Most Rolled Values (With Bonus Analysis!) Part 1: The Campaigns

WhatZitTooya93 asked: What number gets rolled most often?

Well now you’ve done it. You got us interested in a thing, and we went way overboard, as usual.

The short version first: if you’re talking natural rolls, i.e. the number that shows up on a d20, the most-rolled value is 10, across both campaigns. If you’re more interested in the total roll, or what was the value after modifiers have been added, the most rolled value is 19, again across both campaigns.

For the long version, we’ve split the rolls by campaign, then by player to get a sense of why each distribution looks the way it does. For this analysis, we’re limiting ourselves to all d20 rolls, i.e. no damage, deflect missiles, healing, or other non-d20 rolls. We’re also obviously limiting ourselves to known rolls. We’ll start by breaking down rolls by campaign, then move to a by-player analysis in part 2.

Campaign 1

  • Most rolled natural D20 roll: 10 (of 8755 known rolls)
  • Most rolled total D20 roll: 19 (of 7991 known rolls)

A typical distribution for natural rolls should be flat, i.e. every value gets rolled an equal amount of times. A quick glance at the distribution of natural rolls in the first campaign shows a huge peak at 10, and a general skew towards higher values. We’ll discuss that peak at 10 a little bit later when we get to a certain rogue, but the skew towards higher values is likely caused by Vox Machina’s many abilities that grant advantage. When the players roll advantage, they don’t often tell us what the lower roll was, so our known roll values have a tendency to skew towards higher values. We often also don’t hear the high value for rolls that have disadvantage, but Vox Machina had advantage far more often than they had disadvantage, so the effect from advantage is stronger.

The expected distribution for total rolls is a bit tricker. If all the modifiers were equal, we’d expect to see a distribution similar to that seen in the natural rolls, i.e. flat, but slightly skewed towards higher values. Instead, we see something similar to a Gaussian distribution. This would seem to imply that the modifiers for Vox Machina have roughly a Gaussian distribution. This makes sense; ability modifiers are typically designed to result in this kind of distribution, and the proficiency system wouldn’t disrupt this too much, since it covers only a few different skills for each character, and each character usually has different skill proficiencies.

Campaign 2

  • Most rolled natural D20 roll in Campaign 2: 20 (of 2483 known rolls)
  • Most rolled total D20 roll in Campaign 2: 15 (of 2284 known rolls)

Unlike Vox Machina, The Mighty Nein don’t have the abilities to get advantage on a ton of rolls just yet, so the natural roll distribution for campaign 2 is much closer to a true flat distribution. The number of rolls, however, hasn’t quite gotten to the point where we see that true flat distribution, so you do see some odd bumps and peaks.

The total roll distribution for campaign 2 looks even more like a Gaussian; again, the Mighty Nein haven’t quite leveled to the point where they can disrupt the shape of their ability score distribution yet. One thing to note here, though, is where the peak of the distribution lies, and where the maximum values are. Vox Machina peaked around 19, with maximum roll values around 45 (again, we’ll show who got that one later, but let’s be real, you probably already know). The Mighty Nein’s distribution, however, peaks closer to 14 and maxxes out around 35. This distribution will start to shift up towards the one for campaign 1 as they level, increasing their proficiency bonuses and ability scores.