Variance Supplemental 2: SotC (Wonkish)

Introduction

This is the second supplement to the Variance and Game Design article. While there are some new observations, it covers much the same ground as the first supplement but for a different system, Spirit of the Century. So if you haven’t read the first supplement you should do that. If you have and are a glutton for punishment then this article is for you.

The System

For my first test I chose a system I was familiar with and had some old questions about. For the second test I chose Spirit of the Century (SotC) because it is a game I haven’t played but really want to, due to some cool sounding mechanics. My biggest reservation about the game, however, was that combat would be heavily influenced by skill level compared to non-combat rolls. So, I looked at SotC mostly to satisfy my own curiosity. Continue reading

Variance Supplemental: Combat (Wonkish)

Introduction

In my post about variance in game design I discussed the effect of rolling multiple times for combat resolution and how this reduces variability of combat results compared to non-combat results. This was supported by some simple logic and probability. However, I was interested in getting some actual numbers to back up that hypothesis. Herein I present the results of one of those tests. Now, the variance article was written to try to present the concepts of variance to a more general audience. No such attempt has been made here. You have been warned.

The System

In order to get a more accurate idea of how skill levels determine success in combat I conducted a Monte Carlo analysis of Feng Shui. I chose to look at Feng Shui because I have a fair amount of experience with the system and one of the things we always complained about was that a point of combat skill seemed as valuable as 3 points in a non-combat skill. Thus, I had some idea of how the results would turn out and was curious as to how close our gut interpretation of the difference between combat and non-combat skills would be to the numbers. Continue reading

Variance and Game Design

Variance: or

How Common Is Average Anyway?

Introduction

Most games incorporate an element of chance, usually with dice, though others use cards, coin flips, etc. While we are familiar with the concept of mean or average of a roll (a measure of central tendency), one aspect that often seems overlooked as designers search for a cool or easy to use mechanic is the question of variability, or how often do you get the same or similar results from the mechanic. The most commonly used measure of variability or dispersion of results around the mean is the variance. I think that it is easiest to look at an example.

Figure 1 shows the resulting distribution of four mechanics with very different probability curves but very similar average values. The possible rolls are given along the bottom while the lines show the percentage chance of rolling that number. The famous twenty sided die, 1d20, is shown in blue and every result on the die, from 1 to 20 has an equal possibility of occurring of 5%, resulting in an average roll value of 10.5. Two d10 added together are shown in red, with average total of 11. Three d6 added together are in green, average total of 10.5, while the black line shows a mechanic where the value is “Always 11”, thus the average is also 11.

Continue reading

%d bloggers like this: