How contagious is Magic the Gathering?
By Neil T Stacey
Scientists have long been interested in how diseases spread, for obvious reasons. It’s a fascinating and complicated field of study, but it boils down to some quite straightforward mathematics.
The Basic Reproduction Number, R0, is the average number of people who are infected by an individual who has contracted a disease, in an otherwise uninfected population. If R0 > 1 then the disease spreads exponentially. If R0 < 1 then the disease dies out.
Picture this in action. Let’s say that one thousand people have a ‘flu virus that isn’t all that contagious. With this fairly tame virus those thousand people are contagious for two days and between them only infect nine hundred new people. That’s an R0 of 0.9 and after a month only two hundred people have the ‘flu. A few months later the disease has died out totally.
Now imagine a slightly different ‘flu virus with an R0 of 1.1 instead. Those same thousand people are now the starting point of an epidemic. They infect eleven hundred new people after two days and those people in turn infect twelve hundred and ten new people over the next two days. A month later, over twenty thousand people have the ‘flu and within months, millions of people are infected. A tiny difference in the R0 comes with a dramatic difference in the end results. There is a very clear threshold and in the region of that threshold, small differences make a huge difference.
Fortunately, epidemics don’t continue in this fashion indefinitely. There are other factors that come into play to slow them down. People who already have the disease aren’t susceptible to it because they’ve got it already. Likewise, people who have recovered from the disease acquire immunity from it. As the disease spreads, the fraction of the population that is susceptible to infection decreases and the Effective Reproduction Rate, R, starts to drop.
Not all contagions spread as epidemics. Others reach an equilibrium point where R = 1. In these cases, the number of people carrying a contagion stabilizes at a particular level. Small fluctuations tend to iron themselves out. While the number of infected people is above the equilibrium level, R drops below 1 because of various factors, causing the disease to retreat back to equilibrium. When the number of infected people is below the equilibrium level, R rises above 1 and the rate of infection goes up until the endemic is back at equilibrium.
Context matters too. If you live in a crowded city you’ll encounter more people per day than if you live in a sparsely populated rural area. As a result, you’ll infect more people on average. For the same contagion, R is higher in one context than in the other. I noted earlier that small differences can tip an epidemic over the threshold into exponential growth; those small differences can be small changes in the environment rather than the contagion itself.
Magic the Gathering, while not literally a contagious disease, can be thought of as a conceptual contagion. Knowledge of the game is spread from person to person more so than it arises from dedicated advertising by a central source. Consequently, the popularity of the game is tied to how it behaves as a contagion more than it is tied to how many people are reached by advertising. That isn’t to say that marketing is ineffective or unnecessary. Rather, marketing the game should be aimed at modifying the context for the transmission of the contagion from one person to another, rather than being focused on directly selling the game to people. Marketing activities are a major factor affecting the R value for the game and as such will determine whether or not exponential growth occurs.
Disease control focuses its efforts on ensuring that the R of an outbreak is less than one. As people involved in Magic one way or another, we have the opposite goal. For the game to really take off, we need to ensure that R is above that key threshold.
Tracking the epidemic: Grand Prix attendance
In some places, Magic is clearly in epidemic mode already. Hasbro doesn’t publicly release sales figures or market statistics but Grand Prix attendance is public information and serves as an indicator of the overall popularity of the game. I’ve charted the total annual GP attendance as well as the average attendance per GP for every year since GPs were first held in 1997, using attendance data from the Wikipedia page on Grands Prix.
That looks like an epidemic to me. Actually, it looks like two separate epidemics. There was an initial phase of rapid growth from 1997 to about 2001, at which point a sort of equilibrium was reached. From 2001 until about 2007/2008 the tendency to play GPs was endemic, with annual attendance hovering around twelve thousand and average attendance per GP hovering around five hundred.
Then, at some point around 2007/2008, something changed. Endemic became epidemic. R rose above 1 and the result is what you see in the charts above. We can’t identify the value of R without also knowing the average duration of infection but we can note an annual increase of roughly 30%.
At this point it’s impossible to tell where the new equilibrium point will be but if you go by the GPs so far in 2015 things are a long way from flattening out. With fewer than half of this year’s GPs completed, total attendance is already at forty six thousand, with average attendance over eighteen hundred. Linear extrapolation suggests that total attendance in 2015 will surpass ninety thousand, in line with what is predicted by exponential growth with annual increase of 30%. Realistically it will likely be somewhere below that mark; the numbers thus far are doubtless skewed by outliers such as GP Las Vegas with its seven and a half thousand players.
Regardless, despite some fluctuations in individual years, the general trend closely fits that of a typical epidemic which kicked off sometime around 2008. It’s difficult to identify exactly what that change could have been. It could have been something seemingly trivial; a small increase in R is all that’s needed to tip an endemic into a full-blown epidemic.
Besides that, GP attendance is far from the whole picture. These numbers are constantly fuzzed by changes in the specific incentives offered at GPs, so they are only partially reflective of the state of the player base as a whole. It’s likely that a higher percentage of players are attending GPs, rather than a fixed percentage of a player base that has grown in proportion to the curves seen on the graph.
It’s important to remember that Magic the Gathering is an infection with two very distinct stages. The first stage is casual play. Casual players make up the majority of the total player base and virtually all tournament players started out playing casually. You could say that casual play is the foundation of the epidemic even if the symptoms are much more visible when a player progresses to the second stage: tournament play. This is the group that we are tracking when we look at tournament attendance. Unfortunately this isn’t the best metric for tracking the progress of Magic the Gathering as a contagion. Casual players, while less lucrative in terms of revenue, are the basis of the whole epidemic. Moreover, pursuing tournament attendance as a metric of success could well be counter-productive. I postulate that competitive tournament players are in fact less contagious than casual players.
New players enjoy the game more when they play against other new players than when they play against competitive players, so exposure to competitive players is less likely to result in successful infection. As competitive players we also self-quarantine by spending our free time in tournament venues and around other competitive players. This reduces our contact with the susceptible population in much the same way that ‘flu sufferers do when they stay home from work.
We also acquire mannerisms that make us less contagious. We say off-putting things like “Yeah I’m working extra shifts so I can build Twin,” or “the addiction counselling is going well, thanks. Put me down for three boxes.” Focusing on competitive play has short-term gains for WoTC as well as for store owners and dealers but it has a negative impact on the R for the game as a whole. Competitive players are also inclined to try upgrade casual players into tournament players, compounding that effect. Too high a concentration of competitive players is a dangerous thing for the contagiousness of the game.
So there’s one possible answer to the question of what happened around 2007/2008 to tip Magic into epidemic mode. It was around that time that WoTC started to change its design philosophy to make the game more accessible. “New World Order” is what they called this shift in philosophy and it involved reducing the apparent complexity of the game. At the time there was an outcry among competitive players. They complained that this shift would dumb down the game but really what it was designed to do was to increase R. In the years since the change we have seen growth which is in line with an increase in Rtaking place at that point. Yes, they designed Magic to be simpler than before but more than that, they designed it to spread.
The new design philosophy represented a change in the contagion itself rather than a change in the context for its transmission. Of course, the context changed in that period too; WoTC has constantly adapted their marketing approaches and of course, the advent of online content is certainly a big factor in the recent success of Magic. Nevertheless, the numbers point clearly to a tipping point in 2007/2008 and it just so happens that at that point in time, WoTC took conscious steps to raise R. Doubtless there were other factors involved but Occams’ Razor points to the “New World Order” as a likely candidate for the tipping point that pushed Magic into an era of exponential growth.
It feels strange to point to a controversial decision eight years ago as the source of explosive growth in the last few years but such is the nature of epidemics. Small changes can make a big difference and exponential growth takes a while to really show itself dramatically. If you look at GPs on different continents, you find that they all separately exhibit similar growth trends. With their “New World Order” WoTC did a superb job of re-designing their contagion, though it helps that Magic was a great game to begin with.
Despite the obvious success of the contagion itself, there are contexts in which the epidemic has not yet taken hold. Next week I’ll be looking at a case study closer to home; here in South Africa we haven’t experienced the same trend of exponential growth and I’ll be looking at some possible explanations for this.