- Frivolous. Some are clearly more interested in humor than any serious typology.
- Anecdotal. These typologies sort players into groups based on experience and perceived common traits. However, there is no correlation between them implied. For example, one group may not be the opposite of another. They are very qualitative. Some examples might be Robin Law's typology, or this typology from the 80s.
- Systematic. These typologies set up defined axises, then define the player groups based on how they fit to the axis. An example is the Bartle classification (Player/World vs. Action/Interaction) or the WOTC survey (Long Term/Short Term vs. Tactical/Story).
There are many real-world typologies for people that describe their temperament. You may be familiar with the Myers-Briggs Temperment Indicator, Keirsey Temperment Sorter, the Big 5, Enneagram, or many of the other ones. Because of my penchant for archaic systems, I like Galen's old theory of "Humorism" which many of the other four-category systems evolved from. I also like that the four categories are easy to grok; using shades between the categories gives you up to eight.
Humorism relies on the interaction of two factors. One measured "length of response" (rapid & hot vs. slow & cold) and the other measured "duration of response" (long & dry vs. short & wet). For example, a choleric, who has a short (hot) and lengthy (dry) response, may be quick to anger and long to hold a grudge. Of course, the four humours were correlated to the classical elements, and all the correlations that entails. Modern psychology has related the former axis to either emotional stability or to task vs. relationship orientation. The latter axis has been related to extraversion vs. introversion.
I think that you can relate these to the Bartle and WOTC typologies as well. Bartle himself admitted that his original pairing of typologies to card suits was done without knowledge of the ancient correlations and that tieing his theory to humourism is viable. So, how would you relate them?
- EXTRAVERT/INTROVERT: I link this axis to the Bartle Player vs. World focus or the WOTC Short vs. Long term. In this linkage, extraverts tend to be interested in the other players and short term outcomes. Introverts tend to get absorbed in the imaginery world and require less immediate stimulus.
- TASK/RELATIONSHIP ORIENTED: I have linked this axis to the Bartle action vs. interaction and the WOTC Tactic vs. Story distinction.
- CHOLERIC (FIRE): Power Gamer (Short Term Tactical) / Killer (Acting on Players)
- MELANCHOLIC (EARTH): Thinker (Long Term Tactical) / Achiever (Acting on World)
- PHLEGMATIC (WATER): Storyteller (Long Term Story) / Explorer (Interacting with World)
- SANGUINE (AIR): Character Actor (Short Term Story) / Socializer (Interacting with Players)
What does this suggest about each "element's" powers?
- FIRE: This school should focus on short term effects. It should also allow action on the other allied player characters. One might think of certain leaders from 4E that can actually slide their allies around, give them attacks, and so on. You're helping your team, but you are in the driver's seat. One can also imagine some mechanics that allow Fire to get their team involved in quests -- thus giving the Fire focused character a limited amount of control over the background/narrative of the other characters! The player is likely task oriented and should be rewarded for completing somewhat shorter term tasks.
- EARTH: This school focuses on long term effects. It should allow action on the world. This sort of player would likely enjoy controlling fiefdoms and larger numbers of obedient soldiers or hirelings. The player is likely goal oriented and should be rewarded for achieving long term tasks.
- WATER: This school also has a long term focus, however, unlike earth, it is expert at interaction with the world and story rather than imposing action. Water is about learning, divination, and subtlety. The player is likely relationship oriented and should be rewarded for developing genuine long term relationships.
- AIR: This school, like fire, is short term in focus but instead of being focused on imposing or acting on the other PCs it focuses on interaction with them. An air character might be interested in conducting multiple quests, coming up with new and novel ways to communicate or share experiences and information. The player may actually be interested in interacting out of character with other players or be particularly theatrical. This character should literally be a breath of fresh air, and the player may want to be able to act somewhat irresponsibly without dooming the party or their character. The player should be rewarded for entertaining and engaging others.