# Superstition and Dice Rolls

/*Travis is more dice superstitious with Fjord than he was with Grog. What are the ratios for Travis-as-Grog vs. Travis-as-Fjord?*

Ok, if y’all are gonna call us out like this, you could at least @ us. (We kid. These are fun, and good practice for one of our actual jobs.)

So, the base question: how do Travis’ rolls compare between campaigns? As some commenters on the above post pointed out, this gets complicated because we don’t necessarily know all the rolls, but we’ll do the best we can. We previously did an analysis of all rolls here and here, but we didn’t really have enough rolls to break out the campaign 2 characters individually back then. We do now, so here we go.

### Distributions

Here’s what Travis’ rolls looked like for Grog (left, entire main campaign) and Fjord (right, updated through Ep 79):

In a perfect statistical world, these distributions would be perfectly flat: all values with an equal number of rolls. However, because we exist in the real world and because of the quirks of D&D, specifically the advantage system, we get a lot of unknowns, particularly a lot of lower value unknowns. This skews the distribution towards the higher values (with a spike at 1 because the players tend to announce critical fails, even with advantage). These skews look pretty similar for both Grog and Fjord on a graph, so we’ll have to go a little more in-depth.

### Statistical Tests

We’ll start with a chi-squared test to see which distribution is more different from the perfect statistical flat distribution. We know most of you aren’t fluent in statistical tests, but what you need to know for this one is that you get a measure known as a p-value. In this case, the smaller the p-value, the less likely it is that the distribution you’re testing is the same as a flat distribution. Both Grog and Fjord have incredibly small p-values, which makes sense, because the distributions are very much not flat. Grog’s is wildly smaller than Fjord’s, indicating that his distribution is even more skewed. The means seem to indicate that the skew is focused more towards 20s than 1s, so it definitely seems like Grog generally rolled better than Fjord. Let’s check in still more detail.

Here’s the breakdown of actual counts for each of their roll distributions. For both Grog and Fjord, there’s one column that shows the raw count of dice rolls at each value, and a second that shows the frequency of that roll value. The colored column to the far right is the ratio of their frequencies for each roll value. Teal (lower ratios) means Fjord rolled a value more often, while orange (higher ratios) means Grog rolled a value more often.

At a glance, it looks like the higher roll values are definitely more orange than teal! It seems that Grog generally rolled better than Fjord’s currently doing, despite Travis’ seemingly greater dice superstition.

### But Why?

We’ll leave the superstition question up to the viewers, but if we’re looking for a reason within the rules of D&D, it’s likely due to advantage. We mentioned above that we’re restricted to the rolls we know, and when the cast rolls with advantage, they typically only announce the higher value. The more missing values, the more skewed the distribution.

Grog, in the later stages of campaign 1, had advantage on:

Reckless attacks

This was up to 3 times per round by the last episodes (5 with an action surge)

Initiative rolls

Constitution Saves against poison

Dexterity Saves against any effect he could see

Any strength-based skill check while raging

Any situations where characters are generally granted advantage

By contrast, Fjord currently has advantage on:

Concentration Checks

Any situations where characters are generally granted advantage

More opportunities for advantage means we’re missing more values from Grog’s distribution. More missing values means that Grog’s distribution is more skewed to the higher values than Fjord’s is, giving the appearance that Grog rolled better than Fjord. We’ll see if Fjord manages to catch him as he starts leveling up under the Wildmother’s protection.