Archery Halving Evasion: Broken Mechanic

[DavidMedley]

From the Sil Manual:

Archery

• Helps you hit an opponent in ranged combat.
• difficulty = half opponent's evasion
• You can also get critical hits (if you succeed by enough).
• See Combat section for full details.

Despite being someone who has spent a ton of time thinking about these issues for his own game systems, I didn't spot the issue here for quite a while.

With Sil skill checks, as in most game mechanics, it's the differential between two numbers and not the ratio which counts. Whether it's Perception vs Stealth or Melee vs Evasion or Song vs Will, a skill of 20 vs 10 is the same as 10 vs 0 and 40 vs 30. 20 vs 10 is not the same as 10 vs 5 or 40 vs 20. Halving a target's evasion doesn't do much at lower skill levels, but it's entirely out of proportion at higher levels.

Other problematic scaling:

- If you are unfortunate enough to be fighting from within a pit or a web, both your evasion and melee scores are halved
- Melee, Evasion, and Archery are halved against foes you cannot see
- Free attacks made by enemies when you fire at point blank range: your evasion is halved (Sil-Q)

So, a basic orc
P:[+3,1d4]
B:HIT:HURT: (+2,2d6)

trying to hit his twin is at net -1 to hit, 47.5%. If he's shooting or his foe is in a web, his twin's evasion is reduced to +1 and he has a 57.25% chance to hit. Nice advantage, right?

Meanwhile, a Vampire Lord
P:[+26,1d4]
B:CLAW:WOUND: (+29,3d7)

trying to hit his equal is at +3 to hit, xx%. If he's shooting or his foe is in a pit, his target's evasion is 13 and he has a 98.5% chance to hit!! Not to mention all the accompanying criticals.

What is the solution? Well, depends partly on what we're trying to accomplish. If the idea is that there's only so much even a very swift character could do to avoid a missile, well... I don't see a ton you can do within the constraints of opposed d20 rolls, and I won't go into alternative systems. Could halve the *rolls* of these disadvantaged souls, which is like a -5 penalty but with less variance. Then you wouldn't have to make exceptions for the minimum evasion already in place for stationary enemies. Or don't mess with the dice and just apply a flat [-X] to these situations.

[Quirk]

So, just to begin, orcs aren't foolish enough to blunder into webs and pits. It's only the hapless player who does so, and who is well advised to keep handy a source of free action, or perhaps even a staff or song of freedom, in order to neutralise these dangers.

You are roughly correct in your concerns about archery scaling, but there are a few other contextual things that need to be considered.

Firstly, most importantly, is damage. The real question is not how often you hit your enemy, but how fast you can expect to kill your enemy. If your bow did 1d1 damage, you could be shooting with Archery of 100 against an asleep enemy at -5 Evasion, scoring 13 criticals or so, and still rarely piercing the armour of some of the lower enemies*.

Bows are not however 1d1 and in fact in Sil 1.3, Archery had multiple significant advantages, some of which I lay out here: http://angband.oook.cz/forum/showthread.php?p=133300. Where archery base damage is competitive with or superior to melee, the bonus criticals are a big deal.

In Sil-Q Flaming Arrows has since gone, as has Precision and bows with slay effects. Arrows of slay or poison still attract an extra damage die.

I dialled back damage sides on longbows and dragon-horn bows (the latter getting several damage dice to compensate). We're not at 1d1 territory, but broadly speaking the damage without crits is worse than typical melee weapons now.

Secondly, archers are open to attacks of opportunity. Firing point blank at an enemy without having the skill Point Blank gets you attacked twice each round. Being surrounded is terrible, as even with the skill Point Blank everyone you're not aiming at is attacking you twice. In another change from Sil 1.3, in Sil-Q your own evasion is halved against attacks of opportunity - you can't parry very well with a bow. Archery is still powerful - at distance.

Thirdly, some enemies resist or negate crits. Those that resist crits halve your critical damage dice, those that negate crits do away with them altogether. Mostly the crit-resisting enemies are undead, some are rauko; the crit-negating ones are plants or stone.

Fourthly, of course, archery needs arrows. Run out of arrows and you're suddenly falling back on skills that haven't had much investment.

*13 criticals: assumption based on the critical base being 7 (no skill now exists to lower this for archery) with a 1 lb bow - heavier bows of course will score fewer criticals.

1d1 with 13 criticals is 14d1. 6d4, the armour of some of the deeper serpents, averages 15 protection. About 43% of the time you will do no damage; 90% of the time you will do 4 damage or less. Being able to hit an enemy is not the same as beating it.

[DavidMedley]

You are roughly correct in your concerns about archery scaling, but there are a few other contextual things that need to be considered.

Of course there's a lot to it. That doesn't change the fact that halving a skill is not amenable to a system that relies on differential. And I know that you know this. And I know you've worked hard on the balance. But it's like trying to describe the solar system from an earth-centric point of view. It can be done, but everything is so much simpler if you put the sun at the center.

(OK, technically you should put the center of mass at the origin point, but that's damn near the center of the sun.)

[DavidMedley]

I did read the post you linked to before I wrote my little manifesto. I also wrote a couple pages on this very topic (differential vs ratio) a month or two ago, related to a game system I was working on. I didn't want to get too off-topic in my first post, but some items that were of interest:

• Differential systems are good for easy math
• Differential systems are inherently exponential
• When you treat a differential system as linear you can get expectation-breaking results

As an illustration, I used very low and high strength characters from D&D (GURPS is even more out of whack in this case). A STR 1 character can carry 15 lbs while a STR 9 character can carry 135 - 9x as much. If they're rolling and adding their STR bonus, the stronger gets +4. A STR 20 giant can carry 300 lbs while a giant can carry 420 lbs - 1.4x as much. If they're rolling and adding their STR bonus, it's the same +4 differential.

The two things are out of whack because one is treating STR scores as linear and one, perhaps without really knowing it, is treating STR scores as exponential.

[Quirk]

People do get confused by multiple dice systems all the time, I agree. It's one of many reasons I'm sceptical when people laud the simplicity of this game - it's transparent enough that results can be calculated, but probability is not intuitive.

However, one consequence of a system such as this is that acquiring sufficiently high Evasion over their current enemies' Melee makes a player effectively invincible. Small offsets to this will not put the player back in the danger zone. Large offsets will overly punish low Evasion players. Webs and pits are actually quite well placed IMO as dangerous but survivable hazards.

Player archery is definitely harder to balance than melee, for many reasons of which this is not the least. In reality also archery could be somewhat overpowered, and as simulation you can argue that the system works quite well: a good archer will hit their target, and there is only so much that defensive skills can do to prevent it. The main line of defence is to be well protected by armour that an arrow cannot penetrate.

Reality is not linear; much of nature follows the normal distribution. This means that unfortunately, whether we are modelling this reality with a differential or a ratio system, linear modifiers don't really work very well. The ratio system needs nearly exponential inputs to be able to model skill - Kasparov's chess skill has to be many orders of magnitude larger than a rank novice - so a linear modifier which describes Kasparov getting slightly better against his peers turns a contest between novices massively lop-sided. The differential system's flaws with linear modifiers are similarly obvious. When the behaviour being modelled is non-linear, linear bonuses deform the simulation. However human beings like the security of seeing "simple" numbers like +1 that plug neatly into an easy calculation even if that calculation just happens to output non-linear behaviour.

[DavidMedley]

Archery aside, does it make sense to you that two high level monsters fighting each other would be so massively impacted by a pit or a web? Much, much moreso than two low level monsters?

[Quirk]

Archery aside, does it make sense to you that two high level monsters fighting each other would be so massively impacted by a pit or a web? Much, much moreso than two low level monsters?

Broadly, yes. I would expect a highly skilled fighter to dispatch a partly incapacitated opponent much more rapidly and effectively than a less skilled one.

To revisit the chess analogy, if two novice players find one of the pawns is missing and play some games anyway, it's less likely to change the results than if a grandmaster has to play another grandmaster at a pawn down. Margin for error decreases as skill improves.

[wobbly]

I like the archery mechanic. Not as much as I like a good gamer logics argument. If 2 monsters in seperate pits fight, what is an appropriate penalty? I don't know, are they webbed as well?

Halved evasion is the only reason late game archery works on melee guys. People might argue that you should have to invest in archery & I'd argue skill systems lead to lopsided min-maxed builds. It's also the reason enemy archers are dangerous to lightly armoured characters. Now I'm not disputing that there's broken things about it. Just saying I enjoy the resulting balance.

[DavidMedley]

How about negative skills? Should they also be halved when in a web, pit, or being shot at?

[Quirk]

How about negative skills? Should they also be halved when in a web, pit, or being shot at?

I think the only case of negative skills that is normally seen is the -5 Evasion for sleeping monsters. To be honest the existence of the -5 is a bit nonsensical / arbitrary, it would seem more fitting for 0 to be the baseline for making no defence whatsoever.

Anyway, negative skills are not penalised in this way and in the case of sleeping shouldn't be (no defence is no defence, webbed or not) though arguably starting at Evasion 0 models this better than hackily ignoring negatives.

Of course the player is able to apply linear penalties to very low Evasion or Melee and reach negative skills, which again IMO doesn't make much sense, but at least it's relatively rare in practice.

[DavidMedley]

Rare or not it illustrates that halving a skill doesn't make much sense at the extremes.

[Quirk]

Rare or not it illustrates that halving a skill doesn't make much sense at the extremes.

Not sure how you get that. Negative skill levels don't make a lot of sense (and they make even less sense in a ratio system than a differential one). Extrapolating anything about mechanics from the way said mechanics interact with them is dubious IMO.

[DavidMedley]

You don't believe analyzing a function's end behavior or asymptotes is useful?

[Quirk]

I do, but behaviour at the end point would logically be at zero, as I have now indicated three times. I am not going to repeat myself a fourth.

I am not any more interested in the behaviour with negative skills than I am in exploring what mechanics work with skills represented by complex numbers. Negative skills are an old hack, there to boost Assassination and/or provide advantage to players with early game Melee low numbers; making these and enemy Evasion higher would also work but require a different design than the current stat+skill.

[DavidMedley]

I count 5 monsters with evasion -5. I don't know why that's not valid to talk about. The game already concedes that halving evasion in these cases doesn't make sense, and leaves them at -5. But, starting at zero, it still doesn't make sense. A creature should still be hindered by webs and pits. But the game says otherwise.

And I'm not using low skill characters as my only example of how broke it is. I chose the deepest non-unique humanoid (Vampire Lord) as an example of how devastating, and in my opinion thematically inappropriate, the halving penalty is. There are even more extreme examples where a web or a pit or other halving penalty turns an even fight into one where the hindered character literally cannot possibly hit or avoid being hit, and/or the unhindered character cannot possibly miss or get hit.