It’s surprising how much have we learnt and advanced in video game technology, compared to the little advance that’s been made on the science of gaming itself: analysing the mechanisms of interactive entertainment and, more specifically, the nature of gameplay. A few luminaries such as Chris Crawford or Sid Meier have proposed formal definitions of gameplay (usually involving the amount of choices/decisions the player can actually make in the course of a gaming session). Still, we haven’t moved much beyond that.

So, in an effort to contribute, I’d like to express some ideas on the mathematical foundations of gameplay, so these theories help build better ones and, thru them, further advance what I consider to be today a minimal amount of knowledge.

Gameplay is not a one-dimensional property: the same way comparing an eagle with a cow doesn’t make much sense, comparing the type of gameplay exhibited by a game like The Sims with Tekken is not a very good idea: eagles and cows are not the same kind of animal, the same way Tekken’s gameplay is not the same kind exhibited by The Sims. So, one interesting question is: how many of these “kinds” are there? The same way we have rodents, felines, birds, etc. How many primitive gameplay types are there?

In my first analysis, I’ve reduced the count to three types, that actually cover all games in the market today. The more time I spend thinking about it, the more convinced I am that all game production until the year 2002 or so can be described with three primitive elements. As these “types” or “elements” can be freely combined to create unique blends, I’ve decided to call them Dimensions of Play, as in Vector Space Algebra: the same way a point in 3D space is defined by three numbers, we will describe a game as a combination of three values, representing each one of the primitive gameplay types. Let’s now review these dimensions one by one.


The Narrative Dimension

The Narrative Dimension (N) is strong in those games that actually tell stories, have characters, a flow of events through them, etc. One might think all games have a narrative dimension, but examples like Tetris make us forget that idea. Narrative is usually expressed both in terms of a back-drop setting and an event flow. In the popular Half-Life, the setting would be Black Mesa’s military base, and the event flow would be the accident that puts Gordon Freeman’s life in threat.

Some authors (Ernest Adams being an advocate here) have complained that event flow in games often kills gameplay, as it reduces the amount of choices to be made by the player. That’s the reason why many games try to provide rich settings, but reduce the actual script to the bare minimum. Whichever the case, the narrative dimension is useful to create tension, addiction through mystery, and evasion to players. A strong narrative will have the player wanting to learn more about the story and, while doing so, will provide a very convincing sense of immersion.


The Competition Dimension

The second dimension is present in those games that feature some form of competition, whether it’s against human opponents, the CPU, the player himself, etc. So, all sports games, most action titles, and many other game types are in fact variations of this dimension. Obviously, we can combine the two dimensions we have already explored. Take a look at the following list:

Quake III: non-narrative, competitive
Splinter Cell: narrative, competitive
Myst: narrative, non-competitive

One could argue that all games are essentially competitive: we can always compete with our friends to discover who has completed more screens, reached a higher level, etc. Still, for the sake of this article, we will focus on competition that’s built into the game system, not outside of it.


The Control Dimension

The third and last dimension is the control dimension, which is present whenever a game exposes a dynamic system to the player, and the fun consists in tweaking such a system to evaluate the results. A real-world example of such a system would be a model railroad system: we can choose which trains go where, using switches and controls.

Most strategy games have strong control dimensions. In Age of Empires, for example, we oversee an army, managing its resources, battles, etc. God Games are another type of control-centric titles.  Again, we can mix and blend as needed. Here is a complete chart of the three properties, along with some games that represent each group:

Quake III: non-narrative, competitive, no control
Splinter Cell: narrative, competitive, no control
Myst: narrative, non-competitive, no control
Warcraft: narrative, competitive, control
Age of Empires: non-narrative, competitive, control


Completeness of the model

I exposed this theory four years ago in an informal chat and, since then, no game has defied the 3-dimension rule. Only some recent advances in mobile platforms have spawned new gaming systems that will one day or another need more dimensions to be added to the system. Still, so far all games can be described with these three properties. It makes no real sense to evaluate each one of them numerically, as these are slippery concepts. Still, most people will agree to subjective “low”, “mid”, “hi” ratings for each one of them.

Another interesting conclusion is that very different games still exist inside a fixed formula. Take, for example, the definition:

Narrative: mid
Competitive: high
Control: none

Which is very popular in game consoles. The same category fits games such as Half-Life and Mario, which are indeed very different. If you think about this specific example, the elements that set both games apart are:

- violence level and gore
- use of suspense in the narrative
- rhythm (Mario is generally considered a faster-paced game)

In the three cases, these differences mark an age target difference: Mario is rated E for Everyone by the ESRB, while Half-Life is rated R. Still, a gamer that enjoys Mario’s gameplay will likely enjoy Half-Life. Now, imagine comparing Mario to Age of Empires: we simply cannot extrapolate if a gamer might enjoy the latter, based on his opinion of the former. Clearly, both games advance in different directions or, in mathematical terms, the dot product of their gameplay values (and thus, the angle between them) is too big.


Social gaming

Some recent games have somehow made me wonder if a new dimension of play might be emerging in recent times. The best way to picture it is to think of the kind of games that are currently being developed for cell phones. As an example, let me tell you about a hypothetical game, called the Dating Game.

The Dating Game would work over Bluetooth enabled devices (PDAs, cell phones, etc.). The game would be started when we entered a socially active event (like a party, etc.). At load-time, we would enter a profile of ourselves into the game engine, which would store it using personality tests. Then, using the Bluetooth protocol, the device would ping other devices in the vicinity, trying to find people with matching characteristics, so we could actually meet them.

When I heard this idea about six months ago, my whole 3 dimensional gaming theory shook. The Dating Game is playable (we make decisions on which type of profile we will enter). So, let’s try to characterize it in each of the three dimensions. First of all, the Dating Game has no narrative at all. In fact, many current-generation mobile game are just this: data managers, menu systems, etc. which are triggered by SMS or WAP.

The game has a competitive edge, but it actually escapes the game system: we can compete with friends on who builds the best profile so we find the most matching people. This is real-world competition based on our virtual-world choices, but note how the competition is not built into the gaming system.

Finally, the game does have a strong control component: we influence the system (creating the profile) and watch it evolve (by receiving matches). So, we could describe this game as:

- Narrative: none
- Competition: mid
- Control: high

Which is the kind of profile we would also apply to a game like Age of Empires. Still, both games cannot be considered as belonging to the same global family: our dimensional system is not perfect for these games that mix real and virtual, and become social activities.

I suspect a fourth dimension of play might need to be added for completeness, so we have narration, competition, control and socialization. Funnily enough, these are the four typical ways human beings use to have fun on their free time: we read books or go to the movies, we play sports, we create and design stuff, and we like to be around people.

While this is an obvious conclusion, it’s funny how games slowly mimic on a virtual scale the formulas of entertainment found in classic anthropology. I really doubt in 50 years time we will only have 4 dimensions of play: probably there’s some more. However, the process of classifying them in groups will probably be as interesting and educational as learning to distinguish mammals from birds and fish.

Daniel Sanchez-Crespo
Barcelona, Sept, 3rd, 2003