Making Sense of Unequal Returns to Copyright

Typically, describing an article as polarizing refers to two different groups having very different views of an article. But I read an article this week that had a polarizing effect within myself. Indeed, it took me so long to get my thoughts together, I couldn't even get a post up last week. That article is Glynn Lunney's draft Copyright's L Curve Problem, which is now on SSRN. The article is a study of user distribution on the video game platform Steam, and the results are really interesting.

The part that has me torn is the takeaway. I agree with Prof. Lunney's view that copyright need not be extended, and that current protection (especially duration) is overkill for what is needed in the industry. I disagree with his view that you could probably dial back copyright protection all the way with little welfare loss. And I'm scratching my head over whether the data in his paper actually supports one argument or the other. Here's the abstract:

No one ever argues for copyright on the grounds that superstar artists and authors need more money, but what if that is all, or mostly all, that copyright does? This article presents newly available data on the distribution of players across the PC videogame market. This data reveals an L-shaped distribution of demand. A relative handful of games are extremely popular. The vast majority are not. In the face of an L curve, copyright overpays superstars, but does very little for the average author and for works at the margins of profitability. This makes copyright difficult to justify on either efficiency or fairness grounds. To remedy this, I propose two approaches. First, we should incorporate cost recoupment into the fourth fair use factor. Once a work has recouped its costs, any further use, whether for follow-on creativity or mere duplication, would be fair and non-infringing. Through such an interpretation of fair use, copyright would ensure every socially valuable work a reasonable opportunity to recoup its costs without lavishing socially costly excess incentives on the most popular. Second and alternatively, Congress can make copyright short, narrow, and relatively ineffective at preventing unauthorized copying. If we refuse to use fair use or other doctrines to tailor copyright’s protection on a work-by-work basis and insist that copyright provide generally uniform protection, then efficiency and fairness both require that that uniform protection be far shorter, much narrower, and generally less effective than it presently is.

The paper is really an extension of Prof. Lunney's book, Copyright's Excess, which is a good read even if you disagree with it. As Chris Sprigman's JOTWELL review noted, you either buy in to his methodology or you don't. I discuss below why I'm a bit troubled.

Lunney exploits a brief data delivery by Steam that allowed simple algebra to calculate the number of users for each game. There are a few problems with the calculations (assumptions, potential errors, etc), but not so many that I'm going to spend time quibbling with them. So, let's start with the L-Curve, which forms the basis for the article. Here is the graph of user count:


It looks like an L, alright, but the scale bothered me.  So, I looked at the 1000th most popular game, which appears to be about 0 on this chart. But the game (called Cities in Motion) had at the time of the dump (about June 2018) 237,970 users.  At the 70% takehome rate on $19.99, that's revenues of $3.3 million. And that doesn't count the 9 add-ons that range from $2 to $5 each. Nor does it include the followup, Cities in Motion 2, which sits in position 626 with 451,407 users ($6.3 million revenues plus another several add-ons). Cities in Motion 2 also looks to be nearly zero on this curve.

Indeed, the scale is so off, it reminded me of this global warming chart from the National Review:

So, I thought I would be clever and cut off the top outliers to show a more linear progression. But all I got was another L-Shaped graph like Prof. Lunney did. Indeed, no matter where I cut, it was always L-Shaped. The reason for this is that the revenue growth is exponential. Lunney notes as much as well, just to be clear. Now, people misuse that word, but it actually applies here. The number of users at each rank is some exponential power higher than the one before it. So I did what people sometimes do with an exponential curve that's difficult to graph - I took a log of it.

Here's the chart of the logged number of players:
 

The relatively straight line shows a fairly constant exponential growth, though there is a large dropoff at the bottom, and some big outliers at the top.

What to make of all this? It is here where we diverge a bit. Prof. Lunney's basic position is that we don't need super-strong copyright to protect the folks at the very top. They would have made those games for a lot less. Therefore, copyright must, if it is to exist, be there for the large middle. And the problem with the L-Curve is that the large middle isn't making any money.

There are two ways to approach his concerns. The first is the theory, and the second is the empirics.

The primary theoretical answer is that the large middle creates incentives for developers hoping to become outliers. Prof. Lunney calls this the lottery effect, and he poo-poos it as not terribly valid. Let's just say I disagree with him, but I don't want this post to be about that. I frame this question as an expected value question, which means that in a repeat and uncertain game, one must have supracompetitive returns to offset all the losses when things flop. I mathematically illustrated this in an article I wrote nearly 20 years ago, which demonstrated that cutting off copyright protection once some expected value of profits was reached yielded lower expected value than the alternative. Ironically, this proposal is exactly professor Lunney's here today, and I disagree with it as much now as I did then. If you claim that the middle isn't making money, then by cutting off outliers you're just making your average creator earn even less money, which will push incentives downward.

Now, this isn't to say that Prof. Lunney doesn't have a point. As noted above, I agree that some supra-competitive rents may be too much. Where we differ in large part is our views of the uncertainty involved and the motives for participating.

But I'll put that aside, and focus on the second question - even without the lottery effect, does the data support a theory that copyright is providing nothing to the vast middle?

It's hard to get a sense from the data, so I thought I would look at every tenth percentile (deciles):
1. Team Fortress 2, 50,191,347 users, released Oct 2007, free to play (since 2011), first person shooter, formerly $20, developer: 41 games
2. Trick and Treat - Visual Novel, 164,544 users, released Dec. 13, 2016, free to play (visual novel), developer: 3 visual novels
3. Hunahpu: way of the Warrior, 48,807 users, released April 10, 2017, $3.99, very simple graphic landscape game (like Mario Bros. or Defender), developer: 8 games
4. Caravan, 19,612 users, released Sep. 30, 2016, $9.99, low-graphic RPG, developer: only game, publisher: 50 games
5. The Fidelio Incident, 8,547 users, released May 23, 2017, $9.99, first-person adventure, developer: only game
6. Rubek, 4,163 users, released Oct. 14, 2016 , $2.99, very simple graphic strategy game, developer: 2 games
7. Soko Match, 1,904 users, released Sep. 16, 2016, $.99, extremely simple graphic strategy game, developer: 3 games
8. Q-YO Blaster, 828 users, released Jan. 15, 2018, $3.99, pixel graphic landscape game, developer: 1 game
9. EquiMagic - Galashow of Horses, 343 users, released Dec. 19, 2017, $9.99, simple graphic horseshow simulation (trotting horses), developer: 15 games
10. Over My Dead Body (For You), 119 users, released Sept. 11, 2017, $9.99, very simple graphic strategy game, developer: 1 game

Doing this exercise was interesting, and revealed a few patterns to be explored. First, price seems to matter, but Prof. Lunney's data does not take that into consideration. Free games reign supreme, but cheap games do not. This implies that a) there's a quality tradeoff, b) that in-game revenues are not being counted, and c) that perhaps some low-user games make money because they are cheap to develop.

Also, many firms appear to be repeat players. Some of the followons have more users, and some have less. A full study of repeat play and incentives to create better games would be interesting.

Another takeaway is that age seems to matter. A lot. I did a simple regression on the user count (rather the log of user count) and the steamid (which is smaller for older games), and that simple variable explains 40% of the variation in user counts. Older games have more users. Prof. Lunney might consider that for future analysis. That said, there's still remarkable inequality even in what remains after age - so the question remains whether the vast middle must be linear in order for copyright to make sense.

I'm not so sure. but before I consider some of Prof. Lunney's analysis, I should note that in large part I agree with many of the things he's arguing. For example, the existence of strong copyright won't force the unwilling to pay - they will otherwise pirate. On the flip side, content management systems, like Steam's, largely eliminate the need for pure piracy copyright, as they limit copying even in the absence of law. Copyright's added value in platforms like this is much more in avoiding knock-offs, as PUBG (No. 3 on the list) alleged when Fortnite came out with a similar battle royale system.

Now, on to some specifics:
Does the "L-Curve" mean that the average producer can't make a profit? No. I contacted a programmer right around the median, with a $3.99 game. He told me that he worked on it minutes at a time, off and on, for a couple years. He confirmed that the numbers sounded right (he actually had more sales associated with bundles, but the people didn't play), and that he made a very small profit. This was a side business, and the world got a program it wouldn't otherwise have. But he also didn't believe that copy protection helped him make that money.

That's the median creator, still making a profit. How far up or down the line do we go? Prof. Lunney says: "As soon as two games are produced without copyright or with extremely narrow copyright, the welfare losses associated with the excess incentives for these two games likely outweigh the welfare gains from enacting or expanding copyright to ensure the expected profitability of the third game." I think it may be this statement that gives me the most heartburn.

There are a few reasons I'm troubled by this. First, this seems to assume that all consumer welfware can come from owning a couple games - that there's simply nothing to be gained by having more games (that somehow isn't stifled by limiting copying, at least). But the data belies that. These user counts are not individual - if you add them all up, they add to 1.7 billion or so. And Steam had about 150 million users at that time, which means that every user played 10 games on average. So if we stop at 2 games we have a shortage - players willing to pay for games that may or may not be created.

Second, we don't know what the quality of games would look like. If firms are limited to self help protections, it may be that their games will be of lesser quality, taking less investment, and otherwise not fulfilling demand. Or maybe they won't. We certainly can't know this from the data here.

Third, as noted above, Prof. Lunney believes that there is a lot less uncertainty than there is. At one point, he notes: "But whatever the reason some profit motivated production will occur even without copyright, and under our assumptions, the most popular videogames will be produced first." While it's true that the older games have more users, they are more popular because they are older, not because they were created first. I am highly skeptical that producers know in advance which games will be highly played. Many flop. This ties to my point above about expected value - where one does not know whether a game will be successful, one cannot assume that the first one out will be the best one.

Fourth, Prof. Lunney reaches his conclusions by making assumptions about the welfare loss associated with copyright at the top as compared to the welfare gain through added incentives at the median. Those assumptions may work for patents (I don't know enough to know). They might even work for songs, to the extent that songs are limiting new creation. But I seriously question them in video games for several reasons. First, in a world where content management systems control much, it is unclear what copyright is restricting at the top end. Some copying of actual characters, I suppose, but is it really dollar for dollar? Second, in a world where much gaming is based on underlying engines, such that gameplay is already half-handled, what limitations are there? Again, it seems to be specific artwork rather than free reuse of games (which, are already free at the top end anyway). Is the restriction on artwork so great that it's causing loss of welfare? I don't know, but I doubt it. The reason people spend money on free-to-play Fortnite is for the original skins that cost money (as stupid as I think that is). If the Fortnite skins look like everyone else's then why bother? Note, of course, that the copyright incentive at the low end may also be too low. It's the upper middle range, where there's a real investment (which is less than half the games, apparently) that matters to me, not the median.

Fifth, the analysis relies on three assumptions that Prof. Lunney lays out: "For this to be the case, we need: (i) revenue to be correlated with demand, so that a more popular game earns more than a less popular game; (ii) for each game to have a constant cost, and thus higher demand games are more profitable per unit cost; and (iii) expected demand cannot be completely uncertain ex ante." The article admits that item (ii) is difficult for videogames, and my analysis of the ten games above shows that. Item (i) is also difficult to show in practice; the pricing varies so much that some games with 4000 users make $40,000 and some games with 4000 users make $12,000. Item (iii) probably holds - expected demand is not completely uncertain, especially given quality of investment, but it's probably a lot more uncertain than Prof. Lunney gives credit for. In any event, the assumptions of his analysis don't hold up on their own terms.

I suppose the real issue for me comes down to this passage in the article (in which Prof. Lunney suggests that revenues be capped at costs, a point that I disagreed with above):

Alternatively, some might insist that it is neither fair nor efficient that Sheeran should earn the same for Shape of You [the number highest earning song] as someone earns for a marginal song to which hardly anyone listens. But it is entirely fair and efficient. In a competitive market economy, a heart surgeon who saves your life earns the same market reward as a doctor who gives you a vaccine. Neither earns the value of their work, in the sense of the maximum reservation price a patient could be forced to pay to avoid dying. Rather, both earn the cost of the service they provided. To the extent the market prices for the surgery and the vaccine differ, that price difference should reflect an underlying difference in cost. In a competitive market economy, it is not value, but cost that dictates what you earn. If copyright intends to create a market that mimics a competitive market, it should strive to do the same. As a result, if Shape of You cost the same as a marginal song to author and distribute, then that cost is all the market return that fairness and efficiency require each to earn.

I'm troubled by this analysis and analogy in a couple of ways. Primarily, it mixes the apples of price per unit and the oranges of total demand. Sheeran and noname song both earn the same cost: Spotify pays them exactly the same per play. Sheeran makes more money not because the price of his song is higher, but because more people want it. There are no rents in his individual demand/supply curve; indeed, if he knew the popularity, he probably would have charged more (see Taylor Swift refusing to go on Spotify). Now, Lunney is saying that if too many people want the song, then it's not efficient because there are others who could copy it for free and that's a welfare loss because the gain in incentives to create music is outweighed by the joy we would all get if we could just listen to the music for free once Sheeran got enough to make the music in the first place. But if that's the argument he wants to make, he should own it, rather than claiming that somehow Sheeran is selling something at other than the cost of making it. Because if you take this argument to the extreme, it means that even though the heart surgeon has now exceeded the cost of running the practice by June (it was an unexpectedly cholesterol filled year), then the incentives for people to become heart surgeons are outweighed by the value we'd all get if we just forced the surgeon to operate for free after July 1. Maybe it's ok for copyright because of "promote the progress" in the constitution and all, but it's a pretty unsettling way to look at the world, in my view.

I'm also troubled because this treats music (and other copyrighted works) as fungible goods, as you would in a market. Sheeran and noname - either one is the same, so if they are priced similarly then they should make similar profits. But that's not how even efficient markets work. In an efficient market, a better product has a larger demand, and thus garners more revenue because more people will buy it. Even with a flat marginal cost (and it's not actually flat, even with music), if the demand curve shifts out, more people will buy the product at the same price. And so cutting off the revenues in fact distorts the market. It's a wealth transfer. It may be justified in the name of welfare maximization (though I'm not convinced), but again, Prof. Lunney should own that. He proposes taking an otherwise efficiently behaving market, in which everyone sells the similar but slightly differentiated goods for the same price, and putting a thumb on the scale to cap demand at the competitive price before it is sated, so that consumers and have all of the welfare associated with not having to pay for a product they prefer to another product they could just as easily buy for the exact same cost but do not prefer. This is not an efficient market proposal, in my view. (On a side note, it's not even clear that Spotify is the way to measure this, as customers pay a fixed price, and can consume as much of the product as they want, detaching demand analysis from pricing).

To recap this very long rant post, I agree with Prof. Lunney that we likely don't need more copyright protection to get more video games, or music, or books, or whatever. Indeed, we likely would be fine with a lot less of it. But I just cannot get to that conclusion from the data presented here, except to say that a lot of people seem to make video games on Steam without the expectation of huge profits.