Request for Comment: Subdual damage comparison

[Blankbeard]

After our recent thread on subdual damage, I decided to try to run the numbers as a reference.  I'd like to request comment and correction.  Please be specific.


Subdual Damage and the Special Character

In combat, PCs can face two sorts of opponents, standard and special characters, and have three basic damage types to inflict on them: Lethal, Subdual, and Stress.  How do these compare? 

Let's first get standard characters out of the way.  All three types perform the exact same way. Your GC may state that subdual damage causes knockouts and that stress causes surrender or fleeing but all three types are equally effective at removing standard characters from combat.

What about special characters?  Against specials, lethal damage is straight up damage while stress and subdual act as "save or suck" condition inflicting effects. Both apply up to 4 grades of their condition and then cause unconsciousness on a fifth failed save.  In both cases non-lethal damage accumulates until a save is failed then it is reset to zero, leaving only the inflicted condition.

Critial hits also act differently.  Stress and subdual damage both stun on a critical while lethal damage is applied directly to the targets wounds.

Bearing this in mind, let's find out how long it takes for these damage types to remove a target from combat.  Since stress and subdual damage are nearly identical in mechanism, I'll present only subdual and lethal and deal with stress damage after.  Let's meet our target dummy!

Code:

TL 10
Def V, Res X, Health X
Con 18  Fort +16  Def 20
500 Vitality 18 Wounds

Not too difficult to hit but very hard to kill.  This should be a worse case scenario as most specials simply aren't this tough.  And here's the guy who'll be doing the beating:

Code:

Soldier 10, Str 18, weapon forte, Crunch!, Killer Instinct using Superior weapon
To Hit +15  (80% hit rate versus Def 20)
War Hammer (1d12+8 Sub AP2 Keen 4 crit 20) and Long Sword (1d12+8 AP 2 Keen 4 crit 20)

For our purposes we're leaving out the effects of feats, tricks and will discuss those later.

Subdual Damage

Hits		1		2		3		4
Accumulated Dmg		14		29		43		58
Save DC		17		24		32		39
% Failing		0		35		75		100

The percent failing is per round so 35% fail in 2 hits, 49% in 3, and 16% in 4 hits.
That means that the average failure time is (0.35 * 2) + (0.49 * 3) + (0.16* 4) = 2.81 hits to fail a save
and (2.81 * 5) = 14.05 hits to fail 5.  It takes our soldier (14.05 / 0.80 hit chance) = 17.56 i.e. 18 swings to knock out our special.  Since being fatigued drops Dexterity by 2 per grade and thus Defense by 1 per grade, we can knock two swings off and say that it takes 16 swings to finish our creature.

Lethal Damage 
No Crits:   518/14.5 = 38 hits /0.80 hit chance = 45 swings.
Crits:  Since a single critical will kill with average damage, the important number is the average time to achieve a critical.  That should be (1/2 / 0.5) = 10 swings.
Silly: Use a 14th level Soldier.  One in a million gives a crit on the first swing, most deadly saves the action die, damage is high enough for an instakill.  1 swing.

Summary:  Crits rule.  Soldiers rule.  If criticals are possible, lethal damage is the quickest method of removing specials from combat.  Higher Health than Resiliance favors subdual with the reverse favoring lethal.

Grade X is a bit harsh.  How does grade V change things?
Making health and resistance grade V gives 250 health (and 23 swings to slog through it) and a +11 Fortitude save.  That changes our last line on the subdual chart to 25% failing on the first hit, 45% on the second, and the remaining 30% on the third hit.  Average time to fail a save is 2.05 hits, resulting in 13 swings, 11 or 12 after the "death spiral" is taken into account. 

What does increased critical range do?
For subdual damage, nothing.  The stun protects the party from damage but doesn't directly decrease the time to knock out the target.  For lethal, more likely crits are usually quicker crits.

But I have to spend an action die to activate a critical.  I need those!
Action dice, unlike action points, refresh every session.  Don't hoard them.  There are several class abilities and feats that either reduce the cost of activating criticals or give extra dice.  Failing access to one of those, you could try roleplay to get more.

What happens as Threat Levels scale?
Fortitude saves and Vitality scale but Wounds doesn't.  PC Damage by itself doesn't scale but can be increased through magic and feats. In most cases PC damage will either keep up with or somewhat outpacing the increase in saves.  However, higher TL creatures are often higher XP and may have more defenses (Tough, No Pain, ect.)

What about Stress?
Everything said about subdual applies to stress.  No weapon inflicts stress damage as its primary damage type.  Two weapons (scourge and razor) have the excrutiating quality that causes them to inflict 1/2 their normal damage in stress in addition to their normal damage type.  The whip feat chain allows whips to inflict stress damage.  Most types of stress are very hard to boost damage on significantly but are skill based and thus easy to score damage with.  Fewer specials will have high defenses against stress than subdual.  Stress will in general not be significantly more effective than subdual and often slower.

How do feats and tricks affect outcomes?
Rather than trying to list every trick that could affect the outcome, I thought I'd just point out that the only weapon (unarmed excluded) that inflicts full subdual damage and has a damage affecting trick is the sap with pummel, which gives triple damage as a full action.  There are several damage multiplying tricks available for non-subdual weapons. 

[Crafty_Alex]

Thanks for running the numbers, Blankbeard. The issues we're seeing with subdual damage really become apparent in higher levels of play where effectiveness gap between lethal and subdual starts to get noticably wider. Pat and I had a VERY long conversation about damage in the game in regards to Spycraft and Mastercraft in general, and discussed with fans during Gencon, and subdual damage is getting a very close look. Expect changes on this front - what they will be is still up in the air, but we are definitely aware.

[MikeS]

Am I reading correctly that the dummy has 18 Wounds and the Soldier does 1d12+8?

With average rolling, you'll need two crits then to kill the dummy, bringing your lethal swings up to 20 if you're simplifying the probabilities, which is worse than the subdual.

What am I missing?

[Doublebond]

I don't *think* the matter of critical hits is a legitimate point concerning the effectiveness of lethal. If combat is to become a game of surviving until you can land critical hits, then why track vitality at all at later levels?

[Coyote0273]

I don't like the matter of critical hits is a legitimate point concerning the effectiveness of lethal. If combat is to become a game of surviving until you can land critical hits, then why track vitality at all at later levels?

It isn't so much that critical hits are required as much as they can change a field real quick. I've had a soldier in a game walk up to a special NPC with 60 vitality, and kill it in two swings because he went Crit/Crit. Hence, keeping track of how often they happen radically changes how long bad guys last.

I think the main problem in regards to subdual damage actually isn't in the subdual at all. Vitality in bad guys just scales way way way too fast, and no other type of damage resistance scales nearly as fast. So that subdual damage that rocks the NPCs at level 1 is almost as effective at level 10, which the same bad guy has 10 times the vitality, but maybe 2 or 3 times the save bonus vs subdual.

[foproy]

with a assassin character i did it in one using just a couple of tricks.

[spinningdice]

On the question of Vitality, I'm currently running a game with only 2 PC's, I've taken the step of 1/2 NPC vitality across the board (my theory - average players = 4/5, so 2 players is a 1/2 size party), which is a lot better at least for my purposes.

[SilvercatMoonpaw]

Hm, at threat level 20 NPC vitality can range between 100 and 500.  But if you took out the "x 5" it'd be 20 and 100.  More reasonable?

[Blankbeard]

Am I reading correctly that the dummy has 18 Wounds and the Soldier does 1d12+8?

With average rolling, you'll need two crits then to kill the dummy, bringing your lethal swings up to 20 if you're simplifying the probabilities, which is worse than the subdual.

What am I missing?

Keen adds its value to damage on criticals.  When you score a critical, you can add an action die to your damage roll.  Also, remember that these are 10th level soldiers with 10 feats available.  If they both have have the supremacy feats for their weapons, the long sword guy's average damage goes up to 20.5 while the hammer guy doesn't change.   I just wanted to show equal amounts of lethal and subdual against an opponent.

And yes, crit guy ends up spending 1 or 2 action dice.  But adding them into subdual guy's damage doesn't change the average time by even a swing.

Hm, at threat level 20 NPC vitality can range between 100 and 500.  But if you took out the "x 5" it'd be 20 and 100.  More reasonable?

My immediate sense is that a high level combat focused character will tear through 100 vitality in a single round.  I need to run TL20, it looks like. 

[Antilles]

Not quite Blankbeard. Keen is imaginary damage, to see if you inflict massive damage or a critical injury (a roll on the table of ouch), not an actual increase in damage.
Otherwise, great job running the numbers, I was thinking about doing it myself a while back but couldn't be arsed to do any actual math...

[Blankbeard]

Ack.  You're right.  I've been using that wrong for as long as it's been around.  I'll correct it on the 20 TL

[Sletchman]

How do feats and tricks affect outcomes?
Rather than trying to list every trick that could affect the outcome, I thought I'd just point out that the only weapon (unarmed excluded) that inflicts full subdual damage and has a damage affecting trick is the sap with pummel, which gives triple damage as a full action.  There are several damage multiplying tricks available for non-subdual weapons.  

I'm not pointing this out to be a dick, but technically every trick can be applied to subdual weapons - both Rootwalker construction and Greenstone material (AC) make the weapon subdual, and don't lower damage.  While both are setting dependant things, in my mind they serve to completely level the playing field - you can't go "oh but lethal has (Trick X)", because the counter argument is that a Rootwalker (weapon) also has (Trick X) in subdual form.

EDIT: Also, interesting take.  I'd done this in my head previously, but not quite to this extent.  Of course unlike others I have no problem with the current subdual rules set.

[Blankbeard]

How do feats and tricks affect outcomes?
Rather than trying to list every trick that could affect the outcome, I thought I'd just point out that the only weapon (unarmed excluded) that inflicts full subdual damage and has a damage affecting trick is the sap with pummel, which gives triple damage as a full action.  There are several damage multiplying tricks available for non-subdual weapons.  

I'm not pointing this out to be a dick, but technically every trick can be applied to subdual weapons - both Rootwalker construction and Greenstone material (AC) make the weapon subdual, and don't lower damage.  While both are setting dependant things, in my mind they serve to completely level the playing field - you can't go "oh but lethal has (Trick X)", because the counter argument is that a Rootwalker (weapon) also has (Trick X) in subdual form.

EDIT: Also, interesting take.  I'd done this in my head previously, but not quite to this extent.  Of course unlike others I have no problem with the current subdual rules set.

No, this is exactly the sort of feedback I'm looking for.  It means that a lot of the extra weapons comparison I was thinking about is not needed.

Following are tables that hopefully show a bit more of the issue.  Since the second and third Res values appear across the table, they correspond to more than one vitality value. 

Res +20 (1000 Vitality)

Damage per strike		2		10		20		40		64
time to fail save		22		4.42		2.58		1.55		1
time to knock out		110		22.1		12.9		7.75		5
total damage (subdual)		220		221		258		310		320

Res +12 (Vitality 500-520ish)

Damage per strike		10		20
time to fail save		2.74		1.75
time to knock out		13.7		8.75
total damage (subdual)		137		175

Res +6 (Vitality 90-150ish)

Damage per strike		6		10		20
time to fail save		2.12		1.83		1.35
time to knock out		10.6		91.5		6.75
total damage (subdual)		64		92		135

The issue is concentrated on the right side and worse towards the bottom. 

[Morgenstern]

I actually have some concerns with your methodology. Average times don't mean quite what you think they'd mean in a cascading event system. With vitality attacks you are looking to amass a sum, and sums are well explored through averages, but in the critical hit AND subdual/stress systems you are trying to increment events, and your variations work differently. Average is generally taken to be "there's a 50% chance it'll take more, and a 50% chance it'll take less to get the job done, and looked at that way the crit system is FAR more lethal than you are giving credit for.

Asuming a single crit event will end the fight (and thats a pretty sound assumption), you are suggesting the average time for a crit based kill with a threat range 19-20 is 10 rounds. That is NOT true. That methodology postulates that in ten rolls made at the same time, there is a 50% chance one of them will be a threat - that says very little about what happens when you take 10 rolls in order and are strongly concerned with when the event result actually occurs. The actual chance a fight will go on after N hits looks like this...

% Chance fight continues after…
Hit   20   19-20   18-20   17-20
 1   95   90   85   80
 2   90.3   81   72.3   64
 3   85.7   72.9   61.4   51.2
 4   81.5   65.6   52.2   41.0
 5   77.4   59.0   44.4   32.8
 6   73.5   53.1   37.7   26.2
 7   69.8   47.8   32.1   21.0
 8   66.3   43.0   27.2   16.8
 9   63.0   38.7   23.2   13.4
10   59.9   34.9   19.7   10.7
11   56.9   31.4   16.7   8.9
12   54.0   28.2   14.2   6.9
13   51.3   25.4   12.1   5.5
14   48.8   22.9   10.3   4.4

In other words, the 'average' time to kill an opponent via crits (19-20) is less than 7 hits, not 10. Moreover, that lethaltity basically does not scale with level or vitality, so all other rates are compared to that curve at all threat levels. The real lethality of lethal damage attacks vs. named opponents has always been determined by crit range. Piling on heaps of vitality is the streak breaker function for a long series of non-threatening rolls . That is to say "If you don't kill the bigbad with a crit before then, the average damage will eventually take them down with 100% reliability."

[Morgenstern]

So, we have two unrelated conditions - standard opponents where, as has been noted, the three damage types are completely symetrical, and special characters, where lethal damage leaves both the other types completely in the dust (allowing instant kills on the very first hit and likely kills in as few as 6 hits with a threat range of 19-20 being compared to two attack forms where you cannot possibly drop the foe in less than 5 hits, and only become likely to do so after 10 hits... and people are worried subdual is too strong?

I'm gratified that people think subdual is valuable at all!

Irony is we've had this conversation before, but about weapons. Someone new to the game from D&D freaked out saying essentially "OMG, longswords are uber!!1!" I said it then and I'll say it again now, the longsword is a trap, a suductive bit of fluff. The deadliest weapon on that table is a stilletto, and not by accident.