This entry is part 2 in the series This Means WAR!

Part 1 began discussing the fundamental concepts needed to simulate a unit of 100 soldiers, dealing with the number of hits that they could inflict in a round of battle, and the amount of damage that they could inflict.

Part 2 picks up right where we left off…


Part 2: Fundamental Concepts (continued)

Ranged Attacks

Some units have ranged attack capabilities. These don’t normally mean throwing daggers, but do include bows and spears and the like. Because these units have a different chance to hit depending on the number of range increments to the enemy, the amount of damage they inflict has to be calculated for each different range increment. Furthermore, cover may reduce the damage inflicted to 1/2 or 1/4 normal, which should also be calculated in advance. These units trade the ability to inflict damage at a distance for complexity of prep.

Weapons with a reloading requirement such as crossbows permit any enemy unit within range to make a free attack while the crossbows are being reloaded. The commanders of such units have a choice: they can either have all their crossbowmen in a unit fire in unison, inflicting maximum damage, but suffering maximum damage in reply, or they can stagger their attacks, doing half damage at a time but suffering half the normal damage in response. (An army making a normal attack against such a unit still does full damage, this rule applies only to the extra ‘free’ attack).

Capacity to absorb damage, ie Hit Points

Dumbell probability curveThis varies from one individual to another. Usually, multiple die rolls are involved per creature, which produces a dumbbell probability curve, with the central values most likely to result. There is a substantial difference between this set of rolls and those for attacks: with new attack rolls being made every round, a statistical approach works, because one poor round is likely to be balanced by a good round at some other point in time. Hit Point rolls are made once, and remain fixed thereafter; they are not transitory.

So the initial thought is that of the 100 troops in an army unit – I called it a Century ealier – they should occupy the entire spectrum of possible hit point totals according to the statistics of the iniital rolls. If the statistics say that 30% of results will be 10 hit points, then 30 of those troops will have 10 hit points. Individuals don’t matter.

But when selecting an army, would the obviously unfit be chosen? Or would it be the fittest? And where would the cut-off point be?

This introduces the concept of professionalism in armies and elite units; these are often percieved as inventions of the 20th century, but in fact that was merely when militaries began to actively persue the task of building these qualities into their forces from top to bottom. They still existed in the past, but were products of survival and success: of 1000 men fighting a battle, 900 get killed, and the rest can either form an elite unit, or be dispersed among a fresh crop of 900 new men – all of whom will be somewhat better than the last crop by virtue of the experience of the elite 100, ie an officer’s core. Sometimes, a compromise might be reached – an elite core of 50 experienced officers and an elite half-unit of 50 men.

Before we can decide how to handle the capacity to absorb damage, we need to first have a method of quantifying and simulating these effects. So I came up with one:

Unit Quality

An army unit starts with a quality rating of between 0 and 5. “0″ means that they include everyone (ie exclude no-one) and 5 means that they are an elite force. Most armies in an RPG would probably rate a 1 – the weak and inform don’t get sent to war, but things don’t get much more selective than that.

  • For every past battle in which this unit has achieved overwhelming victory, add 1 to their current rating.
  • For every battle in which they have won but with moderate to heavy losses, add 1/2 to their current rating.
  • For any battle in which they were defeated but suffered low casualties, the rating afterwards is (current + base -1) / 2.
  • For every battle in which they suffered overwhelming defeat, the rating afterwards is (current -2) /2.
  • Round all fractions down to the nearest 0.1. No unit can have a rating of better than 10 or worse than 0.

eg: An elite unit started with a rating of 3, and achieved overwhelming victory 4 times in a row. They then suffered a minor defeat, followed by 2 minor victories, another minor defeat, an overwhelming victory, and finally, a catastrophic defeat. What is their current rating?
   Initial rating: 3.
   4 overwhelming victories: +4 = 8.
   minor defeat: (8+3-1)/2 = 10/2 = 5.
   2 minor victories: + 1 = 6.
   overwhelming victory: +1 = 7.
   catastrophic defeat: (7-2)/2 = 2.5.
The unit is currently weaker than when it was first formed. Another catastrophic defeat and it’s legend will be sorely tarnished.

Unit Hit Points

For each point of unit quality:

  • 10% of the unit’s hit dice (round off) are assumed to have roled maximums.
  • 10% of the remaining dice (round off) are assumed to have rolled maximum-1.
  • 10% of what’s left (round off) are assumed to have rolled maximum-2.
  • …. and so on, until your assumed roll reaches the minimum, ie 1, or you have only 1 or 2 dice left to allocate.
  • if any % of hit dice round to zero, use 20% for the next step. If two round to zero, use 30%, and so on (this rule is rarely required).
  • 0.5 rounds down to 0.

The remaining dice is assumed to have rolled an average result.
Exception: if the unit has a rating of 0, all dice are assumed to have rolled average.

eg: Our elite unit example above has a current rating of 2.5. Let’s assume that each member of the unit has 7d10 hit dice, and receives +2 hp per hit die from CON.
   2.5 x 10 = 25%.
   25% of 7 hd remaining = 1.75, which rounds up to 2 hd at maximum result (=10). This leaves 5 hd.
   25% of 5 hd remaining = 1.25, round down to 1 hd at maximum -1 (=9). This leaves 4 hd.
   25% of 4 hd remaining = 1 hd at maximum -2 (=8). This leaves 3 hd.
   25% of 3 hd remaining = 0.75, which rounds up to 1 hd at maximum -3 (=7).
   2 dice remain, which are assumed to have rolled averages, ie 5.5.
Each unit member can be assumed to have hit points of 20 + 9 + 8 + 7 + 5.5 + 5.5 + 2×7 = 69. The unit of 100 men has 6900 hit points.

It might seem that this still seems to complicated; certainly, 4hd aren’t enough to show the details of this subsystem. So what if the unit’s men had 12hd each instead? And had a typical unit rating of 1? Or had its peak rating of 8?

eg2: Our elite unit example above has a current rating of 2.5. Each member of the unit has 12d10 hit dice, and receives +2 hp per hit die from CON.
   2.5 x 10 = 25%. So 25% of 12d10 = 3 hd at maximum (=10).
   25% of 9 hd remaining = 2.25, rounds down to 2 hd at maximum -1 (=9).
   25% of 7 hd remaining = 1.75, rounds up to 2 hd at maximum -2 (=8).
   25% of 5 hd remaining = 1.25, rounds down to 1 hd at maximum-3 (=7).
   25% of 4 hd remaining = 1 hd at maximum-4 (=6).
   25% of 3 hd remaining = 0.75, rounds up to 1 hd at maximum-5(=5).
   2 hd remain, which are assumed to have rolled averages, ie 5.5.
Each man can be assumed to have hit points of 30 + 18 + 16 + 7 + 6 + 5 + 5.5 + 5.5 + 12×4 = 141. The unit of 100 men has 14,100 hit points.

eg3: The same unit, but with a rating of 1, each member having 12d10 hit dice, and receiving +2 hp per hit die from CON:
   10% of 12 hd remaining = 1.2, rounds down to 1 hd at maximum (=10).
   10% of 11 hd remaining = 1.1, rounds down to 1 hd at maximum-1( =9).
   10% of 10 hd remaining = 1 hd at maximum-2 (=8).
   10% of 9 hd remaining = 0.9, rounds up to 1 hd at maximum-3 (=7).
   10% of 8 hd remaining = 0.8, rounds up to 1 hd at maximum-4 (=6).
   10% of 7 hd remaining = 0.7, rounds up to 1 hd at maximum-5 (=5).
   10% of 6 hd remaining =0.6, rounds up to 1 hd at maximum-6 (=4).
   10% of 5 hd remaining = 0.5, rounds down to 0 hd at maximum-7(=3).
   20% of 5 hd remaining = 1 hd at maximum-8 (=2).
   10% of 4 hd remaining = 0.4, rounds down to 0 hd at maximum-9 (=1, ie minimum).
   4 hd remain, which are assumed to have rolled averages, ie 5.5.
Each man can be assumed to have hit points of 10 + 9 + 8 + 7 +6 + 5 +4 + 2 + 5.5 + 5.5 + 5.5 + 5.5 + 12×4 = 121. The unit of 100 men has 12,100 hit points. So the elite rating of 2.5 is worth an extra 2,000 hp to the unit, or 20 hp per trooper.

eg4: The same unit, with with a rating of 8, each member having 12d10 hit dice, and receiving +2 per hit die from CON:
   10×8=80%. So 80% of 12 hd = 9.6 hd rounds up to 10 hd at maximum (=10).
   2 hd remain, which are assumed to have rolled averages, ie 5.5.
Each man can be assumed to have hit points of 100 + 5.5 + 5.5 + 12×4 = 159. The unit of 100 men has 15,900 hit points. That’s 1,800 hp more than the current unit would have with the same number of hit dice, showing that small differences to a low rating count for more than massive improvements to an already good rating. But they DO make a difference.

eg5: How about a unit with a rating of 1.5, and 4d10 hd each, with a bonus of +3 hp per hit die from Con? This matches our description of Army #1.
   1.5 x 10 = 15%.
   15% of 4 hd remaining = 0.6, rounds up to 1 hd at maximum hp (=10).
   15% of 3 hd remaining = 0.45, rounds down to 0 hd at maximum -1.
   15% x 2 x 3 hd remaining = 0.9, rounds up to 1 hd at maximum -2 (=8).
   2 dice remain, which are assumed to roll averages.
Each member of the unit has 10 + 8 + 5.5 + 5.5 + 3 x 4 = 41 hp. The unit has 4,100 hp.

Unit Parity

GMs tend to like either a fair fight, with the PCs tipping the balance one way or the other, or to stack the odds against the PCs to make them work hard for their victory. The alternative – an easy fight – is not only often dull, it’s usually an anticlimax. For that reason, we should be able to make some rough assessment of opposing armies and what is needed to balance the forces on either side.

Force rating = Number Units x 
                    [(Unit HP total / Damage inflicted by the enemy) + ½ x (Quality + 1) x (Quality + 1)].

Damage inflicted needs clarification. If the force being rated has a higher movement rate than their enemies, second (and third, and so on) attacks by those enemies count for 1/4 their actual value, since it is assumed that they will only get to make such attacks some of the time. If the faster force is the unit being rated, second attacks (etc) contribute 2/3 of the possible damage resulting from them.

Modifiers:

  • Unit being rated is faster than opposing force: x1.25
  • Unit being rated has a higher initiative modifier (we’ll get to that in a moment): x1.25
  • Terrain and circumstances favour unit being rated: x1.25
  • Unit being rated is protected by a fort or stronghold: x2
  • Unit being rated outnumbers opponants: x1.1.

If the results, multiplied by the number of units, are roughly equal, so will the fight will be a roughly even contest.

EG: Army 2: inflicts 500.5 points on a first attack on Army 1 and an additional 1995.5 on a second attack, per unit. Army 1 has a current quality rating of 1.5, and 4,500 hp per unit. Assuming that Army 2 has the better initiative modifier, that terrain favours neither side, that neither side has defences, and that Army 2 will outnumber Army 1 considerably. We can also assume that Army 1 will have a better movement rate, which means that for the purposes of calculating a Force Rating, only 1/4 of Army #2′s second attack will contribute.

Army 1 inflicts 783.75 points on Army 2 each round. Army 2 has a current quality rating of 2.5 and 6900 hp per unit. They also have the better initiative modifer.

Force rating, Army #1 vs Army #2
   = N1 units x [(4500 / {500.5 + 1995.5/4}) + ½ x (1.5 +1) x (1.5 +1)]
   = N1 x [(4500 / {500.5 + 498.875}) + (2.5)x(2.5)/2]
   = N1 x [(4500 / 999.375) + (2.5 x 2.5 / 2)]
   = aprox N1 x [4.5 + 6.25 / 2]
   = N1 x [4.5 + 3.125] = N1 x 7.625.
      x1.25 for being faster, x 1.1 for outnumbering opponants = N1 x 7.625 x 1.25 x 1.1       = N1 x 10.484375. Call it x 10.5.

Force Rating, Army #2 vs Army #1
   = N2 units x [(6900 / 783.75) + ½ x (3.5 x 3.5)]
   = aprox N2 x [8.8 + 6.125]
   = N2 x 14.925.
     x 1.25 fpr higher initiative modifer = N2 x 14.925 x 1.25 = 18.65625. Call it 18.7.

For the battle to be an even contest, there need to be 18.7 Army 1 units for every 10.5 Army 2 units.

If Army 2 had 250 men (2½ units\), Army 1 would need 250 x 18.7 / 10.5 = 445 men – call it 4½ units. A 2:1 advantage would JUST favour Army 2. To be confident of victory, at least 2½:1 would be needed, and 3:1 would be better.

If Army 1 has 1000 men (10 units), Army 2 would need 1000 x 10.5 / 18.7 = 561.5 – call it 5½ units – to make an even fight of it. Just about anything better than 2:1 against them and they would have a strong chance of winning.

A note on scale

Armies take up a lot of space. A single unit would fill an entire map at the usual D&D miniatures scale. That makes the normal scale impractical for game-play purposes. So, instead, wars are conducted at 1/10th the normal scale – a ‘five foot step’ is half a space, a movement rate of 20″ becomes a movement rate of 2 spaces on the map.

This has the advantage of permitting a representative miniature represent an entire unit. That’s not one Orc on the map, that’s a unit of 100 orcs.

This means that 100 medium-sized creatures can fit comfortably in a single space, but there’s room for twice that many. Underneath each ‘unit’, a cardboard disk or square, or a plastic poker chip, or SOMETHING along those lines, permits a ‘unit number’ to be documented, so that when you have 10 units of 100 Ocs apiece, you can tell which one you’re talking about. These also permit you to identify which hexes a PC is in – given that they are a mere fleck at this scale, perhaps 1mm tall!

But even at this scale, wars take up a LOT of space. This is really only adequate for a relatrively small battle. A Helm’s Deep, with 10,000 Orcs, is still 100 figures on the table just for the bad guys! A war with half-a-million troops – which is about as big as it gets – would require 50,000 figures on the table! I don’t care HOW extensive your miniatures collection is, that just doesn’t work.

To handle battles on this scale, the miniatures have to get smaller. To handle these, I once made some tiny chits – you can buy coloured counters (just sheets of precut cardboard about 1cm square) quite cheaply if you hunt around. I cut these into four each, so that each unit now occupies a space about 5mm square. a sheet of 120 chits gives me 480 counters in different colours. I can usually get another 238 pieces from the half-centimeter border around the sheet – so that’s 718 counters per sheet.

On one side of the table, I will stand a miniature and a full-sized chit as a “colour key”. That means that in a single 1″ x 1″ space, I can fit about 28 units – about 2800 men. By making the spaces so small, I can fit a lot more battlefield into a given space without losing the tactical definition of the 1/10th scale. A half-million-man conflict would need 70 sheets – that’s still a considerable investment; I’ve seen these sheets for as little as 10¢ and as much as 50¢, Australian, so that’s $7 to $35. Do-able but it’s something I would have to budget for some time in advance. On the other hand, a more typical 10,000 man war could be accommodated easily with a single sheet – perhaps two half-sheets if I wanted to put the allies in one colour and the enemies in another.

But that was before I scored some counters from another game that was being thrown away. These are small, about the same size as those 5mm squares of cardboard, and are in the shape of tanks. I have about 500 of these in half-a-dozen colours enough to show a variety of factions. I believe these were originally designed for a military wargame of some sort, but don’t know which one. These, supplemented by chits for the more distant units, solve the problem nicely.

This concludes part two of this six-part article. Part three will begin to discuss how to use these building blocks in an actual game setting – the practicalities of refereeing a 10,000 man battle.
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