Hello all. I wanted to share some of the “fun” I had in refining my basic mechanics for my game system. Or maybe refining is too gentle a word – here's a story about the hell I went through in ripping my primary game mechanic out of the game's chest cavity.

This later grew up into my game, Factions.

Goal: I wanted my mechanic to allow for a wide range of success, to be pretty incremental, and to truly reward the better character. I didn't know the concept at the time, but I wanted the game to be “realistic” (Simulationist), or at least to adhere to the world model I had in mind. I also wanted it to be a 3-tiered tree (general attribute, more specific area of knowledge/skill, and specific skill/expertise), with heavy weight on the last area. What I had was:

Attribute (1-5 scale) + Talent (0-15 scale) + Skill (0-20 scale). I had 10 Attributes, between 2 and 8 Talent areas beneath each Attribute, and 2-8ish Skills beneath each Talent.

For static difficulties, the character had to beat a total (5 for super easy, 10, 15.... up to 60). When two characters competed, they just did a roll off and the higher roll won out.

How much a character beat the difficulty/the opponent made for better-than-expected success.

For a randomizer, I added a 1d20 roll. So I had a basic range possibility of 2-60. It didn't seem too bad when 2 characters were fairly evenly matched (within about 10 of each other), because the randomizer didn't seem to make that much difference... the better guy ended up with a consistently better end total, but not all the time.

Then I hit the land mines.

1): A pretty unskilled guy simply couldn't hit a moderate (25 or more) difficulty to save his life. Or, for that matter, even come close to touching a highly skilled person in a roll-off. There was no chance, so no drama, no fun.
2): A highly skilled guy simply couldn't fail. As soon as his base was within 3 of the expected difficulty, success was pretty much assured. And when the base was above the difficulty, there was no point in rolling at all. Again, no drama, no fun.
3): The numbers were too big to be convenient. Yeah, adding 33 and 18 isn't all that hard, but it annoyed me. It slowed game play down.
4): Character creation was hellish. I wanted a point build system, and for there literally to be 150+ Skills, so players could make pretty much any kind of character they wanted. But divvying up 300 or more individual points in Skills was a pain.
5): The mechanic itself seemed flat, dull, uninteresting. It had no fun factor.

So I tore it all down and tinkered for a month.

Eventually, I simply tried cutting all my values in half, with a 1d10 randomizer. It was the best I could do without blatantly copying some other game design. (Attributes 1-3, + Talent 0-7, + Skill 0-10, + 1d10). This actually worked out pretty well, enough to use in a live action run at a small, local Con (JonCon, for any Twin Cities residents). It had the added benefit of being workable with playing cards (1-10) in the player's pocket, instead of a 1d10 (I was into LARPing at the time, and wanted the game to be playable in larp or tabletop with NO mechanics humps or serious conversions).  I was getting closer, but it still wasn't right. I didn't exactly know why at the time, but I later figured out it was partly because my randomizer created a Linear result, as opposed to a Bell-Curve result.

But I didn't know it at the time. I was an English major, and couldn't properly communicate how I wanted the mechanic to behave to my math-savvy friends. So I tried again. This time, I spent about two months simply drawing curves on graph paper, inputing various base totals, and trying to find results that got me closer to my Goal.

Finally, I noodled out that I wanted my less-skilled characters to get less results from their randomizer than the more-skilled ones. I also figured out that I wanted my more-skilled characters to have dependably good results from their randomizer, but to keep things from being a done-deal. I experimented with different dice combinations and played with the graph paper some more.

At last, in a burst of caffeine and nicotine, I stumbled onto my answer. I wish I could say I coldly calculated all of the mathematical possibilities, but more-or-less, I was pretty much throwing darts blindfolded and got lucky. Or intuitive. Both, really.

The more skilled a character, the more dice they would roll. But instead of simply adding up all of the die totals, they'd simply apply the highest one, and discount the rest.

Within minutes, I had refined my mechanic to Attribute (1-5) + Talent (0-7) + Die Result. And Die Result came about from the following:
Unskilled: Roll 1d6
Barely Skilled: Roll 1d10
Normal Skill: Roll 2d10, take highest.
Expert Skill: Roll 3d10, take highest.
Master Skill, Roll 4d10, take highest.

So really, I only had 5 Skill levels (Unskilled-Master), but the base gave me enough variation to keep me happy (and later, I reduced the Talent span from 0-5).

But now I had a system that fulfilled my Goals... because an Unskilled person just MIGHT get a better die result than a Master. Odds are really, really low.... but the possibility meant that die rolls contained drama. Later, I added even more drama (fun) to the mechanic, with Explosion and Crash results.

Explosion: If any die comes up 10, roll another 1d10 and add it to the first. Die can only explode once.
Crash: If the highest die is a 1, roll a 1d10 and subtract it from the base.

These gameplay tweaks added *more fun factor, but it didn't get completely crazy results. Explosions were really only likely for the highly Skilled, and Crashes were only likely by the Unskilled. Also, no matter how many explosions, or bonus results from secondary d10's there were, the Die Result could never be more than 20, so no one could roll above 30 without some additional tweaks or bonuses.

I changed my Static difficulties to a range of 3-25, and I had the mechanic I end up publishing.

Now, I *know there are easier routes to take than the tortured one I did. A better statistics background would have helped. Still, I know that I only got to stumble onto my answer by being able to conceptualize what I wanted the dice to do. That was the lesson I learned.

This reminds me of the struggle I had before settling on a mechanic for one of my games. It involved a trait you could choose, for which you rolled dice to determine the numeric effect. Originally, it was 1d10 per trait, reroll 1s and 2s. this gave a range, obviously of 3-10, which was acceptable for me.

Others were less inclined to take this trait because of the randomness; You could basically waste one or more of 4 trait picks and get 3 points, and this didn't sit well with some of my playtesters.

So I started fiddling around and discussing the idea. Someone (anonymouse, I believe was the user name he used) suggested something that I eventually adapted and adopted, but not before I futzed with it continually to make sure the desired results were what I wanted.

One thing that really helped me was basic knowledge of how to use Excel to set up formulae with random number generators. I created a single line, and replicated it over about 200-300 rows. I then used another formula to average the results, as well as to allow me if any results were above or below certain maximums and minimums I'd determined. By running the random numbers several times, and watching the average and max/mins, I was able to get an idea for what the results were, and thereby make a judgement.

Eventually, I made one final tweak (involving a maximum number of rolls), but I was satisfied with the result.

Some of my playtesters still weren't satisfied, but more on the principle than because they thought it was unfair or not worth it.

Glad I'm not the only one.

I got hung up a lot more on the *shape* of the results, instead of the average, min, and max. Here's an example of the things that keep me up at night (the statistical shapes, not the subject matter).

http://www.mwilliams.info/archive/2005/01/men_and_women_are_different_2.php

Scroll down a little bit, until you hit the graph.

Both groups have the same average performance, but the "men" category has a longer head and tail (for lack of knowing better terms) for the curve. The "women" category has a higher peak, and a shorter head and tail.

For some types of rolls, I want a long, flat performance (like rolling percentile, or a single die). Every number has the same chance of being rolled as every other number. And, sometimes I want a higher peak, with more bunching toward the middle; like Gurps use of 3d6. The more dice cast, the more likely that performance of any single roll is going to fall close to the average.

Consider the difference between the three mechanics:
A): 3d6
B): 1d20
C): 2d10

In A, you end up with a total possible range of 3-18. However, odds are really good that result is going to fall between 8 and 12.
In B, you end up with a total possible range of 1-20. Each result is just as likely as any other. To me, this is too unpredictable to use for most types of skill tests, unless the base is quite a large number (such as, Skill Base range of 0-50 + 1d20, vs. difficulties of 10-70). If the Skill Base range is much lower than that, too much of the end result is from this totally random factor. Not great in a Simulationist style of game.
In C, you end up with a total possible range of 2-20. You're going to end up with a bunching result between A and B.

And that's just for the random factor. Then one has to decide on the base total vs. randomized range. Or, ask yourself, "How much of the end effect do I want to be because of Skill, and how much because of random chance?"

Let's use a raw game mechanic of Skill Level + 3d6, vs. a Target Number. With a Skill Level range of 1-5, you can expect to add between 8 and 12 to this number. Because of this, you won't see much difference in how well a Skill Level 1 rolls out, compared to a Skill Level 5. And, if you make Skill Level 5 equivalent to "best in the world" as a skill level, you're going to disappoint the player who invests so heavily in a character trait, only to have flaky results in play.

Go to far in the other direction (say, with Skill Level range of 1-100, +3d6), and there's very little random effect going on. Also, a Skill Level *difference* of 10 or more means it's pretty unlikely that the lower Skill Level will ever outperform the higher Skill Level. Also, a difference of more than 15 becomes impossible to overcome.

So, designers have to ask themselves questions. How "impossible" do I want to make it for an unskilled individual to outperform the most skilled individual? Do I want to make it possible at all? How often do I want said situation to come up in actual gameplay? And so on.

*Then* we can get into the mechanic effects of "special situations." Like a natural 20 always hits! Or rolling a minimum effect on all dice always fails! That sort of thing.

Yeah, those unexpected consequences can be a real hassle. In the same game I mentioned above, I had certain stats with beginning values of 1-5, and other stats with randomly rolled values of 1-10. Both sets of stats were essentially rolled for the same types of things... I think the idiocy of this should be readily apparent. I kept this system for quite a while through several playtests, and the longer it went, the more I realized how unworkable it was. But due to the circumstances (the origins of the randomly rolled stats were external and somewhat fleeting) I couldn't find anything that worked that would fulfill my goals.

Eventually, I came up with the system that I'm using now, which involves a roll x amount of dice -vs- y difficulty, where x is equal to the lower based stats, and y is equal to the randomly rolled, more ephemeral stat. I realize that there are those who think that variable number of dice and variable difficulty is a bad design choice, but I typically like the outcomes I've seen with it. I'm not entirely sure how well it'll work for this, as I've not had a great deal of opportunity to test it, but it has been better thought out and is less arbitrary than the last system.

Have you actually plotted curves for your results? I've not really attempted that, so much as I use some tools to lay out some results, and then use a zen approach to determining if I like them.

I myself haven't plotted out the curves, but one of my playtesters, who is smarter than I am (note: use playtesters who are smarter than you are!), and better at math/statistics than I am (note: see above note), charted out some things and tried to explain it to me. I'm pretty sure I got what he was saying, and was pretty sure it confirmed how I had "Zenned" it out on my own.

The mechanic did some interesting things where I wanted it to, was consistent where I wanted it to be, and was unreliably random where this was appropriate. Made me happy.

Can you run me through a mechanic example for your game? I'm curious to see how things roll out.

-a-

In the process of trying to write out an example, I've actually uncovered a gap in the mechanics. Once I get that figured out, I'll be glad to return here and give you an example.

...thanks!