So, it’s been a while, hasn’t it?

I’ve been taking some time off from Tyrannis, but I’ve got some new things in the works. And I can’t wait to show those off when they’re ready.

But for now? Just a lot of research and playing free-to-play mobile games. And research about free-to-play mobile games.

Because I like video games. I mean, that probably goes for most people who work in games, and I’m no exception.

That being said, I also like having income to afford healthcare, which means I need to make money one way or another. And game studios are no exception, if all the gacha/lootbox mechanics are anything to go by.

So let’s talk about those mobile games and monetization. And while we’re at it, let’s do some math on it, so I can justify my math degree.

**Calculating the Number of Draws Required**

Let’s start by calculating the number of attempts it’d take to randomly get every piece of content in a “Set” on a mobile game through random draws.

- Pc = Percent Chance for Desired Content
- Df = Free Draws (or as I like to call them “Free Samples”)
- Dp = Paid Draws (on average)
- N = Amount of Content in a Set

# Pc•(Df+Dp) = N

This equation shows the relationship between percent chance and the average number of draws required to obtain all content. We can, of course, rearrange the equation to determine the average number of draws required:

# Dp = (N/Pc) – Df

Of course, the value Dp this isn’t a guarantee that you’ll get everything by that attempt. It’s an average, and ultimately, it’s all up to chance.

This doesn’t factor in duplicates, either, though we could factor that in by adding in a modifier, “Nd,” to represent the number of duplicates.

# Dp = ((N+Nd)/Pc) – Df

Like I said, it’s all up to chance, but this equation, or more importantly, the value Dp, is a good way to visualize how many draws you can expect to get all the content in a set.

Plus, we can use it in a second equation to understand the cost of obtaining all this content.

**Calculating Costs**

- Dp = Paid Draws (on average)
- Cr = Cost (real currency)
- Er = Exchange Rate (in-game currency to real currency)
- Ca = Cost per Draw (in-game currency)

# Cr = Ca/Er•Dp

Of course, this equation isn’t a guarantee for the same reasons that Dp isn’t a guarantee. You could get lucky and get the content on your first draw, or you could be like me and not get it after your fortieth. Still, it’s a good way to visualize just how much money this content would cost based on random draws alone.

For example, we can use it to determine how much each individual piece of content costs through random draws:

- Co = Cost of One Piece of Content (through random draws) (real currency)

# Co = Cr/N

Moreover, we can use Cr to determine how long it would take for a player to acquire this amount of money through gameplay, and by extension, the rate at which the players are grinding at.

**Calculating Time and Effective Player Income**

- T = Time Required to Obtain In-Game Currency via Gameplay (hours)
- Rc = Rate at which In-Game Currency is Obtained via Gameplay (in-game currency / hours)
- Ie = Effective Player Income (real currency / hours)

# T = (Cr•Er)/Rc

# Ie = Cr/T

The value “Ie” is the most useful value here, since it is, ultimately, determining how much the player’s time is worth. It shows how much in-game money (and by extension, real money) the player is making per an hour.

That, and it can be used for gacha/lootbox games, just as well as any other game with microtransactions (ie GTA Online).

**Balancing the Effective Player Income**

It’s a balancing act, though.

Too low an Ie value, and microtransactions are practically necessary for theaverage player to stay competitive against richer players. This leads to accusations of “Pay to Win,” which alienates the Free-to-Play players. And while they aren’t paying, they’re probably going to make up the bulk of all your community, and at the bare minimum they provide content through gameplay. They’re also the lifeblood of content and community, and they’re also potential customers. So losing them means losing potential revenue.

That being said, too high an Ie value isn’t that good, either. Well, for the developer, anyways, because the player’s going to enjoy not feeling the need to pay any money. I hate to say it, since I’m a gamer myself, but it’s a business. You need to have an incentive to encourage players to keep paying you money.

It’s all a balancing act, and there’s no one-size-fits-all system. What works for, say, Fire Emblem: Heroes isn’t necessarily going to work for Call of Duty Mobile, let alone non-randomized games like Grand Theft Auto Online.

**What Can Be Done?**

I have two ideas that can mitigate these issues.

First is providing an alternative means to obtaining a set of content.

One example is what Fire Emblem: Heroes does for their events, where forty summons allows players to summon one of the event-exclusive Heroes in a set. In a general context, this is what I’d call a “Draw Threshold” that provides players with the content they have been making draws for.

The presence of alternative means, such as the “Draw Threshold,” allows Free to Play players to have a way to reliably obtain content with their Free-to-Play methods (usually grinding), while also incentivizing purchase of in-game currency to reach that threshold. Play

A second option is simply letting players buy lootbox/gacha content at a markup.

We can calculate the markup price of an individual piece of content in a Set, “Ci,” by multiplying its cost by a percent multiplier, “M.”

# Ci = Co•(1+M)

That, or we could calculate the markup price of the entire set’s content as a whole, “Cs,” by multiplying its calculated cost, “Cr,” by the percent multiplier, “M.”

# Cs = Cr•(1+M)

This one provides the best of both worlds scenario.

Players who want the content directly, or players disliking random chance can purchase it at a markup, which provides the developer a reliable source of income for any Set.

Meanwhile, Free-to-Play players, as well as more chance-minded players have the option of obtaining the content via random chance, albeit on average at a lower cost than the players who purchase directly.

Of course, there are ways to encourage certain behavior.

For example, random draws can be encouraged by implementing a time delay on direct purchases of the Set’s content, while allowing randomized draws, as this would incentivize impatient players to try to obtain the content through random draws.

Meanwhile, a decreased percent chance for the desired content can encourage players to purchase the content at a markup, seeing that it’s guaranteed, despite the price.

**Conclusion**

Granted, these are all hypothetical, but the math checks out, and the math’s useful for mobile game monetization.

Mathematics can put a price on randomly obtained content, whether gacha or lootbox mechanics. And through this, developers can use the analysis to design both pricing and monetization strategies to maximize revenue while maintaining player goodwill.

Of course, this isn’t a silver bullet, and what matters above all else is a solid core game that can enjoyed by all types of players.

But companies need to keeps the lights on, so they might as well try to find a good way to keep players playing.