Kill Modelling

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*** IMPORTANT NOTE ADDED LATER BY AUTHOR ***
As explained below, this model was designed for Experience_Training. I hope to re-collect my data and present another model oriented more for in-game kill probability, when fighting for your life(!). The problem is not that the model isn't well understood - it is - the problem is that I presumed you wanted to keep the target alive, and so I presented the "two side" model. Later I realized folks are also curious about "what's the best weapon, period". These tables definitely roughly approach the answer to this, but not with great precision. (Who can't easily win at Superhuman with 3 of 4 appendages tied behind their back? But then, some challenge themselves by allowing themselves only particular paramaters or weapons.) I hope to address this additional question sometime. In the meantime, I have not changed a thing.
*** END IMPORTANT NOTE ***


This table shows how many hits it takes to kill a target with a particular weapon. For example, it takes an average of 1.65 Laser Pistol hits to kill a newbie soldier (30 Health) in coveralls (12 Front armor, 8 Side armor).

These results are from computer modelling, not in-game testing. However, we think that all aspects of damage are entirely understood (fingers crossed). Each number represents an average of one million modelled kills. Across several runs of a million trials each, the averages only showed variability at the fourth or fifth significant figure. So they are quite solid (fingers crossed that I modelled everything right, though).

The reasoning behind this table goes like this: I knew Mutons were hard to kill with a standard pistol, and way hard with a standard grenade at its edge (more explanation below). Thus, they are good choices for experience training. But how do those two compare? Or are other aliens better targets? And, as long as I had it set up, it was easy to throw in other weapons (and soldiers too!), just for the halibut.

For Ground Zero (GZ) HE hits, only the Under armor is being damaged. For all other situations, the model attempted to target Front armor and one Side's armor. Specifically, with each successive shot, it would shoot either at the Front or the one Side, whichever had more armor. (For experience training, you're trying to keep them alive, not kill them!) The reason two armor aspects was chosen is because 1) it's too much trouble in real life to truly target all four sides all the time, always shooting at the strongest armor, but conversely 2) it's pretty easy to not always be shooting at exactly the same aspect. Thus, two aspects were chosen as a compromise (the Front, and one of the Sides).

See Endnotes for more details on these tables, and Kill Model - Extended Results for deeper info on the model. Also see the Talk page for a note about 2x2 aliens.

Table 1: Overview

Target HPs Armor
(F/S/U)
SG
@Edge
10HE
Standard
Pistol
26 AP
Laser
Pistol
46 LA
SG
@GZ
50 HE
Laser
Rifle
60 LA
Aln.G
@GZ
90 HE
Heavy
Plasma
115 PL
Blaster
@GZ
200 HE
SOLDIERS
Coveralls Noob 30 12/8/2 17.41 2.61 1.65 1.14 1.46 Dead 1.21 Dead
Pers. Armor Soldier 40 50/40/30 Inv 106.25 5.24 2.54 2.94 1.28 1.59 Dead
Power Suit Vet 50 100/80/60 Inv Inv Inv 16.44 25.60 2.25 2.56 1.05
Flying Suit Elite 60 110/90/70 Inv Inv Inv 63.16 71.81 3.28 3.09 1.15
TANKS
Tank 90 90/75/60 Inv- Inv 240.61 Inv- 19.98 8.70- 3.05 1.69-
Hovertank 90 130/130/100 Inv- Inv Inv Inv- Inv Inv- 5.57 2.76-
ALIENS, high armor ( > Beginner difficulty level)
Sectoid 30 4/3/2 4.72 1.98 1.46 1.14 1.33 Dead 1.16 Dead
Floater 35 8/6/12 9.03 2.50 1.64 1.44 1.46 1.02 1.21 Dead
Snakeman 45 20/18/12 Inv 5.15 2.33 1.68 1.87 1.13 1.35 Dead
Celatid 68 20/20/20 Inv 7.38 3.23 2.71 2.34 1.49 1.51 Dead
Zombie 84 4/4/4 13.60- 6.96- 3.58- 2.73- 2.91- 1.74- 1.75- 1.05-
Ethereal 55 35/35/35 Inv 18.01 4.14 3.81 2.66 1.56 1.56 Dead
Muton 125 20/20/10 Inv 34.24- 5.06 3.38 3.72 2.14 1.97 1.17
Chryssalid 96 34/34/34 Inv 24.34 6.02 5.35 4.00 2.26 1.92 1.15
Reaper 148 28/28/4 Inv 20.73 7.07 3.57 4.88 2.24 2.35 1.25
Cyberdisc 120 34/34/34 Inv- 74.70- 7.16 22.67- 4.69 5.39- 2.15 1.90-
Silacoid 114 50/50/10 Inv+ 246.79 11.99 2.50+ 6.45 1.56+ 2.38 Dead+
Sectopod 96 145/130/90 Inv- Inv Inv+ Inv- 24.54+ 26.15- 21.12- 1.97-
ALIENS, low armor (Beginner difficulty level)
Sectoid 30 2/1/1 3.86 1.86 1.42 1.12 1.31 Dead 1.15 Dead
Floater 35 4/3/6 5.29 2.19 1.55 1.31 1.39 Dead 1.19 Dead
Snakeman 45 10/9/6 16.32 3.38 1.92 1.51 1.64 1.07 1.28 Dead
Celatid 68 10/10/10 21.99 4.60 2.53 2.24 2.00 1.36 1.42 Dead
Zombie 84 2/2/2 11.72- 6.38- 3.41- 2.67- 2.81- 1.70- 1.72- 1.04-
Ethereal 55 17/17/17 Inv 5.36 2.51 2.20 1.97 1.30 1.40 Dead
Muton 125 10/10/5 28.22 13.81- 4.04 3.16 3.18 2.03 1.84 1.15
Chryssalid 96 17/17/17 Inv 8.18 3.85 3.21 2.91 1.82 1.70 1.06
Reaper 148 14/14/2 74.83 9.86 5.01 3.53 3.81 2.23 2.10 1.24
Cyberdisc 120 17/17/17 Inv- 14.23- 4.56 6.98- 3.45 3.47- 1.89 1.66-
Silacoid 114 25/25/5 Inv+ 14.38 5.33 2.37+ 3.79 1.52+ 1.95 Dead+
Sectopod 96 72/65/45 Inv- Inv 6.73+ 18.77- 3.85+ 3.80- 3.69- 1.39-

Table 2: Weakest Weapons

Here are kill stats for hitting a Muton Soldier, at Beginner difficulty level, with the two weakest possible types of hits in the game. At Beginner level, all four facings of Muton Soldier armor (Front, Left, Right, Rear) are 10 Armor. The numbers are stats for one million trials, as usual.

This table demonstrates the difference it makes, if you could (magically) ensure that every single hit targetted the armor that is currently strongest, whichever facing that might be. The model rolls each shot's strength randomly and tracks each facing, always choosing the highest armor facing for the next hit. Thus, "1 armor facing" means only one armor panel (of 10 AC) was shot at. "2 armor facings" means that two were targetted (and whichever was strongest as of the next shot, was targetted by it). So on, up to 4 facings. As you can see, having two armor facings does not mean it takes twice as long to kill as with one armor facing, because penetrating damage is cutting away at Health, over and above armor damage.

Also, because I have a lot more room for this little table, I have shown the minimum number of hits it took to kill, the maximum number, and the standard deviation (of the sample). The bolded numbers are ones that are also shown in Table 1; thus this table helps show how it would look if it had been extended to be more than just two armor facings.

Armor  Min  Average  Std.    Max
Faces Hits    Hits   Dev.   Hits                                            _
  1     5    11.33 ± 2.49    26         Standard Pistol (0-31 AP; 40% resist)
  2     7    13.81 ± 3.14    32
  3     7    15.31 ± 3.47    33
  4     7    16.21 ± 3.75    37                                             _
  1    14    20.68 ± 2.82    35            Standard Grenade at Edge (5-15 HE)
  2    19    28.28 ± 3.98    50
  3    23    35.31 ± 4.78    59
  4    27    41.38 ± 5.95    66

The minima and maxima are interesting numbers. They are not the theoretical min and maxxes. They are the observed min and maxxes. Since one million trials were run, this is actually a clear cut case of "one in a million" numbers, especially for the maxxes. The minima have somewhat tighter constraints, especially with a strong weapon vs. a weak critter (especially when the minimum can be 1!). But the maxima could in theory be infinitely high... how many times in a row might the random number generator roll zeroes? Who knows. Quite a bit of variation is seen for the maxima if the model is re-run; considerably less for the minima; and the averages only varied at the fourth or fifth significant figure. Indeed, there is a difference between the Grenade results from this table (28.28) and the one in Table 1 (28.22) due to this, but the Pistol results happened to coincide. (This table is from a different run than Table 1.)

The point of this table is to demonstrate to players dedicated to Experience Training, how important it is (or not) to worry about armor levels, when trying to prolong the kill. As you can see, it is a complex function of weapon type and target. When the damage is close to the armor level, it can take a long time. This is especially true for HE. In the above example, the Grenade is delivering an average of 10 damage - equal to Beginner Muton Soldier armor - but it can only have a maximum of 15. Conversely, the Pistol can do up to 31.

Endnotes

  • HPs = Hitpoints a.k.a. Health
  • Armor (F/S/U) = Armor (Front/Side/Under). Underarmor is used for Ground Zero (GZ) explosions; everything else targets Front and Side armor.
  • SG @ Edge (10 HE) = Standard Grenade at edge, 10 high explosive. See below.
  • Inv in the table means "Invulnerable" - the damage in question can't possibly harm the target.
  • Dead means just that. A guaranteed kill with one hit; survival is impossible. Only happens with explosions, when minimum damage is greater than armor plus HPs. (Unlike HE, firearms can have minimum damage of 0, which means it's always theoretically possible to survive them.)
  • The plusses and minuses after the kill numbers indicate the target is more or less sensitive to the weapon type than the normal 100% - see Modifiers, below.
  • The Soldiers have somewhat arbitrary combinations of HPs and armor, to show a range of what you can expect. (Armor is much more important than HPs.)
  • Alien Health does not vary by difficulty level. However, alien armor has two levels: one level for Beginner difficulty level, and then twice that for all higher difficulty levels. XCOM tanks and of course soldiers have the same armor stats, regardless.
  • All aliens show armor levels corresponding to the Soldier rank for that alien race. (Alien terrorists don't have ranks, however.) Other, higher ranks will have slightly better armor. Because Soldiers are the most common rank (and thus the ones you'll be training on the most), I kept the table simple.
  • The table is roughly sorted so as to have the easiest targets in the upper left, and the hardest in the lower right. More specifically, it is first grouped by category, and then sorted on the Laser Pistol kill number. Then low-armor aliens mimic the sort for high-armor aliens, so that the eye can readily compare them. (There's too much going on for there to be one simple sort that will both show vulnerability, and have all columns smoothly changing.)

Modifiers

Here are the modifiers used for Kill Modelling; they were taken directly from the Damage Modifiers listing. However, they are presented below as their offset from 100%. For example, a silacoid takes +30% (i.e., 130%) High Explosive damage.

  Race            HE       AP      LA      PL

  Soldier*        -        -       -       -
  XCOM Tank     -30%       -       -       -

  Celatid         -        -       -       -
  Chryssalid      -        -       -       -
  Cyberdisc     -40%     -20%      -       -
  Ethereal        -        -       -       -
  Floater         -        -       -       -
  Muton           -      -40%      -       -
  Reaper          -        -       -       -
  Sectoid         -        -       -       -
  Sectopod      -20%       -     +50%    -20%
  Silacoid      +30%       -       -       -
  Snakeman        -        -       -       -
  Zombie        -20%     -40%    -30%    -30%

*Soldiers have normal susceptibility to all four of these damage types. However, Personal Armor and higher is somewhat stun resistant, and entirely invulnerable to incendiary damage.

Putting it all together

I started out just wondering whether Mutons at the edge of a grenade blast were worth bothering with for experience training, relative to the standard pistol firing squad (Table 2). But once that model was set up, it was easy to expand - and show a lot more.

For one thing, I knew in theory that probably some critters were invulnerable to weapon damage. But I hadn't worked through the numbers.

With the table, though, it's clear that many critters are invulnerable to a grenade at its edge. But it's more work to train experience with grenades, and they only provide Firing Accuracy experience. The really interesting finding is for the Standard Pistol (SP), which gives both Firing Accuracy and Reaction experience.

Although the sectopod would be great for target practice - being invulnerable to a SP or even laser pistol - it can't be disarmed. Same for the cyberdisc, another tough creature.

Mutons, reapers, chryssalids, and especially silacoids are great for target practice. Indeed the silacoid (a muton pet) is invulnerable to SPs, and better for training, at higher difficulty levels - an interesting twist due to its higher armor. So it can be moved away with mind control every other turn, then reaction-shot when it moves toward your soldiers.

Once one pistol clip is shot off (12 rounds), you've got more than the eleven Reaction shots needed for maximal Reaction shot increase potential. You've probably also got a good head start on landing 11 hits, for the maximal Firing Accuracy increase. Then just shoot off a second SP clip with direct fire, and you should be good to go.

If unsure of the number of hits landed, you can always peek at Unitref[81]. This (and the Reaction counter at [80]) needs to be at 11 or more, for maximal increase potential (a 2-6 skill point increase dice roll).

Mutons, reapers (floater pet), and chryssalids (snakeman pet) are also good targets - but of course, the latter two have to be kept out of melee range via mind control.

For the record, pets - oops, I mean Terrorists - only accompany their masters on these types of missions/scenarios:

Note that you can use Table 1 to see how many soldiers you can give 11+ or 3+ experience points - these are the best "bang for buck" breakpoints. Example: You're on a Snakeman mission at higher difficulty level (greater than Beginner). Table 1 shows you they'll die from 5.15 SP hits, on average. If there are, say, 8 Snakemen, that's approx. 40 hits to go around. IOW, approx. 13 soldiers can get 3 hits, or approx. 4 soldiers can get 11 hits. Don't forget that Table 1 is for Soldier ranks - higher-ranked aliens have a little better armor, and can take a little more shooting. Also, it models the target being hit on two armor facings - do your best to vary the facings that you target, to prolong their life.

See also