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

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