards a more expensive/volatile experience.

Once the range of responses is established for the various segments of the Player base, then we have a standard with which we can compare our slightly different games.  In essence, what we are doing is asking how does jumbling the money in the game around compare to just giving money directly to the player.

The open questions to me are: how stable will the Player segmentation be?  what is the best way to establish the wealth effect...should the Player know she is getting a discount...should it be based not on what you pay but maybe a random but frequent small award?  This is the kind of research program that could help us test the hypotheses of the previous posts.

For Players It's Not Just Risk and Reward

One area where formal academic economics is very behind is modelling the gambler.  There are definitely many interesting ideas out there about how to model a gambler, particularly as concerns his seeming taste for risk.  However like most projects aimed at modelling irrational people, there is little consensus and even less data backing up one theory versus another.  Rather than try to answer the question once and for all, it may be more useful to try and model the Player who chooses to play slot machines.  We will see that even a little bit of formal thought helps us to tell a compelling story about the direction of the slot machine market.

I think it is important when looking at a slot machine to realize that when a Player puts money in it, a whole lot of different outcomes can occur, and here we are not just talking about monetary outcomes.  As a consequence we should think about modelling slot machine demand as a demand for many different goods at once, all of which live inside the slot machine.  Above all we must recognize that Players will differ in their demands for the sub-components of the slot machine, just as their taste in art or music varies.

Some Players are mostly in it for the big win, and slot machines offer some of the highest returns.  Other players may be more interested in a more casual experience comprised of seeing a lot of different symbol combinations paying moderately well.  Since slot machines have a lot of possible combinations, understanding every Player’s experience can be difficult, but understanding the big wins is not.  They happen rarely, and they pay in large ratios, sometimes over 1000x’s bet.

Thinking back to the Great Tightening, when Casinos across the board reduced their Returns to Players, not all Players were affected equally.  Manufacturers are reluctant to take the biggest prizes out of a game and often might leave the odds of bigger prizes relatively unchanged.  Usually in order to reduce for example a 90% RTP to an 85% RTP, smaller prizes will be adjusted.

As we noted in the Great Tightening post, reducing the RTP has at least a wealth effect in that it makes Players on average feel poorer.  However, that wealth effect may not have been big enough to drive out players chasing big wins.  That 5% difference in expected return, was probably not coming from that 1 in a million payout that the big win chaser is after.  To think about it simply, that 1000x’s bet is still 1000x’s bet, and its odds haven’t changed much, if at all.

What that means is that as Casinos tighten up their slots, they observe an increasing percentage of Players being the kind of Player chasing big wins. They could intuit this by observing that games traditionally considered volatile would still be doing well.  This in turn causes the Casinos to request the Manufacturers make more volatile games.  And when these games take a larger share of the floor, more Players who are not big win chasers feel that their particular sub-demands are not being met.  In fact Players are made to feel less wealthy by the increased risk they have to take on for the same returns compared to the previous floor composition, and again marginal Players are driven out of the market.

This is a vicious cycle, and unless you can make up for the lost Players with just the big win chasers, I don’t think it is optimal for any of the parties involved.  The most important take away here is that thinking about Players simultaneously as rational agents in a risk-reward trade off and as having demands for sub-components of the full slot machine experience helps us understand shifts and trends in the market composition.

The Great Tightening

The 2007-2009 “Great Recession” had a profound influence on almost every market in the US and globally and to greater or lesser degrees, most are still affected.  Among U.S. states Nevada, by far, fared the worst, and it can’t really be denied that the gaming industry is the largest culprit.  It seems intuitive that when a potential Player’s income drops, that Player will choose or be forced to gamble less.  But are there peculiarities to the Casino Industry’s infrastructure and decision making process that could have exacerbated the scenario?  I suspect yes, and will argue on more or less Keynesian lines how this could have happened.

To begin, we have to consider the text-book story.  When Players get poorer, in order to induce them to keep playing, Casinos should drop their prices.  Right here we run into the first problem, how do you lower the price to the Player of a slot machine?  Once it’s on the floor the minimum bet is fixed as is the all features loaded bet.

It would seem that land based slot machines have “sticky” prices.  But this is not the end of the story.  The slot floor operator has some levers he can pull.  When games are sold to the Casino, they are sold with multiple different Returns to Player.  In theory it shouldn't be too difficult for the operator to choose how much Return he expects on the given machine.  Now in normal times, especially on the Las Vegas Strip, the Casino would “tighten” its games to squeeze more profit out of its machine.  This is a valid strategy if Casinos expect that this is within the Players’ budgets, or if they believe that they can consistently trick Players into playing tighter games.

In fact it is a mathematical law that in the long run an 85% RTP game will have a higher return to the Casino than a 90% RTP game.  But these returns are marginal returns, i.e. based on how much the Player bets, and the Player is sensitive to both returns and Wealth.  We consider a Player's Wealth to be money in her possession and money she expects to make from playing games.  Regardless of whether the Player has an accurate understanding of the fact that playing slots makes her less wealthy, she is sophisticated enough to realize she is on average getting poorer faster than she was when playing games before the recession.

So what happened, and this is well documented, is that even Casinos off the strip tightened up, in order to squeeze out more returns on their assets.  But this decision made their Players poorer, and on the margin Players, already facing their own financial constraints, chose to stop playing.  We can think of this as a lesson in What Goes Around Comes Around.  If Casinos had loosened their slot machines, would that have helped?  The model seems to suggest this is a strong possibility.

As a last consideration that I will elaborate on in the future, could this tightening have had a serious influence on the style of Players that remained?  The answer is probably yes, and this led to the same kind of push and pull of information that we see between the Casino and Manufacturer that can lead to market failures.

The Market for Lemons as Slot Machines

In 1970 George Akerloff published a formal model describing how asymmetric information between buyers and sellers could lead to severe market failures.  The idea has had so many applications it is no surprise he would later win the Nobel Prize in economics for it.  Here we will consider the implications of his ideas in the context of the downstream firm model between the buyer of slot machines (the Casino) and the seller (the Manufacturer).

The setup is straight forward, the Casino wants to supply its customer with a high quality slot machine, i.e. is fun to play for a long time.  However the Manufacturer sometimes produces lemons and is thus forced to sell its portfolio at a price that averages its lemons with its top performers.

Now if we had a Manufacturer/Designer that somehow “knew” her game was perfect, she might be unwilling to sell at this average price.  Further if the Casino has no way of verifying that her game was indeed of the highest quality, the Casino wouldn't be willing to pay a higher price than the average price.  In essence we are saying high quality Manufacturers should leave the market.  This is called the Bad driving out the Good.

Is this what we see in the real Casinos of today? Certainly some Players feel that way, but I think the quality of games, if anything, has gone way up.  To account for this we could simply assume that Manufacturers have no earthly idea when they have a good game, and in the long run the quality of games has been driven by technology and the wider selection of games.  However, this would only be a half truth.  Manufacturers sometimes know they have a portfolio of games that are currently popular, and Casinos want access to them.

So why might a Manufacturer sell a superior product at a lower price?  This has to do with the conventions in the industry and innovation on the part of the Manufacturers to try to establish some guarantee of quality.

As an example, leasing agreements for high profile themes or new brands come with ready to swap arrangements at the option of the Casino, meaning that the Casino can switch to any game in the Manufacturer's library if the Casino is unhappy with one particular theme.  So long as the Manufacturer is selling or renting enough of the low quality games to make up for the loss of selling the high quality game at a lower price, the deal seems fair to the Manufacturer.  It would seem this is a mutually beneficial arrangement.

Nevertheless, we want to relate all of this back to the downstream model in the previous post.  The main point there was that the Casino wants some ambiguity to help protect their bottom line from the Manufacturer.  Combined, this could have the interesting implication that even though the Casino has a strong incentive to provide the Player with the best possible game, in the interest of maximizing profit it may want to occasionally purchase bad games to keep the Manufacturer off its trail.

Trying to fit all of this in one model tells us, among other things, that at some level the quality of games being made is tied to the amount of information the Casino is willing to share back with the Manufacturer.  And really, that shouldn't surprise anybody, until we realize it is the amount of information the Casino doesn't want to share back to the Manufacturer that is operative.  This could manifest itself in many ways, including prices that the Casino is willing to pay for the Manufacturer's various programs.  So the prices are neither accurately signalling quality nor consumer demand, what then are they signaling?