Diving into the Numbers

Though in my day job, I’m a software engineer, the math associated with most types of engineering has never been my strong suit. I use computers to do a lot of the number crunching for me, and that always ends up with interesting results. Because of that, it becomes more about algorithms than results most of the time. But occasionally I have to look at the numbers…

So, with the Inverse20 system that Aliens & Asteroids is using, I’ve started using the AnyDice.com site to help me analyze a few things.

Here are a few things I’ve discovered:

  • Each attribute uses 6+2d6 as its base. This leads to a reduced range of numbers for stats, with a low of 7 8 (corrected, thanks Doug!) and a high of 18. The mean value is 13, which I find intriguing. I had been using 12 as my “default” value but after this investigation, it might shift to “lucky 13.”  http://anydice.com/program/e36
  • Our Advantage (2d20, take lowest) and Disadvantage (2d20, take highest) has a mean value of 21. The odds that you’ll get two 1s or two 20s is 0.25%. I had to look that up after two players at different ends of the table each rolled a 20 and failed a task — back to back. The odds were insane. http://anydice.com/program/472

How does this help me?

Well, I was recently asked about the system and how it scales the difficulty for different tasks. The base idea for the system is that you roll a single d20 (or two with Advantage or Disadvantage, as stated above) against a target number, which defaults to the appropriate attribute for whatever it may be. For instance, if you’re rolling to shoot a gun, you use your Accuracy as the target. If you’re straining to lift something heavy, you use your Toughness. If you’re trying to remember something useful in the heat of battle, you rely on your Education. And so on.

The problem lies in the fact that we want there to be some variability. When you have a potential 19 for an attribute, the success rate is, as you might suspect, very high. As a result, we’ve decided to scale the attributes a bit.

Instead of 6+2d6, we’re going to go with 8+2d3. This puts us at a low of 10, a high of 14, and a mean of 12. When you add in an Origin bonus, that goes to a max of 15.

As soon as you add that wiggle room, the potential for not succeeding every time seriously changes. And it puts the onus more on a selection of traits. Having two dice to potentially get the value you seek vs. just one becomes the edge.

We’ll give this a try at our next playtest and see how it works.

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