DLC Blog

Video Games and Virtual Economies (Part 2)

The focus of this update is the Korean MMORPG Maple Story. Recently, I've become involved in Maple Story, and as a result, I've been over-analyzing the various gameplay mechanics and mathematical algorithms in order to better optimize the time I spend in the game. Allow me to share some of the results.

We'll call this the Experience Points Acquisition Curve (EPAC). I generated it in Microsoft Excel, with data from Levels 1 ~ 70 obtained from the site Hidden Street. As you can see from the trendline, it looks like a cubic function, and actually, the proportional increase of required experience from level to level actually decreases as one ascends through the hierarchy. Theoretically, this should make training easier... but in reality, the experience gain from the mobs does not increase in the same proportion. In fact, there is a 0% increase in most situations, because the player will train on the same section of enemies for several levels. Is this true, however, in all circumstances? What accounts for the "grinding" becoming more and more tedious as the player rises in the level chain?

Let's call this one the Next Level Differential Curve (NLDC). The NLDC, like the EPAC, was generated in Microsoft Excel with data from the always awesome Hidden Street. In the previous section, I indicated that "the proportional increase of required experience from level to level actually decreases as one ascends through the hierarchy." Well, further investigation indicates that is not entirely true. As you can see, there is a dramatic spike in which the differential increases; this occurs at Level 5, where the differential rebounds from a 147% level requirement to a 275% level requirement to attain Level 6. It's "spikes" like these, along with the aforementioned "experience gain from the mobs not increasing in the same proportion" which accounts for the tedium of the grind.

So, what's the point of it all? These results are a far cry from "groundbreaking" in any sense of the word. In fact, they basically confirm common sense. The point, however, is that mathematics is a powerful tool for understanding the natural world. When investing a hundred hours in a classroom, a place of employment, or a recreational pursuit, an intelligent person would want to maximize the benefit obtained from their time investment. Mathematics, combined with logical thinking, are the tools of this process! Even in video games, there are complicated algorithms at work behind the scenes, and an economically-conscious gamer can become much more efficient if he/she takes his/her curiosity of these inner-workings and has the motivation to explore them.

Posted by Ryan at June 8, 2006 01:03 AM in Math.