This entry is part 1 in the series This Means WAR!

The subject of this month’s blog carnival is War. As part of that canival, I present an article on how to referee a war in an rpg. Not one that happens in some distant country, or a neighbouring city, but up close and personal – so close that the PCs can touch it. And not some small skirmish on the fringes – thousands of troops in conflict, maybe tens or hundreds of thousands.

Part 1 and Part 2 deal with the fundamental concepts and prep work needed to make War a practical option within an RPG.
Part 3 and Part 4 describe how to use those fundamental concepts in play.
Part 5 describes how to integrate PC-scale one-on-one combat with a war.
Part 6 concludes the series with miscellenious notes on how to implement unusual abilities and exotic armaments within the system.
So, without further ado…

Campaign Mastery Presents:
“This Means War!” – a system to make huge armies practical to DM

Part 1: Fundamental Concepts & Required Prep

It’s something that every GM inevitably comes across at some point, and it usually ends up causing nightmares: How can it be made practical to GM a huge army, or even more to the point, to have two or more of them engage in battle? The first time I ran up against it, I had very little experience, and opted to create ubermonsters out of each “army” – this was using AD&D, which dates it a LONG time ago. That worked, after a fashion, but it left quite a lot to be desired; the PCs weren’t able to interact with the army as they were on entirely different scales.

The second time around, I had about ten years experience as a GM under my belt, and chose to employ a narrative approach. The PCs interacted with those enemies in their immediate vicinity as individuals, and I simply making up whatever was going on outside of that as it suited me, with reversals, failures, successes, and high drama. The PCs were able to get down and dirty one-on-many, so it corrected the problems of the first method, but it made the battle almost impossible to run, even after I had decided to take the simple step of rolling a d% for each opponant faced on the PC-scale to decide how many hit points they had already lost in the battle, and choosing their tactics and objectives accordingly. There were just too many rolls to make, and too much to keep track of; it bogged down to a pace that made dawdling seem breakneck, with a single skirmish taking 25 hours to resolve.

So, when the problem began to loom on the horizon for a third time, in the preamble to the climactic finish of the first Fumanor campaign in 2004, I decided to have a good solid think about just what was involved and how to simulate the battle in a way that was practical. The results of that effort have never been published – in fact, they’ve never been fully collected in writing before – so this is definitly original material. All I have in the way of notes taken is the working-out that I did at the time, with no explanatory notes (Naughty Mike! Bad Mike!).

But rather than simply providing the results of that first go-round, which were designed for D&D 3.0, I thought it would be more useful, and more informative, to actually go through the process used to construct the ‘war’ rules, so that GMs can choose to apply it to any game system they happen to be using. I can also take the opportunity to formalise and update the rules to full 3.x spec. In any event, the absence of prepared notes on the subject means that I would have to reconstruct the significance of each calculation from scratch anyway!

To start with, I realised that I needed to simplify combat. The rules in D&D, even those in the miniatures rules, are not really designed to cope with a battle involving armies of 10,000 or more. So I started by thinking about the simplest possible description of combat, to reduce the number of variables. I soon boiled War down to a number of foundation concepts.

Step 1: Chance to ‘hit’ ie inflict damage

Game systems are designed to break this value down into as many variables as possible. In D&D, character level, operating characteristic (usually Strength, sometimes Dex) bonus, quality of equipment, enchantments, defender’s armour (both worn and natural), their ability to dodge (Dex bonus), and so on, combine to give a value that can be enhanced in any number of ways. This is essential to permitting characters sufficient individuality to function as PCs, and to keep encounters from becoming monotonous. When you’re running an army, all that produces headaches you don’t need; all you care about is the bottom line, which is that against opponant X, you have a base chance of inflicting damage of “X” percent.

To assess this percentage, a couple of basic probability rules come into play:

  • The total chance of a result is the sum of all Parallel Chances of achieving that result, added together;
  • Divergant Chances of a result subtract from the total chance; and
  • The chance of achieving multiple conditions is the product of each individual chance.

These are almost certainly known by formal names, but this is the way I remember them, the result of deducing them for myself many years before my formal education addressed the subject.

Parallel ways are where you have multiple ways of achieving a given result – two attack rolls, for example. Divergant chances are where there is only one roll, but the outcomes are different based on the result actually achieved. And if you have a 50% chance of achieving step 1 and a 40% chance of achieving step 2 (which requires step 1 to have been achieved first) then your chances of achieving step 2, in total, are 50 x 40/100 = 20%.

Let’s put these into practice and analyze a couple of attacks in D&D 3.5.

EG 1: +4 BAB, +8 total attack bonus, vs AC=Y:
The attacker gets only one attack per round, at +8 (which is reasonable). To succeed, he has to get a total roll of
   d20+8 >= Y
That means that his die roll has to be
   d20 >= Y-8
Since the highest result that can be rolled on a d20 is 20, that means that he needs at least
   20 – (Y-8) = 20 – Y+8 = 28-Y
So his chance of a successful hit is 100 x (28-AC)/20, or 5% x (28-AC).

That lets his % chances be calculated against every possible AC, if needed. Against an AC of, say, 13, the character has 5%x(28-13) = 5%x15 = 75% chance of success. Against an AC of 28-20 (maximum possible d20 roll) = 8, or less, the character will hit every time. Against an AC of 28+1 (minimum possible d20 roll) = 29 or worse, the character will never hit.

But wait: in D&D, a 1 always misses, and a 20 always hits! That means that against opponants of AC 8 or less, he has only a 95% chance of hitting, and against opponants of AC 29 or worse, he has a 5% chance of hitting.

EG 2: +7/+2 BAB, +9/+4 total attack bonus, vs AC=Y:
This is a little more complicated, because the character has two chances to hit. Fortunately, the statistics rules tell us how to accommodate that. For the first attack roll, the chance of hitting works out to:
   AC  > 29: 5%
   AC 10-29: 5%x(29-AC)
   AC  < 10: 95%
And his second attack works out to:
   AC  > 24: 5%
   AC 5-24: 5%x(24-AC)
   AC  < 5: 95%

Against the same AC13 opponant, these numbers work out to 70% and 45%, respectively. These can be combined to give an overall chance of success, by looking at the number of permutations of result:
2 hits; 70% x 45% = 70% x 45/100 = 31.5%
0 hits: (100-70%) x (100-45)% = 30% x 55% = 16.5%
1 hit: 100% – 31.5% – 16.5% = 52%.

Units Of 100: Centuries

I had gotten this far when I realised that I could simplify life a lot if I treated armies as being divided into units of 100 troops each. That gets rid of the percentage sign right away. Suddenly, we’re talking about an actual number of hits in a round, not a chance of hitting. In any event, with 100 rolls being theoretically made on a d20, the odds are fairly good that the distribution of results will be fairly even.

What’s more, the results scale perfectly.

So our theoretical attack by army unit 1 now reads:

  • 75 hits per round vs AC 13.

And our theoretical attack by army unit 2 reads:

  • 31.5 x 2 hits + 52 x 1 hit = 63 + 52 = 115 hits per round vs AC 13.

We can easily see that if the two forces are to be evenly matched in terms of number of hits per round – not necessarily something that is desireable – there will have to be fewer people of army 2 than there are in army 1. In fact, 100×75/115 = 7500/115 = 62-and-5/23rds people in army 2 can dish out as many hits as 100 members of army 1.

But it’s actually far too early to try and determine relative power levels of the two armies, let alone decide on their numbers. So let’s go back to the base numbers of 100 troops per unit and 75 and 115 hits per unit, respectively.

Step 2: Amount of damage inflicted by a hit

This is defined by rules systems by weapon type, and modified by various factors. Some rules systems allow a critical hit. That means that there is a defineable % chance of doing extra damage. The actual damage that results (on average) from all attacks in a round, in such systems, is

  • (average normal damage) x (number of ordinary hits) +
    (average damage of a critical hit) x (number of critical hits)

This is fairly straightforward. It’s determining the number of critical hits that starts to get complicated. Take D&D 3.5: In order to achieve a critical hit, you have to get a result that both hits and is within a range specified by the weapon type, then hit again. We already know how to work out those numbers.

Let’s look at a longsword, a fairly ubiquitous weapon in D&D. It does 1d8 base damage against medium creatures and 1d6 base damage against small creatures, has a critical range of 19-20, and does x2 damage on a critical hit.

Instead of balancing forces by weight of numbers alone, a disparity in weapons would go a long way, especially since there is every indication that army #2 will have more hit dice (and hence more hit points) than army #1 – something we’ll be getting to in a moment. So let’s assume that army #2 are the only ones using longswords and we’ll equip army number 1 with something a little beefier.

Army #2 got bonuses of +2 to hit over and above their base attack bonus, so the same modifier will apply to their damage totals. That means that the normal damage inflicted by a longsword would be d8+2 against medium targets, and d6+2 against small ones. Let’s assume medium targets: that gives a range of results of 3-10, and (3+10)/2 gives an average normal damage of 6.5. The average damage per critical hit will be double this, because of the x2 damage multiplier, which is 13 points. We already know that the number of hits they typically get in a round is 115. That’s three of the four numbers we need, so next, let’s look at the last one: the chance of a critical hit. That’s a little more complicated, because it is adding another set of permutations, number of critical hits, to our “chance of hitting” result.

A threat range of 19-20 means that on a “natural 19” (ie 5% of the results of each attack), a hit is a possible critical. A “natural 20” (another 5% of the results of each attack) is not only an automatic hit – something we’ve already allowed for – but is also a possible critical.

The easiest way to allow for these is to deal with each attack seperately – so that means that the “115” hits isn’t what we should be using, it’s 70 (first attack) and 45 (second attack), respectively.

First Attack:
   AC  > 28: 5% = 1 hit & critical chance
             95% miss
   AC = 27: 10% = 1 hit & critical chance
             90% miss
   AC 10-26: 10% = 1 hit & critical chance
             5%x(29-AC)-10 = 1 hit
             100-[5%x(29-AC)-10]*-10** = miss
   AC  < 10: 10% = 1 hit & critical chance
             100%-5***-10**=85% = 1 hit
             5% = miss
* this subtracts the chance of 1 hit from 100%
** this subtracts the chance of a critical + hit from the remainder
*** this subtracts the chance of a miss from 100%

Second Attack:
   AC  > 24: 5% = 1 hit & critical chance
             95% miss
   AC = 23: 10% = 1 hit & critical chance
             90% miss
   AC 5-22: 10% = 1 hit & critical chance
             5%x(24-AC)-10 = 1 hit
             100-[5%x(24-AC)-10]*-10** = miss
   AC  < 5: 10% = 1 hit & critical chance
             100-5***-10**=85% = 1 hit
             5% = miss
* this subtracts the chance of 1 hit from 100%
** this subtracts the chance of a critical + hit from the remainder
*** this subtracts the chance of a miss from 100%

Against the target AC of 13, these come to 10% chance of 1 hit + a critical threat, a 60% chance of 1 hit, and a 30% chance of a miss (as before) with the first attack; and a 10% chance of a hit + critical threat, a 35% chance of a hit, and, still, a 55% chance of missing.

The chance of actually converting a critical is the simple attack chance already worked out, 70 and 45 respectively. So we can simplify these numbers:

Attack 1 against AC 13:
10×70/100=7% critical hit, 10×30/100=3% failed critical check & ordinary hit, +60% ordinary hit (no critical chance) = 63%.
Attack 2 against AC 13:
10×45/100=4.5% critical hit, 10×55/100=5.5% failed critical check & ordinary hit, +35% ordinary hit (no critical chance) = 40.5%.

Since all three outcomes (critical threat, hit, and miss) from the second roll are possibilities regardless of the results of the first, there are 8 permutations that result.
   2 critical hits: 7% x 5.5/100 = 0.385%.
   1 critical (first attack) + hit (second attack): 7% x 40.5/100 = 2.835%.
   1 critical (first attack) + miss (second attack): 7% x 55/100 = 3.85%.
   1 hit (first attack) + critical (second attack): 63% x 5.5/100 = 3.465%.
   2 hits, no criticals: 63% x 40.5/100 = 25.515%
   1 hit (first attack) + miss (second attack): 63% x 55/100 = 34.65%.
   1 miss (first attack) + critical (second attack): 30% x 5.5/100 = 1.65%.
   1 miss (first attack) + hit (second attack): 30% x 40.5/100 = 12.15%.
   2 misses: 30% x 55/100 = 16.5%.

Again using units of 100 to simplify these answers and aggregating the outcomes that yield the same result, we get:

   0.385 x 2 = 0.77 criticals; + 2.835 + 3.85 + 3.465 + 1.65 = 12.57 criticals
   25.515 x 2 = 51.03 hits; + 2.835 + 3.465 + 34.65 + 12.15 = 104.13 hits

for every 100 attackers. Since we have already determined that an ordinary hit does 6.5 points of damage and a critical does 13, we can now calculate that Army #2 does

   12.57 x 13 + 104.13 x 6.5 = 163.41 + 2124.33 = 2,496 points of damage per round per 100 troops.

(It was at this point that I realised that a simpler method would have been to multiply the number of criticals by the critical multiplier to get a total number of ordinary hits. Oh, well…)

You only get the second attack in D&D if you don’t move any substantial distance – in fact, if you move 5′ or less. That means that we also need to know how much damage is done with the first attacks only. That’s easily calculated: 7 criticals and 63 ordinary hits, which is the equivalent of 14+63 = 77 ordinary hits, doing 6.5 points each, or a total of 500.5 points.

Note that it’s taken me a lot more room (and a lot more time) to explain it and show the workings than are actually needed in real life. This calculation will easily fit on one side of a small index card, one per army. But it’s performed the critical task of boiling most of the combat system down into the three numbers that matter:

  • the average damage per hit (6.5 points)
  • total damage inflicted per 100 troops in a combat round (500.5 points if they move, 2496 if they don’t.)

It should be possible to set up a spreadsheet to automatically calculate these numbers for you for ALL armour classes within reason, and I’m sure that it’s something that Campaign Mastery will provide at some point.

Army #1

For the sake of brevity, I’m simply going to give the results for Army#1. I decided to equip them with Halberds; against medium targets, they do 1d10 damage. They only have a critical range of 20, but do 3x damage on a critical. The essential numbers are:

  • the average damage per hit (9.5 points)
  • total damage inflicted per 100 troops in a combat round (783.75 points whether they move or not.)

Right away, basic tactics that should be employed by each army leap out and demand attention. On the first strike, Army 1 does in excess of 50% more damage than Army 2; it’s the second attack that is devestatingly effective. So rule number 1 for army number 1 is to keep mobile, and force army number 2 to chase after them.

A logic check: each round, if army #1 withdraws 10 or 15 feet, they will provoke an attack of opportunity. However, when army #2 then moves after them, entering their threatened zones, they will get an attack of opportunity back at the enemy before being able to make their own attack. Army #1 will then take their next round’s action: attack, withdraw 15′ and suffer an attack of opportunity inflicted apon them. In effect, the number of attacks per round is being doubled, which doubles (in effect) the advantage in damage inflicted of army #1. Using these tactics, Army#1 will suffer the first strike against them (always a disadvantage) but will thereafter do 566.5 points more damage per round than army #2 inflicts.

Note that it’s extremely unusual for both armies to have the same AC!

This concludes part one of this six-part article. Part two will continue the discussion of fundamental concepts, including discussions of Ranged Attacks, Unit Hit Points, Unit Quality, and a discussion of map scales.
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