Saturday 29 November 2014

Mass Combat 2 - A Question of Scale

Miniature figures can challenge
even the greatest minds
Scale is something that has to be grappled with, or at least decided on when dealing with mass combat - scale of time as well as distances. D&D and then AD&D used a multi-purpose system based on ignoring the gameworld measurements and instead concentrating on the size of things on the table in front of the players, measured in literal inches as measured with a ruler or tape-measure by the DM. Sounds good, but somehow it all became a little tricky...

One of my most common arguments with other D&Ders is the question of whether one increases the size of area effect spells when using the outdoor ground scale or not. Basically, I say you do and everyone else says you don't. Luckily for me, they're wrong. Which is also lucky for you if you're interested in mass combat with D&D monsters and spells because it eliminates a load of pointless calculations.

The main cause of the arguments is the badly worded section in the PHB on the topic (p39):

Magic and spells ore, most certainly, devices of the game. In order to make them fit the constrictions of the underground labyrinth, a one for three reduction is necessary. It would be folly, after all, to try to have such as effective attack modes if feet were not converted to yards outdoors, where visibility, movement, and conventional weapons attack ranges are based on actual fact. (See MOVEMENT.)

Distance scale and areas of effect for spells (and missiles) are designed to fit the game, The tripling of range outdoors is reasonable, as it allows for recreation of actual ranges for hurled javelins, arrows fired from longbows, or whatever. In order to keep magic spells on a par, their range is also tripled. IT IS IMPERATIVE THAT OUTDOOR SCALE BE USED FOR RANGE ONLY, NEVER FOR SPELL AREA OF EFFECT (which is kept at 1” = 10’) UNLESS A FIGURE RATIO OF 1 :10 OR 1 :20 (1 casting equals 10 or 20 actual creatures or things in most cases) IS USED, AND CONSTRUCTIONS SUCH AS BUILDINGS, CASTLES, WALLS, ETC. ARE SCALED TO FIGURES RATHER THAN TO GROUND SCALE. Note that the foregoing assumes that a ground scale of 1” to 10 yards is used.


Of course, sometimes the players
will enjoy using the wrong scale
The text is, in fact, a slightly modified extract from an extended piece on the subject in issue #15 of The Dragon where Gygax ponders the question of scales in June of '78, a couple of years after the publication of the final D&D supplement: Swords & Spells, which was a mass-combat system

He rightly puts his finger on the fact that for mass combat, ground scale is the most important issue as the players will be constrained by physical space and that time scale is affected by ground scale insofar that movement must be noticeable. He does make some assumptions about what the reader already understands, however, and never fully explains the reason behind the use of "inches" and D&D.

He also assumes a rather generous 5'x10' playing surface—much larger than most people have today—and picks a scale that makes that equal to 600 yards by 1200 which he takes as a typical battlefield for mediƦval combat. Now, when one inch on the table represents 10 yards in the game world (1:360 scale), then a round must be a minute to give reasonable movement rates, where "reasonable" means easily handled by a typical ruler of 12" length. Since the ruler and the table are taken to be fixed sizes, there is a direct relationship between ground scale and time scale; double one and you must double the other or units will be making tiny movements.

Taking the outdoor ground and time scales to be 1":30' and 1rnd=60 seconds this means that the indoor ground scale of 1"=10 feet (1:120 scale), requires a round of 20s to give reasonable open-air movement rates. The important thing is that a fighter makes an attack every round and everyone can only make a charge movement once in ten rounds and so on, all while a combat can be contained on the table in front of the players.

Now, an underground round is not 20s long, of course, it is in fact still a full minute. There's two reasons for that and one of them is the question of moving about in dark corridors with slippery or rotten floors with the chance of sudden ambush around every bend. The other reason—magic— is more problematical and I'll deal with it below.

A significant presence
Next we enter the rabbit hole as Gygax raises the issue of figure scale. If 1"=10yards, then you can get a lot of people into that. With spears or other thrusting weapons, a 10 yard line might take 16 men standing shoulder to shoulder and each being backed by another 16, for 256 men in that one inch. This is very dense packing of the sort probably only encountered in special formations like Alexandrian pike phalanxes or Roman shield tortoises, but that's okay, really. Most figures have slightly smaller bases than that but then they are normally taken as representing 20 men. Except, this is fantasy and a single person can be a massively significant presence on the field of battle and therefore require their own figure.

Life being what it is, the figures used in D&D, Chainmail and other table-top games are all a certain size, and don't come with tiny versions to represent individuals. So, the idea was introduced of using some figures to represent player characters and important NPCs while some other figures the same size represent 10, 20, or 100 people. This was not a good move at all and led directly to the text in the PHB quoted above.

In short, the problem becomes one of spell effects. A spell effect is given in inches as normal for movement and weapon range. So long as the target(s) are/is in the same scale, that's fine. But what happens if the spell, say fireball or flame strike, or even bless land on a group of six figures that represent, not 120 orcs but 6 PCs. Well, Fig-1 shows how this plays out - first the party in marching order (each grid line is 1"), then a fireball is "called" and lands on the Reverend Bill's head.

At first glance, it doesn't look too bad for the party - Villa's safe and Corry and Fred will be saving for half or no damage as they are mostly outside of the fireball's area.

But this is all wrong. That fireball is 4" wide, as required by the PHB, but that's 40 yards wide. On the scale of these figures that... Well, actually it's hard to know what that is. A figure base of 1" is typical of 25-30mm figures, which is roughly 1"=6' (1:72 scale) or 1"=5' (1:60 scale). Taking the latter, as that's currently popular and it's easy to work with, the fireball is now a measly 20' wide in relation to the party. That's not right. The book says that the fireball even in indoor mode should be 40' wide, or twice the size it is here. Villa should be fried with the rest of them.

Well, okay, then, we'll stick with that. But what if the party are near some troops? Now the scale only works part way (fig-2) and we have a problem: if the party's figure/indoor scale is used (i.e., an 8" fireball on the tabletop, the outer circle) then not only the party but all the 120 goblins are turned into leather armour pop-tarts. But a fireball scaled to the goblin's outdoor scale (the inner circle) would have, if centred on the cleric, completely missed them all. And neither circle is even the "official" indoor scale of 1"=10', which would be a third circle bid-way between the other two, again affecting the goblins incorrectly. What a mess.

Transferring the indoor scale to the battlefield leads to the problem which Gygax says in the Dragon article was pointed out by none other than Len Lakofka:

"A huge area can be covered with webs from a lowly magic-user’s second level spell. Of course this is ridiculous, as the 1" = 10 yards scale only applies in cases where all other scales are in proportion."

Which is what we see here with the fireball. This quote sums the problem up but also gives the correct answer at the same time - keep all the scales in proportion. Don't use a separate figure scale in the first place! If you do, you will have headaches; no one wants to have to deal with this crap during a game.

The text in the Players Handbook tries to say this, but fluffs it. It should, for clarity, instead read (my addition in bold): "IT IS IMPERATIVE THAT OUTDOOR SCALE BE USED FOR RANGE ONLY, NEVER FOR SPELL AREA OF EFFECT UNLESS A FIGURE RATIO OF 1 :10 OR 1 :20  IS USED FOR ALL FIGURES".

This means that a single figure or counter is used for a group of PCs, just as it is for a group of orcs, goblins, or knights. This allows us to represent the area of effects consistently as shown as the still unnumbered fig-3 at left where we can clearly see that no goblins were harmed in the production of this diagram.

The crucial factor in all this is that miniature figures are three-dimensional and therefore very hard to overlap. In fact, instead of replacing the party with a single token, we could mostly solve the problem by allowing units to stack.

Stacking also allows us to eliminate the need for different sized tokens for different sized creatures—Swords and Spells uses ⅝" wide stands for humans and 1⅜" wide ones for ogres, trolls, and some horse units. We can instead simply adjust the maximum number of individuals represented by a token or counter. So, if a 1" counter could normally represent 100 men, it can only represent up to 45 horses, say.

Since an individual counter can represent from 1 to 100 or more individuals, it may seem that the DM must have a system for judging the actual placement of those individuals within the area covered by the counter. I personally have never found this necessary and the normal D&D 1" melee-range fuzziness generally covers all rationalizations, at least when the counters are 1" or less in size.

A New Type of Encumbrance (goody).

If the DM keeps an idea of a "stacking limit" in their head, things start to work quite smoothly. Taking 100 men as the normal limit in a 1" square, we can count a centaur as 2 men and say that a counter of 25 men and one of 37 centaurs can stack together and still move normally (other issues, such as facing and formation will have to wait for a future post); if we allow over-stacking to, say, 250 men in a square then we can penalize them for movement as they are perforce moving in a tight formation. The DM can regulate this as s/he sees fit, but it means that it's allowable to have working units of mixed fire giants and hell-hounds, for example.

"This is all jolly interesting, isn't it, Frodo?"
"Strictly's on soon; can we go?"
Magic Problems
I said that magic is one of the things that undermines the idea of completely abstract ground scale adjustments. The reason is that such ground scale adjustments logically require time scale adjustments, as mentioned above. But the players are told in the PHB that a casting time of one round represents a minute and a segment 6 seconds and this runs counter to the intent of the system.

That intent is that a game can be played in a balanced way regardless of how much space the players have to work with. A fireball's width is always a third of an unencumbered human's move rate; walls of force and thorns always represent the same level of obstacle, and charging units are always exposed to ranged fire for the same number of turns. Realism is completely ignored for the same of playability at scales other than 1:360.

Of course, you can scale a fireball up too far
This even works for fighters because we know that to-hit rolls are not made for every single blow; with a different time scale we just gloss over the fact that by the clock the combatants are getting more rolls, the important thing is that they get the same number of rolls per round.

Same for spell-like powers...can you see the problem? If spellcasters are taking a set time to cast spells, then the abstraction breaks and spell-like powers become disproportionately strong compared to real spells. This can, obviously, be fixed by simply ignoring the casting-time to real-time linkage, and that can be fun, but many players will find this hard to swallow, I have found.

There is a further problem, and that is missile (and spell) ranges which have to be "topped out" so that at large scales thieves are not throwing daggers half a mile, but that's much easier to accept than fiddling with time for various reasons.

Counters
In the next post I'll put up some software for making double-sided counters (one side is full strength, the other half strength).

Monday 17 November 2014

Mass Combat 1

Mass combat in D&D can be handled quite nicely by rolling a d20 and applying a bit of binomial theory. I'm not going to bore anyone with the theory but the results are a bunch of to-hit tables which vary based on the number of attackers.

Using the tables is pretty easy. Combat is from an attacking side consisting of identical figures from one or more units and a defending side consisting of figures from a single unit.

First, you decide how many figures on one side can attack the defending unit. If a row of goblins are attacking a unit of humans, perhaps the front 10 goblins can attack. If a mass of archers are firing at a single dragon, maybe hundreds can take a shot while it's in the air while a dozen knights on horseback might be able to charge it on the ground.

Next, find the attackers' to-hit needed using the normal methods. E.g., a gang of berserkers attacking a row of men in mail and shield decide to take a single attack at +2 with their bastard swords rather than once each with that and their hand-axes; they need a 15 to-hit. If using two-handed swords and armour Vs weapon rules, they would need 13. As another example, a 10th level fighter attacking the same men with a longsword would require a 7 (probably a lot less if strength and magic are applicable), and would roll using the "10 attacks" table.

A d20 is rolled for the attackers. This is found on the left-hand side and cross-indexed with the to-hit score to find the number of attackers who hit. E.g., 8 of the berserkers mentioned with the bastard swords are attacking the men-at-arms and roll a 13. The to-hit score was 15, so 3 of them hit.

Damage is then found based on the number of hits.

In the case of the berserkers, damage is easily handled by rolling 3d8 and applying it to the defending unit, moving the defenders down when damage accumulates equal to half the total hit points of the members.

But with larger units this can become unwieldy and it may be easier to become more abstract if you have a calculator to hand. The first option is to simply multiply up the average damage rather than rolling it, so our berserkers do 14 damage (13½ rounded up) and applied as before.

But with bigger units, or units with lots of hit dice (the infernal legions of pit fields, for example) these numbers are still too tedious to work with and we can fall back on calculating damage based on hit-dice. For this, the paper record for each unit is simply a count of total dice, calculated as average hp divided by 4.5. So 20 goblins count as 16 dice, and ten pit fiends have 130 HD, and a dozen trolls is 88 HD.

For this method, each hit has to be related to hit dice - take the average damage and divide by 4.5 (note this with the unit). Each hit in battle does that number of hit dice damage. So, our berserkers' attack simply does 3 damage; if using hand axes they would do 7/9th x 3 = 21/9 = 2 damage; with two-handed swords, 11/9 x 3 = 33/9 = 4 damage. If the berserkers were attacking the trolls, these numbers would become 13/9 x 3 = 4, 5/9 x 3 = 2, and 7/3 x 3 = 7 damage because of the trolls' large size. Of course, the trolls are regenerating 9 damager per round ((3x12)/4), so that's not going to matter much. As I said, the damage per hit against large and small can be recorded with the unit's record and a calculator makes all this tolerably fast.

If the number of figures doesn't fit one of the tables given, make two rolls on those that you have, so 18 figures roll twice on the 9-attacks table, or 13 roll once on the 6-attacks and once on the 7-attacks table etc.

Once a unit has taken half its maximum damage, it's knocked down to a unit of half the original size, and therefore half the original attacking potential.

As an aside, let's assume the trolls can bring 6 of their members to bear on the berserkers for a reply. The berserkers have 8 HD and the trolls' attacks do 13/9, 13/9, and 14/9 each. Their to-hit against AC 7 is 6. Three rolls are made: 6, 2, and 5. This equates to 4, 3, and 4 hits, for a total of 16 HD damage. The berserkers are shredded, even with these relatively poor rolls.

Initiative and stuff

I generally count all units closing as if it were "precipitous" so the longer weapon gets first attack; defender in a tie. After being joined, faster weapon goes first unless it's more than 5 speed factors better than the opposing weapon (in which case, it's deemed to be too short to take advantage). On ties, or when I can't be bothered, just dice for it.

If a unit is partially damaged at the end of a combat, I assume that the percentage hit points or dice lost is reflected in the casualties, but this has to be mapped to individuals' fates. If a unit of 10 2nd level clerics has suffered 16 HD of damage, then a quick estimate is that only 2 have survived with 20% of their hp. A more detailed method is to roll the 16 dice damage (i.e., 16d8) and spread it evenly over the unit. If the end result is that more survived than were still fighting or that none survived then this can be explained as stragglers returning to the unit after combat or dying from wounds as applicable.

Leader figures with individual hit points take proportionately more damage if involved in the combat. For example, our 10 2nd level clerics are lead by their high priestess (9HD), so the unit has 29HD. 16 HD damage is rolled and comes up 82. That would be 7.45hp each, but the high priestess takes 9/2=4½ shares, so she takes 34hp damage, leaving 48 for the others, who suffer 5 damage each. This sort of detail is something that only really comes up when player characters are involved, of course.

I've glossed over things like constitution, magic and strength bonuses, but it should be obvious that they are simply converted to hit-dice equivalents.

Fireball!

Area effects such as fireballs and dragons can affect multiple units, but in each unit the damage done is limited to the hp of one figure and then multiplied by the number of figures struck. So a 5d6 (35/9HD) fireball which hits a unit of 50 orcs (50HD) and affects 20 of them does 20 HD damage to the unit. Against the 12 trolls it does a total 47HD damage as each individual troll has more HD than the spell does damage.

88hp from a dragon is equal to 20HD and would obliterate the trolls, as it should.

Notes

I've used variations of these "rules" many times, sometimes with figures or counters, but mostly without any physical representation at all. They're very loose and the DM can apply whichever rules from standard D&D that they like - morale, multiple attacks (which can be subsumed into one big attack), time and movement, flank and rear attack bonuses, shield use, and even surprise for units of hobbits and elves. It's very much an on-the-fly method but if you're not too much of a wargamer they're probably enough for most needs and the degree of abstraction can be slid up and down to fit the importance or interest of the battle, as can the size of units.

3 Attacks

To-hit
1234567891011121314151617181920
132211111000000000000
232221111110000000000
333222111111000000000
433222211111100000000
533222221111110000000
633322222111111000000
733322222111111100000
833332222211111100000
933332222221111110000
1033333222221111110000
1133333222222111111000
1233333322222211111000
1333333322222221111100
1433333332222221111100
1533333333222222111110
1633333333322222211110
1733333333332222221110
1833333333333222222111
1933333333333332222211
2033333333333333333322

4 Attacks

To-hit
1234567891011121314151617181920
143222111110000000000
243322221111100000000
343332222111110000000
444333222211111000000
544333222221111100000
644333322221111100000
744433332222111110000
844433332222211110000
944433333222211111000
1044443333222221111000
1144443333322221111100
1244444333322222111100
1344444333332222111100
1444444433333222211110
1544444433333222221110
1644444443333322221110
1744444444333332222111
1844444444433333222211
1944444444444333332221
2044444444444444443332

5 Attacks

To-hit
1234567891011121314151617181920
154332221111000000000
254433222211110000000
354433322221111000000
454443332222111100000
555443333222111110000
655444333222211110000
755444333322221111000
855444433322221111000
955544433332222111100
1055544443332222111100
1155544443333222211100
1255554444333322211110
1355554444333322221110
1455555444433332221110
1555555444443332222110
1655555544443333222111
1755555554444333322211
1855555555444433332211
1955555555554444333221
2055555555555555444332

6 Attacks

To-hit
1234567891011121314151617181920
165443322211110000000
265444332221111000000
365544333222111100000
465544433322211110000
565554433322221110000
666554443332221111000
766555443333222111000
866555444333222111100
966555444333322211100
1066655544433322211100
1166655544433332221110
1266655554443332221110
1366665554443333221110
1466665555444333222110
1566666555444433322111
1666666555544433322211
1766666655554443332211
1866666665555444332221
1966666666555544433221
2066666666666655544332

7 Attacks

To-hit
1234567891011121314151617181920
176544332221111000000
276554433322111100000
376655443322211110000
476655444332221110000
576655544333222111000
676665544433222111000
777665544433322211100
877665554443322211100
977666554443332221100
1077666555443332221110
1177766555444333221110
1277766655544333222110
1377766655544433322110
1477776665554433322111
1577776665554443322211
1677777666555443332211
1777777666655544332211
1877777766665544433221
1977777776666555443321
2077777777777666554432

8 Attacks

To-hit
1234567891011121314151617181920
186654433322111000000
287655443332211100000
387665544333221110000
487765554433222111000
587766554433322111000
687766555443322211100
788776655443332211100
888776655444332221100
988776665544333221110
1088777665544433221110
1188777665554433222110
1288877666554443322110
1388877766555443322110
1488877766655443332211
1588887776655544332211
1688887776665544333211
1788888777665554433221
1888888877766555443321
1988888887776655544322
2088888888887766655433

9 Attacks

To-hit
1234567891011121314151617181920
197665543332211100000
298766554433221110000
398776554433322111000
498776655443322211000
598876655443332211100
698877665544332211100
798877665544333221100
899877766554433221110
999887766554433222110
1099887766554443322110
1199887776655443322110
1299888776655443322210
1399988776665544332211
1499988877665544332211
1599988877666554433211
1699998877766554433221
1799998887766655443221
1899999888776655443321
1999999988877666544332
2099999999988777655443

10 Attacks

To-hit
1234567891011121314151617181920
197665543332211100000
298766554433221110000
398776554433322111000
498776655443322211000
598876655443332211100
698877665544332211100
798877665544333221100
899877766554433221110
999887766554433222110
1099887766554443322110
1199887776655443322110
1299888776655443322210
1399988776665544332211
1499988877665544332211
1599988877666554433211
1699998877766554433221
1799998887766655443221
1899999888776655443321
1999999988877666544332
2099999999988777655443

15 Attacks

To-hit
1234567891011121314151617181920
1151311109876654432211000
21513121110986665443221100
315131211101098765543321100
415141312111098776544322100
515141312111099876554332110
6151413121110109876654432110
7151413121111109887654432210
8151413131211109987655433210
91514131312111010987665433210
101514141312111110987765443211
111515141312121110998765543221
1215151413121211101098766543221
1315151413131211111098776544321
1415151414131211111099876554321
15151514141312121110109876654321
16151515141313121111109887654321
171515151414131212111010987655432
181515151414131312111110988765432
1915151515141413131211111098876542
20151515151515141413121211109987653

20 Attacks

To-hit
1234567891011121314151617181920
1201716141211108766544321100
22018161514111010987654332100
320181715141312111098765432110
420181716151312111098765432210
5201817161514131211108766543210
6201917161514131211109876543210
7201918161514131211109876543210
8201918171615141311109876543221
92019181716151413121110987654321
102019181716151413121110987654321
112019181716151413121110987654321
1220191818171615141312111097654321
1320201918171615141312111098765421
1420201918171615141312111098765431
1520201918171615141413121098765432
16202019181817161514131211109875432
17202019191817161514131211109876532
182020201918171716151413121110986542
192020201919181716161514131211987643
2020202020201918171716151413121098754

25 Attacks

To-hit
1234567891011121314151617181920
125222017161413111097654432100
2252221191616151312119876543210
32523211918171514121110976543210
42523212018171614131210987643210
525232220191716151312111087654210
625232220191816151412111097654321
725232221191817151413121098754321
825242221201817161413121198764321
9252422212019171615131211108765321
10252423212019181615141211109765421
11252423222019181715141312109865431
12252423222119181716141312119875431
132524232221201817161513121110876432
142524232221201918161514131110976532
152525242321201918171514131210986532
162525242322211918171615131211987542
1725252423222120191816151413111087642
1825252423222120191817161413121098643
19252525242322212019181715141311108753
202525252524232221201918171615131210864

30 Attacks

To-hit
1234567891011121314151617181920
13026242119171614131110875433210
230272523211918161513101097653210
330272523222018171514121198654210
4302826242221191716141311108754320
5302826242321191816151312109764321
6302826252321201817151412119865321
7302826252322201917151412119875421
83028272524222019171614131110875421
93029272524222119181615131210976431
103029272624232120181715131210976431
113029272624232120181715141211986531
1230292826252322201917161413111086532
1330292826252322211918161513111087542
1430292827252422211918161513121097542
1530292827262423212018171514121197642
1630302827262523222019171614131198642
17303029282625242221191816151312108753
18303029282725242321201917151412119753
193030292827262524222119181615131210864
203030302928272625242321201817151412975

40 Attacks

To-hit
1234567891011121314151617181920
1403632292724222018161412108654310
24036343129262422201816141210875320
34037343229272523211917151311975421
440373432302826232119171513111086421
540373533302826242220181614121086431
640373533312927242220181614121097531
740383533312927252321191715131197531
840383634312927252321191715131197532
9403836343230282624222018161412108642
10403836343230282624222018161412108642
11403836343230282624222018161412108642
12403837353331292725232119171513119642
13403937353331292725232119171513119752
14403937353331302826242220181613119753
154039373634323028262422201816141210753
164039383634323029272523211917141210863
174039383635333129272523211917151311863
184040383735333230282624222018161411964
1940403937363433312927252321191715121074
2040404038373635333129272523211917141295

50 Attacks

To-hit
1234567891011121314151617181920
15044403734312926232118161311975320
250444239363431282623201816131195321
350464340373432292624211916141297531
4504643403835323027252220171512108531
5504744413835333028252320181513108631
6504744413936333128262321181613118642
7504744423936343129262421191614119642
8504745423937343229272422191714129742
95047454240373532302725222017151210752
105048454340383533302825222017151210752
115048454340383533302825232018151310853
125048464341383633312826232118161311853
135048464441393634312926242119161411863
145048464442393734322927242219171411963
155049474442403735323027252220171512963
1650494745424038353330282523201815121074
1750494745434138363431292624211816131074
1850494846444139373432302724221916141185
1950504846444240383533312825232017151295
20505049474644424038353330282522201714116

100 Attacks

To-hit
1234567891011121314151617181920
110090847872666055504540353026221713842
2100928680756964595449443934292420151162
3100938781767165605550454035302521161173
4100938882777166615651464136312621171273
5100948883777267625752474237322722171383
6100948983787368635752474237322823181384
7100948984797368635853484338332823181494
8100958984797469645954494439342924191494
9100959085807569645954494439342924191495
101009590858075706560555045403530252015105
111009591868176716661565146413631252015105
121009691868176716661565146413631262116115
131009691868277726762575247423732272116116
141009692878277726863585348433732272217116
151009792878378736863585348433833282317126
161009793888379746964595449443934292318127
171009793898479757065605550454035292419137
181009894898580767166615651464136302520148
191009895908681777267625752474237322621159
2010099969388847975706661565146403429231711