I've been thinking about Old School mass combat systems. I've started creating my own in the link below, but I am wondering if there are good systems out there that are:

1) Fast to adjudicate.
2) More or less faithful to the results you'd get if attacking individually.

For example, if you pit 20 individual veterans against an elephant, the results of the mass combat system should reflect what would happen by rolling 20 separate attack rolls, etc.

Of course, I find it impossible to get perfect results, as 20 veterans could scatter or attack in waves, and so on.

Here is my first attempt:
https://methodsetmadness.blogspot.com/2023/04/the-hd-game-iii-mass-combat-and-simple.html

Come to think of it, it would be very easy to write "units" of 20 veterans, 20 brigands, etc., by simply adding a formula for damage per round, and keeping every other statistic (HP, AC, etc.) intact, by subtracting their THAC0 from 20.

So, 20 veterans would cause 4.5*[AC+1] per round. Or even easier: 1d8*[AC+1] per round.

Using attack bonus and AAC, 1d8*[20-AC] per round.

(I did this all ion my head and I am not great with math, so please correct me if I'm wrong)

To accurately reflect what happens when 100 warriors swing their weapons at their opponents is to use a binomial distribution. Which produces a bell curve telling you how many of those warriors actually hit.

I ran up this chart based on using the binomial function that excel has.



The best thing to do for OSR systems is just use AD&D Battlesystem 1e as outlined in these posts I wrote.

BattleSystem with Swords & Wizardry
https://batintheattic.blogspot.com/2013/08/quick-battlesystem-with-swords-wizardry.html

Adapting Battlesystem to Swords & Wizardry
https://batintheattic.blogspot.com/2013/08/adapting-1st-edition-battlesystem-to.html

War System or Battlemachine
https://batintheattic.blogspot.com/2010/06/war-system-or-battle-machine-along-with.html

I wish I could do these quickly in excel - I did something somewhat similar with d20 but it took me a while.

Chainmail (2d6) doesn't map perfectly to d20 versions of D&D, but apparently Swords and Spells does.

Will check battlesystem. I've been recommended Swords and Spells, Delta's book of war, and "by this poleaxe", which also uses d6s.

Quote from: Eric Diaz on April 18, 2023, 10:43:22 AM
I wish I could do these quickly in excel - I did something somewhat similar with d20 but it took me a while.

Chainmail (2d6) doesn't map perfectly to d20 versions of D&D, but apparently Swords and Spells does.

Will check battlesystem. I've been recommended Swords and Spells, Delta's book of war, and "by this pollaxe", which I cant find.

For all the math and tables in Swords and Spells it still remains a loose approximation. The Binominal distribution is the only accurate way of reflecting the odds.

What I can't replicate at the moment is the math behind the Battlesystem table. I have various pieces of the puzzle figured out but I can't figure out how to assemble them. Once that is done, then the rest of the system pretty much boils down to preference.


As for how to do it in Excel you set the formula like this.

=BINOM.DIST(# of Hits,# of Combatants , the odds of hitting from 0 to 1,FALSE)

FALSE gives you the odds for a specific number of hits for a specific number of combatants at given set of odds. While TRUE will give you the cumulative odds of that number of hits or less. FALSE is what I normally use as it make the bell curve obvious.

Hope that helps.

Again that is Battlesystem 1e not 2e.

Thank you!

I'll look into it, but TBH first I have to learn what Binominal distribution means.

I am enamored with the idea of rolling 1d8*[20-AC] per round for an unit of 20 veterans, for example (in B/X).

https://oldschoolessentials.necroticgnome.com/srd/index.php/Veteran

Do you see any obvious mistakes or downsides with that?

This is why I like 1E. Only 1E is calibrated to do this, and this is not possible in 3E and beyond since reversed ACs.

0th level fighting men need a 20 to hit AC 1, so they hit 1 in 20. They need a 19 to hit AC 2, so 2 in 20 chance. 3 in 20 to hit AC 3, etc. No +1 adjustment is necessary. The defenders AC is the number of hits per 20 attackers.

So if 20 men with spears (d8 vs L) are attacking an elephant (AC 6), I can just say they do 6d8 damage.

However, since doing this averages out the number of hits and removes that variability, I can also add that variability back in by making just one damage roll and multiplying it by the number of hits (so d8 x6).

Super simple.

Quote from: estar on April 18, 2023, 10:39:57 AM
To accurately reflect what happens when 100 warriors swing their weapons at their opponents is to use a binomial distribution. Which produces a bell curve telling you how many of those warriors actually hit.

I ran up this chart based on using the binomial function that excel has.



The best thing to do for OSR systems is just use AD&D Battlesystem 1e as outlined in these posts I wrote.

BattleSystem with Swords & Wizardry
https://batintheattic.blogspot.com/2013/08/quick-battlesystem-with-swords-wizardry.html

Adapting Battlesystem to Swords & Wizardry
https://batintheattic.blogspot.com/2013/08/adapting-1st-edition-battlesystem-to.html

War System or Battlemachine
https://batintheattic.blogspot.com/2010/06/war-system-or-battle-machine-along-with.html

How does that hit rate interact with armor class? i.e. one would expect a different number of men to hit when an individual warrior needs an 11+ on the die vs. needing a 16+ on the die.

That's always where mass combat rules break down on my end... you essentially need a matrix of hit rate by AC for a given unit size. Once that's been done it plays fine, but calculating the matrix for each unit would be some work.

Quote from: Eric Diaz on April 18, 2023, 11:43:37 AM
I'll look into it, but TBH first I have to learn what Binominal distribution means.

It answers the question of if I have a bunch of folks trying something how many would succeed given the odds (20%, 50%, 75%, etc.). Plot that over the odds of 0% to 100% chance of success then you will have your binomial distribution chart.

Quote from: Eric Diaz on April 18, 2023, 11:43:37 AM
I am enamored with the idea of rolling 1d8*[20-AC] per round for an unit of 20 veterans, for example (in B/X).

https://oldschoolessentials.necroticgnome.com/srd/index.php/Veteran

Do you see any obvious mistakes or downsides with that?

Change it to something with a bell curve like 2d4, 2d6, 2d6-2, 2d10, etc. Then it would reflect how it would happen if you actually rolled all those dice.

Thanks to your question, I got some ideas. I will work them up and share them by tomorrow.

Quote from: estar on April 18, 2023, 12:19:13 PM

Quote from: Eric Diaz on April 18, 2023, 11:43:37 AM
I'll look into it, but TBH first I have to learn what Binominal distribution means.

It answers the question of if I have a bunch of folks trying something how many would succeed given the odds (20%, 50%, 75%, etc.). Plot that over the odds of 0% to 100% chance of success then you will have your binomial distribution chart.

Quote from: Eric Diaz on April 18, 2023, 11:43:37 AM
I am enamored with the idea of rolling 1d8*[20-AC] per round for an unit of 20 veterans, for example (in B/X).

https://oldschoolessentials.necroticgnome.com/srd/index.php/Veteran

Do you see any obvious mistakes or downsides with that?

Change it to something with a bell curve like 2d4, 2d6, 2d6-2, 2d10, etc. Then it would reflect how it would happen if you actually rolled all those dice.

Thanks to your question, I got some ideas. I will work them up and share them by tomorrow.

Thanks! Sounds good!

About the bell curve: I initially thought of just using the dice for that. For example, rolling 3d8 for a group of veterans attacking other veterans.

Also, i think I f'ed up the formula, I meant 1d8*[AC+1]. I keep confusing AAC with DAC. DAC is a bit easier for that.

Quote from: Chris24601 on April 18, 2023, 12:06:21 PM
How does that hit rate interact with armor class? i.e. one would expect a different number of men to hit when an individual warrior needs an 11+ on the die vs. needing a 16+ on the die.

Top number of the chart is what you need to hit the target on a d20 roll.

Quote from: Chris24601 on April 18, 2023, 12:06:21 PM
That's always where mass combat rules break down on my end... you essentially need a matrix of hit rate by AC for a given unit size. Once that's been done it plays fine, but calculating the matrix for each unit would be some work.

Except the designer of Battlesystem 1e figured out how to take all those binomial distributions and smash them into a single chart. It is still an approximation but a far closer one than anything I have seen to date for D&D.

Here is the chart, you use a 2d6 roll plus modifiers. The number is the # of Hit Dice of damage dealt per figure in the unit. Each figure is 10 combatants for a medium sized unit. SO a formation of 20 figures doing 1d8 damage rolled a 22 resulting in 3 HD per figure. Thus their opponent takes 60 HD of damage. If their opponent were 1 HD orcs that means 60 orcs were killed over three rounds (3 minutes) of combat.

The normal to hit roll is  2d6+ THACO-AC + modifiers.
See this for a more detailed explanation
https://batintheattic.blogspot.com/2013/08/adapting-1st-edition-battlesystem-to.html

I was able to adapt to ascending AC with  2d6+Ascending AC-to hit modifier + modifiers.

The nice thing about this chart that it accounts for all the different variations of attack that AD&D 1e monster has. And it works for earlier and later editions of D&D. 

The other thing you need to know how to adjust it for different figure sizes.


I will try to work up an example of how this works. For now I have this up.

One Thousand Four Hundred and Fifty Orcs Slain
https://batintheattic.blogspot.com/2013/08/one-thousand-four-hundred-and-fifty.html

Quote from: estar on April 18, 2023, 12:33:25 PM

Quote from: Chris24601 on April 18, 2023, 12:06:21 PM
How does that hit rate interact with armor class? i.e. one would expect a different number of men to hit when an individual warrior needs an 11+ on the die vs. needing a 16+ on the die.

Top number of the chart is what you need to hit the target on a d20 roll.

Ah, got it.

I was misreading the chart with the top line as the number of units doing the attacking (I think because the first table chunk went 1-10 and it mentioned "10 men" at the top) not as the hit number needed.

Thank you for the correction.

I just realized I made another obvious mistake. The formula for a 20-NPCs unit damage should be:

Unit damage = single damage * [21-THAC0+AC]

Which means an unit of veterans [THAC0 19 in B/X], for example, causes 1d8 * [2+AC]. Against a target with AC 0, they cause 2d8 damage per round.

Likewise, if you're using ascending AC and attack bonus (AB) instead of THAC0, the formula is NPC DMG*(21+AB-AC). The results are exactly the same (e.g., the veterans cause 2d8 damage against AC 20, etc.).

Notice that it needs no conversion if you're using AD&D; just replace the B/X THAC0 for the AD&D THAC0.

Here are some things that might already be included in TSR D&D, please let me know if anyone can answer:

- How many people can attack a single PC or monsters at once?
- Did spears effectively double the number of attacks in chainmail by allowing the second column to attack simultaneously?
- Does B/X have any rules on charging? The spears do double damage against a charge but I can't find it. Also, would you have to LOSE initiative and be attacked for this to work?
- How can anyone, especially in heavy armor, avoid being destroyed by arrows before even getting to the fight? Do archers always win? Is there any penalty to dropping bows and taking swords when the infantry attacks you?