Wednesday, March 2, 2011

I was told there'd be no math!

Recently the Distinguishing RPGs chart came to my attention, and it has kind of a cheap dig in it against two systems I rather like. Worse, the dig is not just unfair, it's done for the wrong reasons.

The Flowchart of Wonder

The chart works like this: You start at the green diamond near the center of the graph. You answer questions and make decisions until you get to the system that's "right" for you.

Cool in theory, but the chart does take liberties, and it busts unnecessarily, like I said, on two systems that I like. It busts on several others, it turns out, but these two in particular seem not only unfair but discussionworthy.

Forest for the trees, or needle for the haystack?

The joke runs like this: One of the first questions out of the main diamond is genre. If you say genre doesn't matter, it asks if you're serious. If you say yes, it gives you a math problem. If you can identify it as a differential equation, it points you to the HERO system. If you identify what's wrong with the differential equation, it points you to GURPS.

Not much of a joke, is it?

No, not really. But I took offense. Partly because I've never really had to do that much complex math in either system, but mostly because I see the simplicity or complexity of a game system being its primary draw as folly.

That's not to say that you can't like or dislike a game for its "simplicity" or its "crunch," but to make that the number one reason for preferring or pooh-poohing a game is dumb.

The Hidden Double-Edged Sword of Complexity

Complexity in games has the potential to be controversial, if only more people thought about it. Sometimes it serves a purpose, and sometimes it doesn't. It can be introduced intentionally, in measured doses, or it can spring up quite unexpectedly, leaving slack jaws and smashed ideas in its wake.

Case in point: The most complex math I've had to work with in a game was in In Nomine, believe it or not. This is a system in which attributes and skill ratings tend not to rise above 6 or 12. It's a level of simplicity that I've claimed to find refreshing in some games, but I'll get into that later.

If you're not familiar with it, In Nomine is about angels and demons doing battle secretly in the mortal realm—humans were not supposed to know about them. This job was made more complex by the inclusion of a mechanic whereby one celestial could "hear" another entering, leaving, or doing something to affect the corporeal realm.

That formula didn't immediately destroy In Nomine's simplicity, but it did set the charges and the tripwire:

The basic range for detecting celestial intervention in the workings of the Symphony is equal to the Perception roll's modifier in yards, times the perceiver's Celestial Forces.


For every additional [Disturbance times Forces in yards] that our average celestial is standing from ground zero, his Perception roll is reduced by 1—from four football fields away, the average angel or demon still has a good chance of detecting a human's untimely death.

In Nomine rulebook, p. 55

It reads straightforward enough, but it's rife with complexity. Here's that formula fully written out:

[Mathematical equation: c equals P times D minus quantity R divided by quantity D times F.]

...where c = the chance of detection on 2D6 (you roll 3D6, but that third die isn't for success or failure), P = the Perception attribute of the perceiver, F = the Celestial forces attribute of the perceiver, D = the degree of disturbance, and R = the range to the disturbance in yards.

That'd be kind of okay during play, but the enterprising GM who wants to see if a plot would wash beforehand would want to do some "reverse-engineering" to make sure something gets picked up or wouldn't go detected. To do that, you have to be able to solve the equation some other ways.

The GM might want to know how far away someone has to be to have a specific chance of hearing the Disturbance. In that case, solving the formula for R isn't that difficult:

[Mathematical equation: R equals D times F times quantity D plus P minus C]

Would you like to know how high someone's stats have to be to have a specific chance to detect a given disturbance at a given range? That isn't quite as useful since the Perception attribute (P) and Celestial Forces attribute (F) are kind of joined at the hip. Still, if you're looking for that information, solving the formula for P isn't too bad:

[Mathematical equation: P equals D plus quantity R divided by quantity D times F, minus C

And F isn't really so horrible:

[Matheatical equation: F equals negative R, divided by quantity D times quantity c minus D minus P]

But did you notice how, in each of those equations, D appears twice? Let's say you want to know how much Disturbance someone would need to generate before someone of a specific attribute level has a certain chance of noticing you at a given range. Here comes the punishment for that hubris:

[Mathematical equation. D equals c divided by two, minus P divided by two, plus or minus the square root of, I can't do this. I can't read this eyetest. I'm sorry, but it's just too hideous to contemplate, much less speak aloud.]

In case you don't remember your high school math, yes, that is indeed based on the quadratic equation. So if you want to figure out how much a celestial can get away with, or how little you need to guarantee detection—the most useful formula of the bunch if you're into plotting out an adventure beforehand—this is how you go about it. The complexity was hidden within a formula that looked kind of simple.

So wait, what was the point of all that?

It was an anecdote, food for thought about several different issues.

Complexity can spring up seemingly out of nowhere, and this makes it hard to manage. The formula started out so simple when it was just about a chance of success—a base chance, and a modifier for range. But a few gyrations later, and boom goes the algebra.

When complexity finally happens, it can have strange and/or tragic effects on play, or it can be removed from play. After working with that formula a few times, it's likely a few GMs cut it out of play completely. Or some GMs would figure that you only have to worry about the best character of the bunch. Or some GMs would use a spreadsheet to handle multiple values.

"So, do I hear that disturbance or not?"

(GM looks at formula. Eyes glaze. Drool seeps from mouth. Hold several seconds, finally looks up) "Yeah, you hear it."

Complexity during play is bad, but complexity before play, when the GM is preparing the adventure, is a bit more tolerable if he's willing to go through that rigamarole and/or a programmable calculator.

But mostly, this came from neither HERO nor GURPS—in fact, it came from a game which, by and large, is simpler than either of them. So if you search other games, you might come across corner cases even more egregious than this.


  1. Elementary chaos theory. Simple rules can create infinite complexity.

    Also, that chart seems suspiciously snarky for something meant to be helpful. I wouldn't take it seriously.

  2. I wonder what it is about flowcharts that encourage that sort of passive-aggressive humor. Admittedly when I saw the joke in the "So You Need a Typeface" flowchart, I giggled like a maniac.