Reflections on Mathematics in Game Design

[This article was originally written for Mathematics Day at CUNY-Hostos and posted on Game Design Aspect under the topic of Game Designer Skills.]

I went to a university so nerdy that answering calculus problems was sometimes the only way to gain entrance to a frat party. Knowledge of mathematics was expected, even of humanities majors like myself. I soon learned that my economics classes were full of calculus proofs and my writing classes, more often than not, had a scientific focus. There was no escape, it seemed, from numbers and mathematics.

Mathematics could be scary. I hated calculating triple integrals. I doubted myself. In my freshman year, I turned down an exciting opportunity to help build a microscope to be sent to outer space because I feared I could not do the calculations. It was not until my class in econometrics that I began to find my way. Unlike today, the tedious number crunching was done by hand rather than computer, but that was helpful to me because then I could clearly see from the large data sets what variables were affecting what.

Despite my initial reluctance, a love affair with numbers would serve me well in my chosen field of game design. It seems odd in these times of free-to-play business models and monetization design, but back then, it was fairly common that I would be asked how my economics background might benefit my career in the game industry. In those days, game companies did not have data divisions devoted to figuring out whether blue or pink lettering sold better. Still, I would point out that in economics, we learn how systems work - how one thing affects another – and that is exactly what a game designer needs to know.

A game designer is often in front of a spreadsheet with a large set of numbers. It's not just about determining prices, but sometimes it's about figuring out hit points, experience points, damage percentages, probabilities, and various character stats. So much of what a game designer does is surrounded by numbers. You could say it's about learning how to think like computer, but even analog games that don't need computers can need numbers. Many beginning game designers ask, “How do we figure out which numbers to use? There are so many things that need numbers.” The answer? By using mathematics.

Moreover, mathematics is truly a universal language. Even in first contact sci-fi movies, we try to communicate with space aliens using mathematics! If a game designer needs to explain how something will work to a computer programmer, then using mathematical equations is one of the best ways. If a game design has to be passed along to a second game designer, then finding mathematical equations in the documentation is such a relief, much better than seeing a bunch of numbers without any explanations. Simply put, mathematics allows you to express the relationships between sets of numbers in a very precise manner. And for game designers, it's best to be precise because the job requires you to know which numbers to use and on what.

This is particularly important to remember when you have loads and loads of numbers that are representing any number of things: weapons, spaceships, armor, potions, psi powers, etc. Since there are newb items or powers ranging up to elite, this means there are number sets. If the game designer finds out that one of the Level 1 items is too strong, then it is much easier to readjust the game balance when all the relationships are known. The entire number set may have to be evaluated and tweaked. You will want to know right away what other numbers are affected by that one change.

The importance of mathematics to game design sometimes comes as a surprise to beginning students. They may have thought of game designers as the “idea people,” but they did not really know what “idea people” actually do. Turning a game idea into reality requires more than hand-waving, especially when there are lots of numbers involved. Game designers can use mathematics to clearly specify their designs.

In short, love math and love games!

Sande Chen is a writer and game designer whose work has spanned 10 years in the industry. Her credits include 1999 IGF winner Terminus, 2007 PC RPG of the Year The Witcher, and Wizard 101. She is one of the founding members of the IGDA Game Design SIG.