The Short Version Is That Rekkon Is Right
So Theorist said this, and Rekkon said this.
I won’t reiterate either post; you’re all literate. But I pulled down Rekkon’s data and played with it for a little while. What he did was called a Wald-Wolfowitz Runs Test, which is useful for… uh, I’ll skip most of the statistical mumbo-jumbo for now. But Wald-Wolfowitz isn’t the best tool here because our data are really nominal—there’s no particular order to the faces, so they don’t have a “middle”, so it’s hard to say whether a die result is greater or less than the mean.
So I ran a different kind of test on the same data set Rekkon generated. I computed Cramer’s V, which is closely related to Pearson’s chi-squared test. Essentially, what this does is spit out a value between 0 and 1 that indicates the level of association between two variables—in this case, between this die result and the next die result. (If you know what a correlation coefficient means, Cramer’s V is the same sort of indicator.) Cramer’s V is preferable to a chi-squared test because they tend to break down with large samples like this one.
Here is the worksheet I used. The association between this die result and the next die result, on a scale from 0 to 1, is 0.03.
So what I found is that results are not clumping together in Vassal, or at least not any more often than you would expect in a random sequence. I didn’t compute a p-value for Cramer’s V, because although some statistical packages will do it, it’s difficult to do by hand. But 0.03 is a very small value, and indicates that there is no real association between this die result and the next die result.
And I even double-checked: there’s no association between the die faces (crit/hit/focus/blank), nor is there an association between the actual die results (1/2/3/etc.)
Does this mean Vassal shouldn’t be changed?
Well, mu0n is right: nothing Theorist has proposed seems likely to break anything, and if it’s perceived as a fix or if I’m simply wrong, it’s to the good. But I’ll double-check the new module when it’s available to confirm the result.
