Converting "Handling Mobs" into a single roll (thinking out loud)

[Zhorn]

So the idea of Handling mobs (DMG p250) is to avoid rolling for each mob individually and spit out a flat "1 hit for every X attackers"

Over on rpg.stackexchange (https://rpg.stackexchange.com/questions/103229/how-does-the-handling-mobs-rule-work-with-advantage-disadvantage) Szega posted a table for handling the same system with Advantage/Disadvantage, which got me thinking; how could you tweak this to handle all mobs attacking a target under a single d20 roll?

Now it wouldn't be as simple as all attackers just using the [roll+attack modifier] vs [target AC], as that'll just produce an
https://raw.githubusercontent.com/sumitc91/data/master/askgif/hd_58e3c6d8-37e1-45fc-8246-61893478b5e5_hail_arrows.gif
or
https://media.giphy.com/media/2V4sl2IGzyiAw/giphy.gif
scenario.

What I'm thinking of is a table to roll on that would yield a 'roll high = more hitting' and 'roll low = more missing' but otherwise following a similar trend to the Handling Mobs table and/or Szega's addition to it.

Has anyone seen or played around with such a concept before? Not sure how to go about it at this moment, as with 3 variables (d20 result, +hit modifier, number of attackers), it would end up as ~twenty tables rather than one :smallfrown:

Note: this is mostly just a for-fun-background-idea, not something I definitely need to find a solution for.

[CheddarChampion]

Well you could find the chance to hit via 5%x(21+accuracy-AC).
As for statistical analysis... I'm going to skip that part. Change my suggestion as you like.

Let's call the odds of hitting "O".
We will combine "O" with the one die roll to figure out how many mobs hit.
Make a single attack roll using a mob's to-hit against the Target's AC.
For every point that the attack roll beats the AC by, add 5% to "O". For every point that the attack roll misses "O" by, subtract 5% from "O".

Example: If a mob has a +5 to hit vs an AC of 19, they hit on a 14+ and have an "O" of 35%. We roll 1d20 for the mob and it comes up as a 12. The attack misses the target of 14 by 2 points, so we take "O" - 10% to get 25%. One in every 4 (rounded down) mobs attacking are successful against that target.

Note this only works when attacking a single target. You'll have to do separate calculations for different targets. It can also take some time so it might not be that much better than separate attack rolls.

For more consistency roll 3d6 instead of 1d20 for the single attack roll.

[iTreeby]

Is this better than rolling attack and damage at the same time or just taking the average damage for "mooks" (however you want to define them)?

[Vogie]

You may be interested in DMDave.com's advanced mob rules - such as his units and this format for a giant mob of Kobolds : https://dmdave.com/advanced-mob-rules/

[Zhorn]

Well you could find the chance to hit via 5%x(21+accuracy-AC).
As for statistical analysis... I'm going to skip that part. Change my suggestion as you like.

Let's call the odds of hitting "O".
We will combine "O" with the one die roll to figure out what how many mobs hit.
Make a single attack roll using a mob's to-hit against the Target's AC.
For every point that the attack roll beats the AC by, add 5% to "O". For every point that the attack roll misses "O" by, subtract 5% from "O".
This is a really good staring point, and have copied it into my draft notes for future reference. Thankyou for the contribution.
I'll still need to tweak it as this can produce results above 100% and below 0%, but it's a foundation to build from :smallsmile:


Is this better than rolling attack and damage at the same time or just taking the average damage for "mooks" (however you want to define them)?
More so for dealing with having a large number of basic npc attackers. No damage roll, just applying a multiple of the creatures average times by however many successful hits. The only roll is the d20, which in turn could be subject to advantage/disadvantage.
The main application would be for groups of ranged attacks (unit of archers for example), be it for either the party attempting to assault a fortified location, or the party having a bunch of hired mercenaries of their own defending.
In a previous game, one of my players on numerous occasions expressed wanting to raise an army and declare a war of conquest, to which I flat out told them "no, I'm not running mass combat in this campaign (SKT)", but since then I've wondered how I could in case the situation presented itself again, or how it could be applied elsewhere.
Another DM I've played with tackled it from the opposite end, with units of commoner archers each dealing a guaranteed 1d8 damage per round.


You may be interested in DMDave.com's advanced mob rules - such as his units and this format for a giant mob of Kobolds : https://dmdave.com/advanced-mob-rules/
Thankyou for the link, this looks like an interesting read.

[Zhorn]

The more I play around with the numbers, the more I come to think this just might not be reasonably produced.

Almost every formula I try to spitting out values that can go into the negatives or hit chances above 100%.
If this was going to be used in a computer emulation, that would be fine, usable even, as I could program in some addition component to add effects to results outside the range (crit damage for above, fumbles for below, etc), or at the very least put hard limits on said range.
But for pen'n'paper that's getting more complex than I'd like.
For now I'll just paste the standard 'Handling Mobs' table onto my DM screen with the adjustments for advantage and disadvantage, and leave this idea on the back-burner for another time when inspiration strikes.

Really do appreciate the tips and links.

[Galithar]

The more I play around with the numbers, the more I come to think this just might not be reasonably produced.

Almost every formula I try to spitting out values that can go into the negatives or hit chances above 100%.
If this was going to be used in a computer emulation, that would be fine, usable even, as I could program in some addition component to add effects to results outside the range (crit damage for above, fumbles for below, etc), or at the very least put hard limits on said range.
But for pen'n'paper that's getting more complex than I'd like.
For now I'll just paste the standard 'Handling Mobs' table onto my DM screen with the adjustments for advantage and disadvantage, and leave this idea on the back-burner for another time when inspiration strikes.

Really do appreciate the tips and links.

What's wrong with values above 100 or below 0? It simply represents a mob of creatures with a good (or bad) chance to hit initially rolling well. It's the same as needing a 14 to hit and rolling a 18. You hit. Nothing special needs to happen. Opposed to that if you needed the 14 and rolled a 5 you just miss. No need to exaggerate the complexity just stick with something similar to what's already there. Which is exceeding the targets AC instead of meeting it doesn't confer a bonus (with the exception of Nat 20 for crits) and being below the targets AC is a miss, regardless of how much you miss it by.

[Zhorn]

What's wrong with values above 100 or below 0? It simply represents a mob of creatures with a good (or bad) chance to hit initially rolling well. It's the same as needing a 14 to hit and rolling a 18.

For a singular hit sure. But that's not entirely the goal of what I was setting out to do.
This is mostly just a misunderstanding of me not properly articulating my intent.
The idea would be the d20 roll represents the average of all attackers, not every attacker getting that roll.

Looking at the initial Handling Mobs table, it sets out a number of successful hits per attacks made.
The lower your chance to hit, the more failed attacks that are made before each successful hit is made. In the baseline table this scales from 1:1 to 1:20.
With the advantage and disadvantage tables this range is expanded out to a lower limit of 1:400, but the upper remains 1:1.
That's the type of results I was trying to model after; something that approaches 0% or 100% expressed as a proper fraction (X/Y, for every Y attacks there are X hits, with X<=Y), and doesn't fall outside those ranges.

Now as far as the noodly concept I'm trying to work with, it would be: the same roll against the same AC made by two different to hit modifiers would yield different results (example: a +5 to hit gets a 1 in 7 hits, where a +8 gets a 1 in 5).
Similarly, a low +to hit against a high AC target (say +3 vs AC 25, representing the city guard sending arrow volleys at a Tarrasque) would still fair poorly even on a natural 20, but still serious enough that a Tucker's Kobolds scenario poses a threat to a decently geared party. Part of that is more a function of damage per hit vs a huge pile of HP, but the intent would be to not 1-round a CR 30 monster with 400 commoner archers and a 5% chance lucky roll.
Avoiding 'all hits' and 'all misses' (as per the gifs in the opening post) for large numbers of attacks. This would be workable once I got the bounds working as I'd like them, but it adds awkward calculation interactions when the numbers don't line up (say the result was 397 out of 400 hits, but our only making 10 attacks, is that 3 misses then 7 hits, 1 miss and 9 hits, or 10 hits?).
A single roll table. The math gets a lot kinder with two variables, but with +to hit, AC, and d20 result, it is just a bit too complex


As I said before, I think I've just tried to do too much, attempting simplicity with a complex set of goals.
T'was but a pipe dream anyway *shrug*