MoM - How does combat work?

[General Ludd]

I've finally gotten the game to work on my computer, and have been playing it again. I don't remember how the combat damage and whatnot was calculated, though, and my books for the game are packed away somewhere... so, anyone want to enlighten me?

EDIT: And a bonus question: What exactly is the differences between the difficulty levels?

[DaveV]

Here's a cut-and-paste from the FAQ:

-------------------------------------------------------------------------------
4.5) How Does Multi-Figure vs Shields Combat Work?
-------------------------------------------------------------------------------

Frequent question on the net: My Swordsmen unit, 6 figures, 4 swords. Is it
a 24 sword attack or six separate 4 sword hits? The answer is the second.

This makes a big difference, depending on the number of shields the opponent
has. For example, a new Stag Beetle has 1 figure, a 15 attack and a 7
defense, while new Swordsmen have six figures with a 3 attack and a 2
defense.

In a fight, each Swordsman has a .3 * 3 = .9 chance of scoring a hit.
However, on average, the Stag Beetle's 7 shields will block 7 * .3 = 2.1 hits
of damage. That means that the Swordsmen will only injure the Stag Beetle
when by luck the Stag Beetle's shield roll below average. Each attack the
Swordsmen do make 6 attacks, improving the odds somewhat.

The Stag Beetle will, on average, score 15 * .3 = 4.5 hits, with Swordsmen
shields stopping only 2 * .3 = .6 hits of damage. The Beetle will tend to do
4.5 - .6 = 3.9 hits of damage each round.

This gives you a reason to play races with higher shields, such as Trolls,
Klackons, and Lizardmen. If you just look at figures*swords, Catapults look
pathetic compared to swordsmen. But against high shield opponents, they
are valuable. The same with high hit, low figure summoned creatures.
[jfardal@infinity.ccsi.com (John Fardal), BLJ]

I think the second part is wrong -- the stag beetle will be blocked by the
first swordsman's defense until it does one hit to kill it, then will have to
overcome the defense of the second swordsman, and so on -- so it will
actually do
4.5 - .6 = 1 (killed it) + 2.9,
2.9 - .6 = 1 (killed it) + 1.3,
1.3 - .6 = .7 (might or might not kill it),
thus killing 2 maybe 3 swordsmen on average, instead of 3 probably 4.
I guess I'll have to run experiments on this, also. [Later: verified my
original theory on this one, anyway. EACH figure gets its own defense
against an attack that killed the previous figure.] [DP]


-------------------------------------------------------------------------------
4.6) Why does my Strength 7 hero get butchered by Strength 4 Swordsmen?
-------------------------------------------------------------------------------

The answer is that there is strength in numbers. Let's say we have High Men
Veteran Swordsmen with 6 figures, 4 swords, 3 defense, and 1 heart per
figure, versus a brand new Spyder The Rogue with 7 swords, 5 shields and 8
hearts. Neither unit has any "to-hit" bonuses.

First round: Each sword represents a 30% chance of landing damage, for each
figure in the unit. Each swordsmen figures will average 4 * .3 = 1.2 raw
hits. But Spyder has 5 shields, representing five 30% chances to stop a hit
of damage, averaging 1.5 stops per attack. Basically, the Swordsmen have to
get lucky and roll a little better than Spyder to slip a hit past his
shields. The table in section 10.16 indicates that a 4 sword figure will, on
average, manage to slip .4 hits past a 5 shield defender. Given 6 figures,
we could predict 6 * .4 = 2.4 hits of damage. Lets round to 3, and say
Spyder takes 3 hits of damage, leaving 5 hearts. Spyder's 7 swords against
the Swordsmen's 3 shields can expect to get in 1.3 hits of damage. Lets say
Spyder gets 1 hit and that will take out the first swordsmen figure.

Second round: Five swordsmen figures: 5 * .4 = 2 hits. Spyder is down to
3 hearts. He does the same attack as last round, doing another hit of
damage, taking out a second swordsmen figure.

Third round: Four swordsmen figures: 4 * .4 = 1.6 hits. 1.6 is closer to 2,
so let's take away 2 hearts, leaving Spyder just one. Let's say Spyder gets
a little lucky this time and round up the expected 1.3 hits to 2 hits. The
first hit takes out a third swordsmen figure. The second hit goes on to
figure number 4, but figure 4 gets to roll his shields. Each of 3 shields
gives a 30% chance of stopping the hit. Let's say one of them does, and
figure 4 survives.

Fourth round: Three remaining swordsmen figures: 3 * .4 = 1.2 hits. Spyder
only had 1 hit left, and dies. But first he gets to swing at the swordsmen,
killing 1 figure.

The Swordsmen have 2 of 6 figures left, and Spyder is dead. Basically,
each Swordsmen figure had an uphill battle with 3 less swords and 2 less
shields, but the swordsmen unit had 6 figures to attack with. Also, it is
hard for Spyder to kill more than one figure per round because shields get
reapplied when extra hits are passed along to the next figure.

However, this analysis is a little biased against Spyder. At a couple of
points we rounded the Swordsmen's hits up. If we had rounded down, Spyder
could have been victorious. Also, we gave the Swordsmen 60 experience
(Veteran level), but Spyder none. Once Spyder gets 20 experience he will
get an additional sword, shield and heart, making him much tougher.

Finally, don't forget random chance. In the first round, the swordsmen get
6*4 rolls against Spyder. If the swordsmen's rolls are high and Spyder's
shield rolls are low, he can get killed right there. Another time Spyder
could roll high and the swordsmen roll low, with no damage to Spyder at all.
[BLJ]

There are lots of complications: ranged units have penalties to hit for shooting at long range; first strike, thrown, and breath weapons do damage before the defenders can counterattack; there are lots of resistances that may keep you from doing any damage in certain situations.

To-hit bonuses are huge; an elite halfling swordsman (4 attack, +2 to hit) is roughly equivalent to a 7 attack unit with no plus to hit.

[General Ludd]

Thanks, that was helpful. I forgot how unique the combat was in MoM.


Another question - is it at all possible for trolls to use mithril/admantium/enchanted weapons?

[bakalov]

Only enchanted, if your wizard has Alchemy.

Edit: in the latest patches only.

[General Ludd]

Bugger. They really get handicapped, don't they? But regeneration is really nice...

[pchang]

you want draconian flying warships (they can be enhanced with adamantium) and a fleet of them will kick just about anything (except blue dragons).

[DaveV]

Or, for the 500 hammers you'd spend building a ship wright's guild, shipyard, and your first airship, you could build 11 draconian bowmen. You get a much lower attack, but 6 figures. Get them some experience and they can handle neutral town garrisons or low- to mid-level monsters. Throw some spells on them and they can be just as effective as the airship. I'd much rather get some medium-strength units on the map early than wait around for an uber-unit.

And regeneration is really nice. The thing I like the most is that your stack of war trolls is immune to attrition, as long as they can keep from being wiped out entirely. Lose 7 out of 9, with the remaing two barely alive? No problem, next turn you have a full-strength stack of 9 again.

[DaveV]

Here are some more tables, showing the chance of hitting (or blocking) a given number of hits, given the attack (or defense) value.

How to interpret these tables: if you have an attack of 3 and no to-hit bonus, you have a 34.3% chance of missing, a 44.1% chance of doing one damage, an 18.9% chance of hitting for 2 damage, and a 2.7% chance of hitting for 3 damage. With an attack of 3 and +2 to-hit bonus, the chances are: 12.5% chance of missing, 37.5% chance of damage 1, 37.5% chance of damage 2, 12.5% chance of damage 3.

No bonus:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
1 0.7000 0.3000
2 0.4900 0.4200 0.0900
3 0.3430 0.4410 0.1890 0.0270
4 0.2401 0.4116 0.2646 0.0756 0.0081
5 0.1681 0.3601 0.3087 0.1323 0.0284 0.0024
6 0.1176 0.3025 0.3241 0.1852 0.0595 0.0102 0.0007
7 0.0824 0.2471 0.3177 0.2269 0.0972 0.0250 0.0036 0.0002
8 0.0576 0.1977 0.2965 0.2541 0.1361 0.0467 0.0100 0.0012 0.0001
9 0.0404 0.1556 0.2668 0.2668 0.1715 0.0735 0.0210 0.0039 0.0004 0.0000
10 0.0282 0.1211 0.2335 0.2668 0.2001 0.1029 0.0368 0.0090 0.0014 0.0001 0.0000
11 0.0198 0.0932 0.1998 0.2568 0.2201 0.1321 0.0566 0.0173 0.0037 0.0005 0.0000 0.0000
12 0.0138 0.0712 0.1678 0.2397 0.2311 0.1585 0.0792 0.0291 0.0078 0.0015 0.0002 0.0000 0.0000
13 0.0097 0.0540 0.1388 0.2181 0.2337 0.1803 0.1030 0.0442 0.0142 0.0034 0.0006 0.0001 0.0000 0.0000
14 0.0068 0.0407 0.1134 0.1943 0.2290 0.1963 0.1262 0.0618 0.0232 0.0066 0.0014 0.0002 0.0000 0.0000 0.0000
15 0.0047 0.0305 0.0916 0.1700 0.2186 0.2061 0.1472 0.0811 0.0348 0.0116 0.0030 0.0006 0.0001 0.0000 0.0000 0.0000
16 0.0033 0.0228 0.0732 0.1465 0.2040 0.2099 0.1649 0.1010 0.0487 0.0185 0.0056 0.0013 0.0002 0.0000 0.0000 0.0000 0.0000
17 0.0023 0.0169 0.0581 0.1245 0.1868 0.2081 0.1784 0.1201 0.0644 0.0276 0.0095 0.0026 0.0006 0.0001 0.0000 0.0000 0.0000 0.0000
18 0.0016 0.0126 0.0458 0.1046 0.1681 0.2017 0.1873 0.1376 0.0811 0.0386 0.0149 0.0046 0.0012 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000
19 0.0011 0.0093 0.0358 0.0869 0.1491 0.1916 0.1916 0.1525 0.0981 0.0514 0.0220 0.0077 0.0022 0.0005 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000
20 0.0008 0.0068 0.0278 0.0716 0.1304 0.1789 0.1916 0.1643 0.1144 0.0654 0.0308 0.0120 0.0039 0.0010 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
21 0.0006 0.0050 0.0215 0.0585 0.1128 0.1643 0.1878 0.1725 0.1294 0.0801 0.0412 0.0176 0.0063 0.0019 0.0005 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
22 0.0004 0.0037 0.0166 0.0474 0.0965 0.1489 0.1808 0.1771 0.1423 0.0949 0.0529 0.0247 0.0097 0.0032 0.0009 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
23 0.0003 0.0027 0.0127 0.0382 0.0818 0.1332 0.1712 0.1782 0.1527 0.1091 0.0655 0.0332 0.0142 0.0052 0.0016 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
24 0.0002 0.0020 0.0097 0.0305 0.0687 0.1177 0.1598 0.1761 0.1604 0.1222 0.0785 0.0428 0.0199 0.0079 0.0026 0.0008 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
25 0.0001 0.0014 0.0074 0.0243 0.0572 0.1030 0.1472 0.1712 0.1651 0.1336 0.0916 0.0536 0.0268 0.0115 0.0042 0.0013 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
50 0.0000 0.0000 0.0000 0.0000 0.0001 0.0006 0.0018 0.0048 0.0110 0.0220 0.0386 0.0602 0.0838 0.1050 0.1189 0.1223 0.1147 0.0983 0.0772 0.0558 0.0370 0.0227 0.0128 0.0067 0.0032 0.0014
0.0006 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000


+1 to hit:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
1 0.6000 0.4000
2 0.3600 0.4800 0.1600
3 0.2160 0.4320 0.2880 0.0640
4 0.1296 0.3456 0.3456 0.1536 0.0256
5 0.0778 0.2592 0.3456 0.2304 0.0768 0.0102
6 0.0467 0.1866 0.3110 0.2765 0.1382 0.0369 0.0041
7 0.0280 0.1306 0.2613 0.2903 0.1935 0.0774 0.0172 0.0016
8 0.0168 0.0896 0.2090 0.2787 0.2322 0.1239 0.0413 0.0079 0.0007
9 0.0101 0.0605 0.1612 0.2508 0.2508 0.1672 0.0743 0.0212 0.0035 0.0003
10 0.0060 0.0403 0.1209 0.2150 0.2508 0.2007 0.1115 0.0425 0.0106 0.0016 0.0001
11 0.0036 0.0266 0.0887 0.1774 0.2365 0.2207 0.1471 0.0701 0.0234 0.0052 0.0007 0.0000
12 0.0022 0.0174 0.0639 0.1419 0.2128 0.2270 0.1766 0.1009 0.0420 0.0125 0.0025 0.0003 0.0000
13 0.0013 0.0113 0.0453 0.1107 0.1845 0.2214 0.1968 0.1312 0.0656 0.0243 0.0065 0.0012 0.0001 0.0000
14 0.0008 0.0073 0.0317 0.0845 0.1549 0.2066 0.2066 0.1574 0.0918 0.0408 0.0136 0.0033 0.0005 0.0001 0.0000
15 0.0005 0.0047 0.0219 0.0634 0.1268 0.1859 0.2066 0.1771 0.1181 0.0612 0.0245 0.0074 0.0016 0.0003 0.0000 0.0000
16 0.0003 0.0030 0.0150 0.0468 0.1014 0.1623 0.1983 0.1889 0.1417 0.0840 0.0392 0.0142 0.0040 0.0008 0.0001 0.0000 0.0000
17 0.0002 0.0019 0.0102 0.0341 0.0796 0.1379 0.1839 0.1927 0.1606 0.1070 0.0571 0.0242 0.0081 0.0021 0.0004 0.0001 0.0000 0.0000
18 0.0001 0.0012 0.0069 0.0246 0.0614 0.1146 0.1655 0.1892 0.1734 0.1284 0.0771 0.0374 0.0145 0.0045 0.0011 0.0002 0.0000 0.0000 0.0000
19 0.0001 0.0008 0.0046 0.0175 0.0467 0.0933 0.1451 0.1797 0.1797 0.1464 0.0976 0.0532 0.0237 0.0085 0.0024 0.0005 0.0001 0.0000 0.0000 0.0000
20 0.0000 0.0005 0.0031 0.0123 0.0350 0.0746 0.1244 0.1659 0.1797 0.1597 0.1171 0.0710 0.0355 0.0146 0.0049 0.0013 0.0003 0.0000 0.0000 0.0000 0.0000
21 0.0000 0.0003 0.0020 0.0086 0.0259 0.0588 0.1045 0.1493 0.1742 0.1677 0.1342 0.0895 0.0497 0.0229 0.0087 0.0027 0.0007 0.0001 0.0000 0.0000 0.0000 0.0000
22 0.0000 0.0002 0.0014 0.0060 0.0190 0.0456 0.0862 0.1314 0.1642 0.1703 0.1476 0.1073 0.0656 0.0336 0.0144 0.0051 0.0015 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000
23 0.0000 0.0001 0.0009 0.0041 0.0138 0.0350 0.0700 0.1133 0.1511 0.1679 0.1567 0.1234 0.0823 0.0464 0.0221 0.0088 0.0029 0.0008 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000
24 0.0000 0.0001 0.0006 0.0028 0.0099 0.0265 0.0560 0.0960 0.1360 0.1612 0.1612 0.1367 0.0988 0.0608 0.0318 0.0141 0.0053 0.0017 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000
25 0.0000 0.0000 0.0004 0.0019 0.0071 0.0199 0.0442 0.0800 0.1200 0.1511 0.1612 0.1465 0.1140 0.0760 0.0434 0.0212 0.0088 0.0031 0.0009 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
50 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0005 0.0014 0.0035 0.0076 0.0147 0.0260 0.0415 0.0606 0.0808 0.0987 0.1109 0.1146 0.1091 0.0959 0.0778 0.0584 0.0405
0.0259 0.0154 0.0084 0.0043 0.0020 0.0009 0.0003 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000


+2 to hit:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
1 0.5000 0.5000
2 0.2500 0.5000 0.2500
3 0.1250 0.3750 0.3750 0.1250
4 0.0625 0.2500 0.3750 0.2500 0.0625
5 0.0313 0.1563 0.3125 0.3125 0.1563 0.0313
6 0.0156 0.0938 0.2344 0.3125 0.2344 0.0938 0.0156
7 0.0078 0.0547 0.1641 0.2734 0.2734 0.1641 0.0547 0.0078
8 0.0039 0.0313 0.1094 0.2188 0.2734 0.2188 0.1094 0.0313 0.0039
9 0.0020 0.0176 0.0703 0.1641 0.2461 0.2461 0.1641 0.0703 0.0176 0.0020
10 0.0010 0.0098 0.0439 0.1172 0.2051 0.2461 0.2051 0.1172 0.0439 0.0098 0.0010
11 0.0005 0.0054 0.0269 0.0806 0.1611 0.2256 0.2256 0.1611 0.0806 0.0269 0.0054 0.0005
12 0.0002 0.0029 0.0161 0.0537 0.1208 0.1934 0.2256 0.1934 0.1208 0.0537 0.0161 0.0029 0.0002
13 0.0001 0.0016 0.0095 0.0349 0.0873 0.1571 0.2095 0.2095 0.1571 0.0873 0.0349 0.0095 0.0016 0.0001
14 0.0001 0.0009 0.0056 0.0222 0.0611 0.1222 0.1833 0.2095 0.1833 0.1222 0.0611 0.0222 0.0056 0.0009 0.0001
15 0.0000 0.0005 0.0032 0.0139 0.0417 0.0916 0.1527 0.1964 0.1964 0.1527 0.0916 0.0417 0.0139 0.0032 0.0005 0.0000
16 0.0000 0.0002 0.0018 0.0085 0.0278 0.0667 0.1222 0.1746 0.1964 0.1746 0.1222 0.0667 0.0278 0.0085 0.0018 0.0002 0.0000
17 0.0000 0.0001 0.0010 0.0052 0.0182 0.0472 0.0944 0.1484 0.1855 0.1855 0.1484 0.0944 0.0472 0.0182 0.0052 0.0010 0.0001 0.0000
18 0.0000 0.0001 0.0006 0.0031 0.0117 0.0327 0.0708 0.1214 0.1669 0.1855 0.1669 0.1214 0.0708 0.0327 0.0117 0.0031 0.0006 0.0001 0.0000
19 0.0000 0.0000 0.0003 0.0018 0.0074 0.0222 0.0518 0.0961 0.1442 0.1762 0.1762 0.1442 0.0961 0.0518 0.0222 0.0074 0.0018 0.0003 0.0000 0.0000
20 0.0000 0.0000 0.0002 0.0011 0.0046 0.0148 0.0370 0.0739 0.1201 0.1602 0.1762 0.1602 0.1201 0.0739 0.0370 0.0148 0.0046 0.0011 0.0002 0.0000 0.0000
21 0.0000 0.0000 0.0001 0.0006 0.0029 0.0097 0.0259 0.0554 0.0970 0.1402 0.1682 0.1682 0.1402 0.0970 0.0554 0.0259 0.0097 0.0029 0.0006 0.0001 0.0000 0.0000
22 0.0000 0.0000 0.0001 0.0004 0.0017 0.0063 0.0178 0.0407 0.0762 0.1186 0.1542 0.1682 0.1542 0.1186 0.0762 0.0407 0.0178 0.0063 0.0017 0.0004 0.0001 0.0000 0.0000
23 0.0000 0.0000 0.0000 0.0002 0.0011 0.0040 0.0120 0.0292 0.0584 0.0974 0.1364 0.1612 0.1612 0.1364 0.0974 0.0584 0.0292 0.0120 0.0040 0.0011 0.0002 0.0000 0.0000 0.0000
24 0.0000 0.0000 0.0000 0.0001 0.0006 0.0025 0.0080 0.0206 0.0438 0.0779 0.1169 0.1488 0.1612 0.1488 0.1169 0.0779 0.0438 0.0206 0.0080 0.0025 0.0006 0.0001 0.0000 0.0000 0.0000
25 0.0000 0.0000 0.0000 0.0001 0.0004 0.0016 0.0053 0.0143 0.0322 0.0609 0.0974 0.1328 0.1550 0.1550 0.1328 0.0974 0.0609 0.0322 0.0143 0.0053 0.0016 0.0004 0.0001 0.0000 0.0000 0.0000
50 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0008 0.0020 0.0044 0.0087 0.0160 0.0270 0.0419 0.0598 0.0788 0.0960 0.1080 0.1123
0.1080 0.0960 0.0788 0.0598 0.0419 0.0270 0.0160 0.0087 0.0044 0.0020 0.0008 0.0003 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000


+3 to hit:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
1 0.4000 0.6000
2 0.1600 0.4800 0.3600
3 0.0640 0.2880 0.4320 0.2160
4 0.0256 0.1536 0.3456 0.3456 0.1296
5 0.0102 0.0768 0.2304 0.3456 0.2592 0.0778
6 0.0041 0.0369 0.1382 0.2765 0.3110 0.1866 0.0467
7 0.0016 0.0172 0.0774 0.1935 0.2903 0.2613 0.1306 0.0280
8 0.0007 0.0079 0.0413 0.1239 0.2322 0.2787 0.2090 0.0896 0.0168
9 0.0003 0.0035 0.0212 0.0743 0.1672 0.2508 0.2508 0.1612 0.0605 0.0101
10 0.0001 0.0016 0.0106 0.0425 0.1115 0.2007 0.2508 0.2150 0.1209 0.0403 0.0060
11 0.0000 0.0007 0.0052 0.0234 0.0701 0.1471 0.2207 0.2365 0.1774 0.0887 0.0266 0.0036
12 0.0000 0.0003 0.0025 0.0125 0.0420 0.1009 0.1766 0.2270 0.2128 0.1419 0.0639 0.0174 0.0022
13 0.0000 0.0001 0.0012 0.0065 0.0243 0.0656 0.1312 0.1968 0.2214 0.1845 0.1107 0.0453 0.0113 0.0013
14 0.0000 0.0001 0.0005 0.0033 0.0136 0.0408 0.0918 0.1574 0.2066 0.2066 0.1549 0.0845 0.0317 0.0073 0.0008
15 0.0000 0.0000 0.0003 0.0016 0.0074 0.0245 0.0612 0.1181 0.1771 0.2066 0.1859 0.1268 0.0634 0.0219 0.0047 0.0005
16 0.0000 0.0000 0.0001 0.0008 0.0040 0.0142 0.0392 0.0840 0.1417 0.1889 0.1983 0.1623 0.1014 0.0468 0.0150 0.0030 0.0003
17 0.0000 0.0000 0.0001 0.0004 0.0021 0.0081 0.0242 0.0571 0.1070 0.1606 0.1927 0.1839 0.1379 0.0796 0.0341 0.0102 0.0019 0.0002
18 0.0000 0.0000 0.0000 0.0002 0.0011 0.0045 0.0145 0.0374 0.0771 0.1284 0.1734 0.1892 0.1655 0.1146 0.0614 0.0246 0.0069 0.0012 0.0001
19 0.0000 0.0000 0.0000 0.0001 0.0005 0.0024 0.0085 0.0237 0.0532 0.0976 0.1464 0.1797 0.1797 0.1451 0.0933 0.0467 0.0175 0.0046 0.0008 0.0001
20 0.0000 0.0000 0.0000 0.0000 0.0003 0.0013 0.0049 0.0146 0.0355 0.0710 0.1171 0.1597 0.1797 0.1659 0.1244 0.0746 0.0350 0.0123 0.0031 0.0005 0.0000
21 0.0000 0.0000 0.0000 0.0000 0.0001 0.0007 0.0027 0.0087 0.0229 0.0497 0.0895 0.1342 0.1677 0.1742 0.1493 0.1045 0.0588 0.0259 0.0086 0.0020 0.0003 0.0000
22 0.0000 0.0000 0.0000 0.0000 0.0001 0.0004 0.0015 0.0051 0.0144 0.0336 0.0656 0.1073 0.1476 0.1703 0.1642 0.1314 0.0862 0.0456 0.0190 0.0060 0.0014 0.0002 0.0000
23 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0008 0.0029 0.0088 0.0221 0.0464 0.0823 0.1234 0.1567 0.1679 0.1511 0.1133 0.0700 0.0350 0.0138 0.0041 0.0009 0.0001 0.0000
24 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0004 0.0017 0.0053 0.0141 0.0318 0.0608 0.0988 0.1367 0.1612 0.1612 0.1360 0.0960 0.0560 0.0265 0.0099 0.0028 0.0006 0.0001 0.0000
25 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0009 0.0031 0.0088 0.0212 0.0434 0.0760 0.1140 0.1465 0.1612 0.1511 0.1200 0.0800 0.0442 0.0199 0.0071 0.0019 0.0004 0.0000 0.0000
50 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0003 0.0009 0.0020 0.0043 0.0084 0.0154 0.0259 0.0405
0.0584 0.0778 0.0959 0.1091 0.1146 0.1109 0.0987 0.0808 0.0606 0.0415 0.0260 0.0147 0.0076 0.0035 0.0014 0.0005 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

[bakalov]

May be it is easier to know the formulae:

Base chance to hit is 0.3
Each plus to hit adds 0.1 (up to +0.3 for normal units))
Magic/Mithril/Adamantium +0.1
Lucky +0.1
- Holy weapon +0.1
- Prayer +0.1
- High Prayer +0.2
* Chance to hit cannot be greater than 1, and 1 means automatic hit.
The average damage for each figure is attack strength multiplied by chance to hit. Of course the target'sdefence should be applied in similar way to calculate the real damage.

The base chance to block is 0.3
lucky adds +0.1
eldritched enemy weapon substracts -0.1
Prayer adds +0.1
High Prayer adds +0.2
So here thr maximum is 0.7 (if I am not missing something).
The average absorbed damage should be the chance to block multiplied by the defence strength.

[DaveV]

The problem with using the "average" numbers is that the curve is pretty flat, and you see "non-average" results a lot. I remember sending Theria, with defense 8, into a node with unicorns (attack 5, +1 to hit), expecting her to be safe (average damage blocked = 8*.3 = 2.4; average damage inflicted = 5*.4 = 2.0). Well, they killed her pretty quickly. Looking at the table, the unicorns have a 31.74% chance of inflicting 3 or more damage, so I'd expect at least one figure to hit for that much on each attack.

I usually look at per-figure expected results on attack. An easy example (and a common early-game unit for me) where the numbers work out exactly is veteran halfling swordsmen with magic weapons (3 attack, +2 to hit). The expected result on each attack: 1 figure misses, 3 figures hit for 1 damage, 3 figures hit for 2 damage, 1 figure hits for 3 damage. That averages to 1.5 damage, just like in bakalov's calculation, but the damage done will tend to be much higher than that average would lead you to estimate (i.e., if the defender has 5 shields, he might expect to block all the damage, but will on average take about 4 hits per attack).

[bakalov]

Of course there is probability the enemy to get luckier and hit harder than the average, or you to defend poorer than the average. There is no such thing as "safe", but you can improve your odds :-) Theoretically there is possibility to have 50 def and to block 0 :-) A very small probability but it can happen ....

[pchang]

Unicorns are special:
They have an armor piercing attack so your shields against them are halved. No wonder Theria got killed pretty easily.

[DaveV]

I opened up my hacking.txt file and my trusty hexeditor, and verified that unicorns do not have armor piercing attack in my game (patch 1.3.1).

Edit: fixed game version.

[pchang]

Guess you are right. I just looked myself. Now I could have sworn they were armor piercing. Where would I have gotten the notion. Oh well, you were just unluckly I guess. In general though, attack is better than defense. There are all sorts of + modifiers to the swords attack calculations but very fiew + modifiers to the shields defense calculations. Thus, the swords are typically hitting with a 50% chance and the shields defending with a 30% chance.

[DaveV]

Originally posted by pchang
Oh well, you were just unluckly I guess.
No, the point I meant to make is that it was bad judgement to send Theria into that situation, rather than bad luck that she died. With 8 shields, Theria still has a 25.53% chance of blocking less than two hits, and a 55.18% chance of blocking less than 3 hits. I'd expect following for a 4-figure unicorn unit: one figure hits for 1 damage, one figure hits for 2 damage, one figure hits for 3 damage. The fourth figure has about an equal probability of doing 0, 2, or 4 damage. Over a number of attacks, Theria's shields *will* fail to block some damage. Long before she can kill a decent number of unicorns, they will be able to kill her.

[pchang]

Why do the unicorns get a 40% chance to hit. I thought it was 33%.

[bakalov]

There is no such chance as 33%. The default chance is 30% and the modifiers increase it by 10% each. Certain summoned creatures have +to hit ability. If the unicorns have +1 to hit, this means their chance will be
30%+1.10% = 40%

[DaveV]

Actually, unicorns turn out to be +2 to hit. No wonder they had such an easy time with Theria...

[pchang]

I just used Theria to wipe out some unicorns and guardian spirits. But, she had been boosted to 13 shields. And, I had to cast 2 heal spells too. That +2 to hit for the unicorn is very powerful.