To Be Finished for (i in 1:length(luckfactor)) { for (j in 1:length(selected)) { for (k in 1:R) { simulationresults <- tibble(Skill = runif(n = N, min = minscore, max = maxscore), Luck = runif(n = N, min = minscore, max = maxscore)) %>% mutate(Score = Skill * (1 - luckfactor[i]) + Luck * luckfactor[i]) luckyFew <- simulationresults %>% mutate(SkillRank = N - rank(Skill) + 1, ScoreRank = N - rank(Score) + 1, SkillSelected = SkillRank <= selected[j] * N) %>% arrange(ScoreRank) %>% head(selected[j] * N) results[[i]][[j]][k,] <- c(mean(luckyFew$Skill), mean(luckyFew$Luck), sum(luckyFew$SkillSelected), luckfactor[i], selected[j]) } results[[i]][[j]] <- as.data.frame(results[[i]][[j]]) } results[[i]] <- bind_rows(results[[i]]) } results <- bind_rows(results) colnames(results) <- c("Skill", "Luck", "SkillSelected", "LuckFactor", "ProportionSelected") results$LuckFactor <- as.

Earlier this year, I posted the first part of a write-up for a project I worked on during a project I worked on last year. As a reminder, my project involved taking 4 different types of correlation, test the baseline and 8 different data shifts, generating 1000 simulations with 100 points of data each. I then compared how three different multivariate control charts, Hotelling T^2, MEWMA, and MCUSUM, were in detecting a shift while holding the false rate fixed over all simulations. For this I use the pretty standard for in control average run length (ARL) of 300. This means, on average when the process is in control, you can expect to see an out of control data point in any 300 sequential points.

Time to mix it up a bit from my usual game probability related simulation. This week I want to talk about a project I worked on last year in doing simulations for Statistical Process Control. For a brief primer, Statistical Process Control or SPC is a method used for monitoring something like a manufacturing process. It’s a form of time series analysis where you monitor results of some statistic taken from observing the process and then compare that statistic to a set of limits on a control chart to determine whether or not the distribution of that statistic has likely changed.

So, after my last Dungeons and Dragons post, I got asked about the Advantage/Disadvantage mechanic in Dungeons and Dragons Fifth Edition, so let’s look into that a bit. In D&D, to succeed at a task, you roll a 20-sided die(d20) and with some math and checking with your Dungeon Master (DM), you determine if you succeed or not. In previous editions you would add your character’s modifier, as well as any additional bonuses or penalties due to the specific scenario. Fifth edition got rid of that except for one specific case, and instead replaced it with Advantage/Disadvantage. Simply put, if your character is in some sort of advantageous situation when attempting a task, you get Advantage.

So, after sharing my post from last week about probabilities and stat arrays. Now, the way I determine which array is better is clearly overly arbitrary. Under that system the standard array is better than an array of (7, 18, 18, 18, 18, 18), when in reality any player looking for maximal stats would take that over the standard array (8, 10, 12, 13, 14, 15). So maybe there is a different way to compare these. Now the first approach would be to just take the ability modifier. Each integer from 3-18 maps to an integer from -4 to +4 that is used for almost everything in the game (except for carrying capacity, which uses the actual Strength score).