Finally, making a choice implies that one has the means to act upon it. It would be of no use to the player to decide where to go if Mario couldn't run or jump. So action is also one of our variable characteristics.
A series of interesting choices implies a structured experience, an overarching context. Such experience can be qualified by how it changes the player (self) or his relation to others (social). If the experience didn't affect the player, it would just be wasted time and energy.
Lastly, if the choices are interesting, they're neither boring nor trivial. They're challenging. In A Theory of Fun, Raph Koster posits that fun stems from dealing with challenging situations and acquiring skills to solve them. Similarly, Daniel Cook tracks the player's mastery with skill trees.
This list of concepts needed some structure to become useful. It eluded me until I remembered Will Wright's amazing Dynamics for Designers lecture at GDC 2003. His ability to describe the possible dynamic systems in a neat multi-dimensional taxonomy was eye-opening. I decided to organize these concepts into orthogonal families that would provide the axes for various tables. The first one describes the categories of variables:
Action is the level of the body, the visceral, immediacy and short feedback loops.
System is the level of the mind, the cognitive, logic and plans.
Self is the level of the soul, reflexive thoughts, goals, private experiences and inner changes.
Social is the level of the community, shared experiences, rituals, culture and relationships.
Freedom deals with measuring choices and opportunities for choices.
Mastery deals with measuring skills, their acquisitions and their uses.
Data deals with measuring content, information, rules and real-life objects.
Freedom at the Action level: Everything that empowers or hinders the player while making short-term choices. Action opportunities (An enemy presenting its weak spot, Finding a key in a Zelda dungeon). New tools allowing new interactions (Zelda's boomerang or grappling hook, Mario's flying cap). New abilities (Increased health, Increased strength).
Freedom at the System level: Everything that empowers or hinders the player while making medium to long-term choices. Avenues of exploration (Free-roaming gameplay), clear goals (Getting a quest), letting the player experiment with the rules and creating safe environments where to do so.
Freedom at the Self level: Everything that empowers or hinders the player while making choices about the nature of his experience. Strategic and creative thinking (Specialization, Self-imposed limitations, Speed runs). Content creating tools (Level building, Customization, Machinima).
Freedom at the Social level: Everything that empowers or hinders the player in his relationship with other people. Facilitated multiplayer experience and modes. Sharing content and experiences. Active community. Community support and community management tools. Social image conveyed by the playing experience (Coolness, Geekiness, Weirdness, Novelty, etc.).
Mastery at the Action level: Everything that empowers or hinders skill acquisition and skill use at the immediate or physical level. Athletic skills. Rapid appreciation of the parameters of a situation and appropriate response (which can imply the forming of a medium-term plan). Training. Immediate feedback. Affordance.
Mastery at the System level: Everything that empowers or hinders cognitive skill acquisition and skill use. Giving the player the level of control he needs to act on his plans (agency). Providing information about the constitutive rules (see below) (Tech tree in Civilization, Graphs in SimCity). The ability to exploit these rules. It's the dynamics in Robin Hunicke, Marc LeBlanc and Robert Zubek's MDA framework.
Mastery at the Self level: Everything that empowers or hinders skill acquisition and skill use that allow for better control over the game experience. Exploiting metagame data (Reading a walkthrough). Ascribing own meaning to the experience. Feedback about the learning process (Being encouraged, congratulated, rewarded, mocked, stirred up, etc.).
Mastery at the Social level: Everything that empowers or hinders skill acquisition and skill use at the social level. Exploiting the metagame. Learning to bluff. Shaping one's image in the community. Being invested with and performing a role. Competing for ranking. Group play (Guild raids). Being a mentor.
Data at the Action level: Information that takes form in the game, that can be interacted with (Health pack, FFVII's materias). Persistent information at this level can take the form of a collection (Pokémon's Pokédex). Katie Salen and Eric Zimmerman in Rules of Play define the operational rules as what we usually call the "rules of the game", the ones you have to know to be able to play (The ranking of hands in poker, Press A to jump, No credit in RTSs or RPGs).
Data at the System level: Information about the game state. Player preparation (Setting-up the Tetris board so as to clear four lines with an I piece, Equipping a dragon-slaying sword before fighting a dragon). The constitutive rules that, according to Salem & Zimmerman, describe the inner workings of the game (AI, Physics, Catch-up behaviors). The player doesn't know them at first but he can learn or guess some of them. It's the mechanics in the MDA framework.
Data at the Self level: Information relative to the relationship between the player and the game, to the act of playing. Trophies, traces left by the experience or created by the player.
Data at the Social level: Information governing the relationships between the player and other people (not necessarily players themselves), as it pertains to the game. Metagame information (Strategy guides, Forum discussions about the game, Fan fiction). Badges and honors linked to reputation and achievements. Salen & Zimmerman's implicit rules, the rules of etiquette, of the magic circle, that should be respected without having to mention them. They include social rules (Don't be a jerk) and game-specific taboos (Don't spy on someone else's monitor in a competitive multiplayer game).
Second caveat: These are not our variables but the categories they belong to. A given game can thus have an influence on several variables in the same category, linked to different processes or systems. For instance, Freedom at the Action level in GTA handles both the choice of paths and of vehicles. This means that this model is still incomplete, each cell being its own dimension. However, I believe this is the most detailed generic model using these variables. A more detailed model would require specific sub-categories for each cell, a work that is well beyond the scope of this article.
Although this table went through many revisions, I cannot affirm that it spans the whole of game design space. After all, I have only experienced a limited subset of the currently known games. However, I seem to be able to describe the effect of any game interaction I can think of as variations in one or several variables belonging to these categories. Whether I'm on to something or have thoroughly blinded myself is for you to judge.