In part 1 of our roll analysis, we focused on splitting rolls by campaign. Here, we’ll focus on each player’s contribution to the full distributions. Remember that we're only looking at d20 rolls, so none of these are damage, deflect missiles, healing, etc.
A quick caveat before we begin: we’ll be focusing mostly on the effects of campaign 1 skills on these distributions, since the vast majority of each individual player’s rolls will be from there and the effects are more obvious. There are a few exceptions, and they’re mentioned explicitly when they come up.
- Most rolled natural D20 value: 10 (of 1934 known rolls)
- Most rolled total D20 value: 20 (of 2994 known rolls)
Remember that weird peak in the first campaign’s natural roll distribution at 10? Check out Liam’s natural roll distribution over both campaigns and take a wild guess at who’s responsible for that peak. Vax’ildan’s Reliable Talent feature gave him the ability to automatically turn any natural roll lower than 10 into a 10 for any skill he’s proficient in. Since rogues get a lot of proficiencies, Vax wound up rolling for a lot of skills he was proficient in, so a lot of the natural rolls that you’d expect to see in the lower values are instead stuck in that peak. Unless Liam stated when he announced the result of his roll, we have no way of knowing which of those 10s were actual rolled 10s and which were Reliable Talent rolls, so we mark all as 10s.
Liam’s total roll distribution again looks pretty similar to a Gaussian, but he’s got an odd double-peak structure to it. This is probably caused by two compounding effects: Reliable Talent and Expertise. Unlike most of Vox Machina, Vax got double his proficiency bonus on four different kinds of skill checks (stealth, perception, thieves’ tools and acrobatics) and his standard proficiency bonus on four more (intimidation, investigation, persuasion, and sleight of hand). Since he gets to treat any natural roll below 10 as a 10 for all eight of those, he winds up with a lot of total rolls around 18 for his standard proficient skills, and a lot of total rolls around 26 for his expert skills, with an odd gap in the center. Expertise also accounts for his maximum total rolls around 40: all of these were stealth rolls with Pass Without a Trace and his stealth bonus were, at absolute minimum, +13. Rogues, man.
- Most rolled natural D20 value: 12 (of 1761 known rolls)
- Most rolled total D20 value: 19 (of 2684 known rolls)
Laura’s roll distributions are probably the closest to the expected values of any player. There’s only a slight shift towards higher values on the natural roll distribution, and, while bumpy, the total roll distribution is very close to a true Gaussian. The total roll distribution is slightly heavier on the high-value side, which is probably caused by Vex’ahlia’s multiclass into rogue and the application of Expertise to her perception and stealth rolls. Her Expertise, however, doesn’t seem to have had enough time to create the double-peak structure seen in Liam’s total roll distribution. It does, however, appear to have given her enough time to get some super-high stealth rolls; like Liam, her total roll values max out around 44.
- Most rolled natural D20 value: 15 (of 1745 known rolls)
- Most rolled total D20 value: 19 (of 2664 known rolls)
Travis’ natural roll distribution is easily the most skewed towards high values of any player, so much so that he is likely driving the general skew seen in the full campaign 1 distribution. This is likely caused by Grog’s Reckless Attack, giving Grog advantage on any attack while raging. Once Grog multiclassed into fighter, he could get up to 5 attacks per turn. In addition, Grog had advantage on any strength check while he was raging. This all adds up to a lot of low-value rolls that we don’t know the values for, and thus the skew towards high values.
There’s a hint of a normal Gaussian distribution in Travis’ total roll distribution, but you can definitely see the effect of the skew towards high total rolls reflected here. Unlike Liam and Laura, however, Travis’ maximum roll value is only around 36. Grog may never have had expertise, but he did have a +8 strength score by the end of the campaign. Note also our first player with a negative minimum value at -1 (Grog has an intelligence of 6, he knows what he’s doing!).
- Most rolled natural D20 value: 20 (of 1610 known rolls)
- Most rolled total D20 value: 21 (of 2348 known rolls)
One quick glance at Taliesin’s natural roll distribution shows that whatever dark deal he made to make the golden snitch amazing paid off. There are no fighter or human features in D&D that would explain away the sudden peak at 20 the same way we can explain Liam’s peak at 10. Neither Molly nor Caduceus have a feature that would explain it, nor have either character’s rolls accumulated to the point where they would overwhelm the sheer number of Percy rolls. Even if Taliesin had advantage on a majority of his rolls, the distribution should skew much like Travis’, not peak at a single value like we see here.
Again, we see a Gaussian form for the total roll distribution, with a little bit of that same peaked structure seen in Liam’s distribution. This might have something to do with the somewhat split nature of Percy’s skill and attack modifiers. All his attacks, acrobatics checks, and dexterity-based tinkering checks (which make up a large percentage of his rolls) were +10 or higher for the entirety of the campaign, and only increased. Many of his other most-used skills, such as stealth and investigation, were lower (around +5), and stayed lower throughout the campaign. This combines to give him one peak around 15 and a second around 25. Like Travis, his maximum value is around 36.
- Most rolled natural D20 value: 13 (of 1434 known rolls)
- Most rolled total D20 value: 21 (of 1660 known rolls)
Like Laura, Marisha’s natural roll distribution is fairly flat. Druids don’t have a lot of abilities to skew their roll distributions one way or the other. Her total roll distribution, however, looks very odd. Unlike Liam and Taliesin, this may be more due to her campaign 2 character than an inherent ability split with Keyleth. Druids do not roll a lot outside of skill checks, so Keyleth’s roll count was fairly low. Monks, on the other hand, roll a lot of attacks, so Beau’s roll count is the highest of the Mighty Nein. She already has roughly half the number of rolls that Keyleth had over the course of the entire first campaign, so Marisha's total roll distribution reflects both Beau’s and Keyleth’s ability modifiers.
- Most rolled natural D20 value: 16 (of 1364 known rolls)
- Most rolled total D20 value: 19 (of 1666 known rolls)
Like Marisha and Laura, Sam’s natural roll distribution is fairly flat, and again like Marisha, there’s a fair amount of strangeness in his total roll distribution. A quick glance at Scanlan’s and Nott’s roll counts reveals a similar situation to Beau and Keyleth: bards don’t roll often outside of skill checks, but rogues do. Artificers roll a decent amount of attacks, but Tary wasn’t around long enough to impact the roll rate significantly. Nott already has about half the number of rolls of Scanlan and Taryon combined, so the roll distribution reflects all three of their ability score splits. That smaller peak around 29 is a combined effect from Scanlan and Nott’s expertise rolls.
- Most rolled natural D20 value: 4 (of 529 known rolls)
- Most rolled total D20 value: 14 (of 740 known rolls)
Ashley’s roll count is much lower than the rest of the crew, since she has to miss fairly often (#ThanksBlindspot), but for whatever reason she apparently rolls a lot of 4s, 13s, and 20s. (As a reminder, Pike’s crit percentage by the end of the first campaign rivaled Percy’s, at above 6%.) The lower number of rolls means her natural roll distribution is fairly messy, which leads to a fairly messy total roll distribution. Like Marisha and Sam, her campaign 2 character makes up a significant chunk of her total rolls, so the distribution reflects both Yasha’s and Pike’s ability modifiers. However, in her case, the two peaks overlap, leading to a wide, slightly skewed Gaussian instead of the double peak structure we saw before.