# Mathematical Principles re: Predicting Fanart

I’ve had an idea, for some time now.

When Undertale first came out, I watched how the online community produced fanart. I saved it all, for the first week, and then, the first month. And I compared the output with other known outputs: the Sailor Moon fan community in the 90s, was one of them. Obviously not the same time frames, so that skews things in some areas, but it worked out well.

Human beings are not mathematical equations. They’re not algorithms. There is never going to be a true 1:1 representation of someone’s personality, using current, modern, contemporary human technology. It’s just not happening, because the systems are far too different. One day, a human might be ‘digitized’, but it’s not going to be the process like you think.

In any case, my point is this: even if humans aren’t algorithms, and their mechanics are mathematically impossible to predict and/or reproduce, there’s one thing you can predict, and that’s behavior.

Take this old thought experiment: does a human being have free will, freedom of choice, when choosing what to eat, in the morning? Suppose you wake up, and you’re feeling great. So, feeling great, you may want to eat healthier: so that you feel even better!

But! If you stub your toe… probabilistically, mathematically, you’re more likely to choose something unhealthy, to eat. As sort of a treat, for yourself. (Pain supposedly makes at least human beings seek out more-sugary foods.)

All of these things are cyclic, and the cycle is hard to even see, let alone understand, or break. As such, most people can have bad times throughout their lives, feeling like shit, because of cycles they can’t even see. (You go to bed late, because you want to enjoy yourself; but, in the morning, you’re more tired, which makes you enjoy yourself less, or not at all. The cycle feeds into itself.)

But, ignoring that, for a second, I’m only really interested in how one could predict the amount of fanart produced for any given thing. With Undertale, in the first week of its, 2,000 paintings were created. And by ‘paintings’, I mean really good, high-quality, artistic work. These things took a lot of time to make.

In the first half-hour to an hour of any reveal of any video game character, you can expect roughly 20 pieces of pornographic fanart. This is a constant; it’s held up, throughout the years. Only a maximum of 4 of them will be any good, and there’s a significant lull in the action, as artists who take more time to do their work, will wait 5+ hours, to a full day or week, to post their creations. (Even if they were done, say, 2 days after the reveal.)

Knowing this, I know it’s perfectly possible to predict how much fanart might be produced for any given thing. I can generate a fairly accurate range.

I started to wonder about this because, as I go through VRChat, I noticed that there is next-to-no Sailor Moon content, and absolutely NO Tenchi Muyo! content. Yet there are fully-rigged, lip-sync-capable, fully-visemed models of relatively-obscure modern animes, like Brand New Animal. There’s even a model of ENA, my latest favorite cartoonie.

So why is this possible? Why is it like this?

It’s simple: anime and video games have a fan-art shelflife. While ENA is a unique example, not really applicable here, Brand New Animal is the perfect example. Brand New Animal barely has any doujinshi made of it; doujinshi is also an indicator of how popular something is. (Even old cartoons get new doujinshi, though.)

I don’t have much more to this thought, just yet, and the mathematical ‘model’ that is attached to this thought, will probably never be useful for more than something fun to think about. But here’s what I’ve come up with, as best as I’ve been able to:

Take the total Internet population. Of the total Internet population, how many of them have the skills necessary to produce viable fanart that they will actually release? Of these, how many have access to the tools necessary, to produce such a thing? And, of those, how many of them are well? Levels of sickness may vary in differing ‘populations’, depending on which groups you choose, and how you choose them; but there are ways to tell an overall base level of sickness.

Once you’ve figured out how many well, and capable people have access to the tools they need, you have the number of people who might produce fanart. But, past that, the problem becomes: of these people, how many will actually like the new anime or video game or whatever, that comes out?

That’s simple. You can figure that out using Venn Diagrams, should you know the number of people who also were exposed to said anime / video game. You can find this through stream numbers, but you’ll also need the number of artists who might be interested, in the fan-art producing community. (For Twitter, it seems that anyone interested in a niche subject will always belong to a relatively-static group of people, not really ever exceeding 20,000 individuals at any one time.)

Of 20,000 individuals, 1.4% in the U.S. will most likely be artists. So, you end up with a very comfortable number of 280 major players, who will be all pretty much operating in the same ‘sphere, producing works that are quite similar in tone to one another.

Now, of all those people creating work, of even one of them, how much work will one person produce, if they really love something?

I’ve been saving artists’ work for the last 26 years, online. And the answer is simple: 2,000. The average artist who has found something that really makes them happy, will produce an upper limit of 2,000 works, until they get sick of it.

So: very roughly, the maximum bound of all fanart produced, for any given work, will not usually exceed 560,000 separate fanart works. But this level is usually never reached. For Sailor Moon on Pixiv, over the past 14 or so years, artists have produced over 43,000 works. Naruto does not far exceed this: 57,582 works, as of this writing.

Memes, however, have impacted the number of Sailor Moon works, quite greatly: over 4,000 of the works produced, were produced during a one-week period, in which the Sailor Moon re-draw meme was very popular.

In the same vein, Undertale has over 77,000 works drawn of it.

Overall, over the course of any given series’ lifetime, the amount of artwork that can be reasonably expected to be drawn of it, will usually exceed 20,000 works, with dedicated singular artists producing up to 10% of it by themselves. Fandoms usually last about 1 to 1.5 years, eventually petering out at the 3-4 year mark, when no new content has been released, for their beloved title. After a fandom begins to decline, you may expect a steep decline in output of artwork, with 1/8th of the artwork you’d expect during a steady period of output, being output, here. These values will halve every year, sadly.

Final answer: You can expect any popular series to have between 20,000 and 80,000 fanarts produced of it, and the timeframe where you’ll see most of this being produced, for any given platform or medium, will be within a year to one and a half years of its release. After that, the fandom will die.

Sorry.

The good news is that every single fandom that I’ve archived will only ever total a maximum of 320 gigabytes. Which is handy for me.