Questions tagged [statistics]

Statistics deals with the mathematics of probability-based games. This tag should be used for questions about tabletop game mathematics that relate to mechanics rather than game elements such as skills or attributes, and have relevance to RPGs in particular.

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7
votes
3answers
1k views

Does bounded accuracy effectively increase randomness in D&D 5e, compared to previous editions?

I have been reading D&D 5e for a forthcoming campaign and I have a small concern with bounded accuracy: Proficiency bonus growth at a low rate (a level 20 character has only a +6 proficiency bonus....
0
votes
0answers
115 views

Is there any way to improve ability score without items, only with spells or class features? [closed]

I found a few, but they are all bad, like true polymorph to improve ability scores (but I lose class features), does someone know any way to improve ability scores without losing class features, and ...
33
votes
24answers
7k views

Simulating these special dice on more regular dice

I've got a game that uses special dice for its resolution. Basically when making an opposed check, each side rolls a bunch of them based on the relevant trait, and whoever rolls most points wins. The ...
4
votes
1answer
164 views

Has anyone done research on average RPG probabilities?

I've been looking at designing an RPG system lately and I'm currently considering where to set the "difficulty" of a roll at to get some satisfying results. I'm wondering - has anyone researched some ...
5
votes
3answers
840 views

How does the double-bladed scimitar compare to using two weapons with the Dual Wielder feat and Two-Weapon Fighting fighting style?

I've often felt that having a consistent bonus-action attack (or other mechanic) is 'optimal' in builds during combat. The more actions/options you have, the 'better' you are able to handle different ...
6
votes
1answer
408 views

With the Great Weapon Fighting fighting style, how does the double-bladed scimitar's damage evolve?

Traditionally, the Greatsword, Maul and Greataxe are considered the strongest two-handed weapons (unless you take the Polearm Master feat, where Glaives and Halberds rock out). Barbarians and Half-...
5
votes
2answers
347 views

Is there an accepted likelihood of hitting that is consistent across tiers, and how has it been determined?

One can easily calculate DPR given a specific build (knowing proficiency bonus, ability scores, other relevant factors) and the AC of opponents, leading to spreadsheets with a matrix of customizable ...
-4
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5answers
303 views

How does one convert disadvantage on the attack of a attacker, into a bonus to AC for a target, in particular for a Cloak of Displacement?

Question: How does one convert disadvantage on the attack of a attacker, into a bonus to AC for a target Assume a monster is attacking with disadvantage, the target is a level 12 PC with an AC of 16....
5
votes
3answers
389 views

Function to calculate “Nd6 take highest 2, sort descending” probabilities in AnyDice

I'm creating an injury-table where the player has to roll a d66 to see how severe the injury her character sustains is. The players roll up to ...
4
votes
1answer
66 views

How does the Impervious Modifier apply to Defenses other than Toughness?

It's been about a Month since i started playing Mutants and Masterminds 3e with my friends, and we absolutely LOVE the system (particularly the one-shot modules), but something in the Impervious ...
6
votes
2answers
218 views

To what extent is a lower DC skill check with disadvantage harder than a higher skill check without?

I'm wondering how mechanically I could calculate a lower DC challenge with disadvantage as a middle-ground between a higher skill DC and that same DC with disadvantage. I'd like to describe a ...
10
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2answers
860 views

Which spell is the better use of concentration for a ranged Valor bard with the Elven Accuracy feat: Greater Invisibility or Swift Quiver?

Assumptions: ranged College of Valor bard the bard has 20 Dex the bard is shooting with a longbow another player can consistently provide the Help action for 1 attack with advantage every turn the ...
4
votes
3answers
251 views

How do I model a fudge dice roll with re-rolls in Anydice?

I need a little help with a probability calculation in Anydice. We are making a fudge based game using 4 fudge dice, so basically a d3 system: -1,0,1 We are allowing your attribute or stats in the ...
1
vote
0answers
105 views

Given an array of probabilities, can AnyDice output the number of specific die type (d6) combinations to best fit? [closed]

Given an array of probabilities: 5% 5% 4% 2% 1% 12% 12% 10% 6% 4% 42% 41% 38% 23% 11% 53% 51% 45% 21% 9% 87% 86% 80% 54% 31% Can AnyDice generate a list ...
5
votes
1answer
222 views

How would this House Rule for combined Advantage/Disadvantage Impact Rolls?

According to the rules for Advantage/Disadvantage: If circumstances cause a roll to have both advantage and disadvantage, you are considered to have neither of them, and you roll one d20. This ...
27
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4answers
4k views

How does one calculate the distribution of the Matt Colville way of rolling stats?

Specifically, the Matt Colville way of rolling stats is: Roll 4d6, drop the lowest value die for 1 stat; If this roll is lower than 8, reroll it; Repeat steps 1 and 2 until you have a set of 6 stats ...
14
votes
1answer
703 views

What is the statistical difference between “choose either total” or “choose new total” when rerolling damage die?

I am reworking a homebrew class I made a while ago where one class feature stated: when making a melee attack you can choose to reroll the damage die. The new total must be used. I wanted to make ...
6
votes
2answers
473 views

How much on average does the Durable feat increase the number of Hit Points gained when spending Hit Dice?

There are other similarly mathy questions on this site such as "How much damage does Great Weapon Fighting add on average?" and "Are features that allow −5 to attack to get +10 to damage ...
16
votes
2answers
4k views

What are the odds of rolling specific ability score totals in D&D?

I am about to start running a new game in 5e and I hate all of the ways of determining ability scores. I have always felt that we play RPGs at least in part for the opportunity to pretend to be more ...
3
votes
1answer
114 views

What is the average expected rounds to 1 Wound, and how is it accurately calculated?

Take a character with Fighting skill d10 who does 2d6 damage, and a standardized bandit as the target. The bandit has d6 in all Traits and in Fighting, so has a Parry of 5, and wears leather armor ...
5
votes
3answers
445 views

How can I calculate the difference between two rolls in AnyDice?

How do I calculate the following in AnyDice? 2d6, subtract lowest result from highest.
1
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1answer
106 views

How can I model the probabilities for highest and lowest of opposing dice pools?

This is a variation of a dice mechanic I'm working on. You create a d6 pool of Edge dice and Snag dice and roll all of them. Compare the highest Edge die and the highest Snag die. If the Edge die ...
6
votes
3answers
1k views

How can I calculate the sum of 2 random dice out of a 3d6 pool in AnyDice?

With AnyDice it's pretty easy to calculate probalities for highest and lowest 2 of a 3d6 pool, namely with: output [highest 2 of 3d6] output [lowest 2 of 3d6] ...
4
votes
1answer
124 views

How can I model the probabilities for this mechanic involving cancelling out dice pools in AnyDice?

So I'm struggling with the probabilities for a dice mechanic. You create a d6 pool of Edge dice and Snag dice and roll all of them. Each Snag die cancels an Edge die of a lower value. After ...
24
votes
4answers
2k views

Is it okay to roll multiple attacks that all have advantage in one cluster?

I am planning to make my first Ranger and going Hunter to eventually get Volley. If I get the preemptive strike from an unseen position, then RAW I get advantage on attack rolls. Let's say I am ...
1
vote
1answer
93 views

How can I calculate the probability of complete success with this mixed dice pool using AnyDice?

I've playing around with dice probabilities and have a spreadsheet that handles the calculation for basic probabilities rolling a set of dice and counting the number of successes. I am completely new ...
16
votes
3answers
953 views

What is the average number of draws it takes before you can not draw any more cards from the Deck of Many Things?

When thinking about this question regarding an upper limit on the number of draws, I wondered what would be the expected number of draws you can actually pull off if you called for a large number of ...
0
votes
1answer
400 views

What is my average burst/nova melee damage and how do I calculate it?

I'm trying to figure out what my average burst/nova damage with this character would be (using a melee attack) but I'm at a loss for how to calculate all of it. Assume the target has an AC of 15 but ...
5
votes
2answers
227 views

AnyDice: How to calculate the winner in opposed rolls over multiple rounds?

I am having some difficulty doing opposed rolls over multiple rounds. I am looking for a character vs. character statistics. I call them "Rookie" and "Enemy" respectively. I want to know what the ...
7
votes
1answer
147 views

How can I calculate the probability of meeting a certain Difficulty Value on 3d6 with critical success/failure modifiers?

In one Fuzion-system variant 3d6 is used to resolve skill checks. A Task is given a Difficulty Value (DV) from 10 (easy) to impossible (30 and beyond). Characters can have primary attribute levels ...
2
votes
1answer
107 views

How do I find the odds in a dice pool contest?

I'm designing a system where overall success is determined using a dice pool where you count the number of max-value faces among dice rolled and compare this number to some difficulty number. In this ...
-1
votes
1answer
105 views

A generalized formula for the probability of a roll? [duplicate]

I'm looking for a formula to calculate the chance that (n) rolls of a d(y) produces any of (x) specific numbers (k) times, where x,y,n,k > 0, k <= n, and x <= y. AnyDice is a neat thing to know ...
2
votes
0answers
91 views

Equipping the dagger vs the shield [closed]

I want to figure out what is the better option, straight up damage or a chance to deflect in a game. I have two options, the first is to equip another dagger for 10% more damage. However, this ...
5
votes
2answers
187 views

How can I calculate the expected number of stunt points per attack?

If I hit on a 3, the Dragon Dice can show anything, the chance of getting a double is 44.44%, so on average it is 1.55 (3.5 * 0.44) Stunt Point per attack. If I hit only on a 18, the Dragon Dice can ...
10
votes
5answers
7k views

Would it be fair to use 1d30 (instead of rolling 2d20 and taking the higher die) for advantage rolls?

Would it be fair to use 1d30 - in place of 2d20 and taking the higher die - for advantage rolls? Recently I have acquired several d30 dice in a bag of factory seconds. I want to offer my players the ...
25
votes
5answers
4k views

How do I compare the result of “1d20+x, with advantage” to “1d20+y, without advantage”, assuming x < y?

I roll a d20. If I have a choice between d20+x with advantage, or d20+y without advantage, what choice do I make to maximise the result? What are the values of x and y where the choice changes (if it ...
20
votes
4answers
840 views

How do I calculate how many of an item I'll have in this inventory system?

I beta tested a game last week with a pretty fun system. This system is called "Dés d'usure" (in French, because it will be a French game). I translate it into "Wear dice", but I'm unsure. When you ...
6
votes
2answers
364 views

What is the average point buy of a stat array from a 6x6 matrix of “roll 4d6, drop the lowest die”?

For character creation my group sometimes uses a weird method to generate stats. We roll 6 stat arrays using 4d6d1 (rolling 4d6 and dropping the lowest), and arrange them on top of one another to make ...
10
votes
2answers
313 views

How to calculate conditional probabilities in AnyDice?

While writing the addendum to this answer, which considers the relative value of skill vs. characteristic in the "3d20 system" of Neuroshima, I found myself wanting an answer to a deceptively simple ...
19
votes
5answers
6k views

If I score a critical hit on an 18 or higher, what are my chances of getting a critical hit if I roll 3d20?

I have Elven Accuracy so with advantage on an attack roll using Dexterity, Intelligence, Wisdom, or Charisma, you can reroll one of the dice once. So what are my crit chance with a crit range of 18/...
18
votes
6answers
5k views

Does the shape of a die affect the probability of a number being rolled?

Let's say I have a standard D4 and a custom D8 that has printed 1-4 and then 1-4 again (for a total of 8 sides). Would both of these dice distribute the probably of rolling any given number equally? ...
17
votes
7answers
3k views

How can the DM most simply and fairly choose 1 out of an odd number of characters to be targeted by an attack or effect?

When DMing and randomly determining a character to take damage or an effect, it's easy to roll a die if you have an even number of characters. But what about if you have an odd number of characters? ...
7
votes
1answer
229 views

How can I generate a heat map from AnyDice results?

I want to show some effects of changing dice rolls on a heat map, where on one axis I have task difficulty (level of a spell, quality of lock to pick etc), and on another character level / proficiency ...
4
votes
4answers
525 views

Is it still a binomial distribution when rolling dice with different probabilities that must be met to count a success?

How do you calculate the probability of success when success is two different criteria/probabilities? I'm theorizing a resolution system for a homebrewed mechanic that involves rolling a pool of ...
4
votes
2answers
370 views

With a known probability, how can I determine a roll to fit that probability to a population of n?

I'm working on making some homebrew settlement downtime activity, and I'd like to create a table that can provide some various outcomes for a group. So I"m looking for the math that allows to figure ...
16
votes
2answers
2k views

How much attack damage does the AC boost from a shield prevent on average?

Statistically, how much attack damage does the AC boost from a shield prevent on average? I've seen claims it results in a 10% reduction in damage taken, is that accurate?
53
votes
8answers
4k views

How to approximate rolls for potions of healing using only d6's?

I want to make tabletop potions of healing out of corked vials (test tubes) filled with dice. Each vial would be labeled and filled based on the potion it represents. For example, a vial for a potion ...
20
votes
1answer
711 views

Which Armor Class values should be used as controls when making damage calculations?

It is known that occasionally questions will pop up that are about attempts to optimize a character's damage output (sometimes shorthanded as DPR, or Damage-per-Round), and veterans of this game know ...
22
votes
6answers
5k views

What is the difference between rolling more dice versus fewer dice?

Let's say there are two attacks: one rolls a 10d10 and the other rolls a 5d20. Assuming the modifier was the same, which rolls would have better chances of rolling average, and which would have ...
18
votes
9answers
3k views

How can the probability of a fumble decrease linearly with more dice?

I'm working on a simplified RPG system that uses only D6s, and I want a mechanic for fumbles/critical fails. Depending on how good the player character is, they have 1-5 dice to roll and they have to ...