Statistics-Based RPG Statistics

The last post looked at some basic mathematics to show why RPG character statistics do not reflect attribute measurement in the real world. We were left with a basic quandary-- if numbers don't work for attributes, then what are we left with?

Fortunately, another class I took comes in handy for explaining a feasible alternative. Introductory statistics teaches the concept of levels of measurement. Depending on what you're measuring and how you are able to do that measurement, there are different operations available on the resulting numbers. For example, if you start classifying objects by color-- red, green, blue-- it is possible to count how many of each you have. You can say what the most common color is (the mode in statistics), but, reasonably enough, you can't say what the average color is. That type of measurement, where things are named with a label, is called nominal.

The next level is of most concern to this discussion. At the ordinal level, measured items can be put into order. There is no detail given as far as the distance between two items in the list, just that A is bigger or better than B. This is the type of measurement done for standardized tests. The test-taker is pitted against other test-takers and given a percentile rank that tells where in the order they fall.

For role-playing games, character statistics almost always come into play when the character is pitted against another character or a challenge in the environment. To use another real-world example, I knew a guy who was in the top ten list of Halo players on XBox Live. The system kept track of their performances and ranked them over time. He was obviously an extremely skilled and experienced player. I, on the other hand, played Halo once in a while and never really got past the stage of being frag bait for whatever experienced player I happened to materialize near.

Imagine the two of us were going to play head to head. In a normal timed death match there would be absolutely no way I would win. Some extremely unlikely circumstances would have to intervene, taking the game out of the realm of skill. For example, if my opponent had been awake for 3 days straight and could not focus on the screen, I might have a chance of killing him. If his controller started randomly changing his movements, I might have a chance. But aside from such outside "miracles" I would stand no chance.

Back to RPG land, a system realizing that character attributes are ordinal would rank all the characters from worst to best. The exact difference in ability between one and the next cannot be known exactly, but we do know who is better in an overall sense. All of the creatures in a current setting (say the adventure) that are capable of a particular trait can be put in order. If ranking intelligence, a small sampling might go: green slime, bugbear child, adult bugbear, Harak the fighter, Grazz the bugbear leader, Shandar the wizard, and the red dragon. Challenges requiring intelligence would be added to the same list, with their difficulty determining the position. So disarming the pole and pit trap may go before Grazz, while answering the ancient's riddle could go after Shandar.

What we end up with is a deterministic list of what any character is capable of. This becomes deterministic in the sense that without any extraordinary circumstances, the lower intelligence character or challenge will be defeated. Grazz or Shandar could disarm the trap, while Harak could not, and only the dragon could answer the ancient's riddle. While this might seem unsettling in games so wrapped up in dice rolling, another view to take is that it opens up the possibilities for strategy, quests, and other ways for the characters to beat the odds.

Imagine the case of Harak the fighter, alone, trying to disarm the pit trap. He is bewildered as he looks at the mechanism involved. But perhaps the inventive player decides on another route. He finds a nearby statue and positions it near the wall to provide cover. Then, he enters the bugbear lair and taunts the adult bugbear into following him, at a run, out into the hall. Harak ducks behind the statue as the bugbear lumbers forward into the trap. Harak watches as it goes off and slowly resets itself. In so doing, he has gained enough experience with that particular trap that he is now able to disarm it.

Of course, there are other implications to a game using this type of statistical statistics system. There are also ways to deal with randomness to introduce more player dice rolling. I will look at some of these issues in the next post.