Thursday, 30 January 2014

Bolting the Stable Door

Important statistical note:

in the following article, I a) forgot; and b) really couldn't be bothered with factoring in the Tearing special property for weapons into my already-nightmarish calculations. Deal with it.

So as an adjunct to my recent faint melancholy about Brother Nikolai, we got talking about the Heavy Bolter. We are not alone in this. The Internet is, in fact, full of people discussing the Heavy Bolter and its OP-ness or perceived lack thereof. In general there's a feeling that it's too good because it does huge amounts of damage. Dan identified a more specific problem, in that the Heavy Bolter is, mechanically speaking, the best possible weapon for:

  • Killing lightly-armoured troops
  • Killing heavily-armoured trooops
  • Killing enormous resilient monsters

and is extremely good (though possibly not quite as good as a heavy flamer) for:

  • Killing hordes
  • Destroying civilian vehicles

and with some serious luck it's actually capable of taking out an actual tank.

A Heavy Bolter rolls 2d10+10 with Pen 6. Each d10 has a 1/10 chance of getting Righteous Fury. Let's assume (extremely conservatively) a 50% chance of confirming Righteous Fury, so a 1/20 chance per d10.

If you roll a single 10, you have a minimum of 27 against the target's Armour, enough to damage a light military vehicle like a bike or walker. You're more likely to have 31.5 as the average roll is 5.5. The Righteous Fury die will tend to increase this to 37, enough to damage a military transport vehicle.

If you manage to roll two 10s (either initially or via Righteous Fury) you have a very reasonable chance of getting the 45 needed to damage a tank.

After some nasty brute-force statistics (which I am willing to concede errors in as I can't really be bothered double-checking)... I reckon you have a 69% chance of damaging Armour 25, a 5% chance of damaging Armour 35, and a 0.36% chance of damaging Armour 45. That, of course, is per hit. A Heavy Bolter will cheerfully get five or six hits, and can get as many as ten. Two rounds of Heavy Bolter fire have about a 50% chance of damaging an armoured personnel carrier like the Rhino. Tanks are vastly, vastly less likely, but it gets complicated with these very low odds and I really can't be bothered calculating the odds allowing for multiple sets of Righteous Fury. Let's just say: it's possible.

The reason this is a problem is twofold. Firstly, it's contrary to canon, where the Heavy Bolter is a very good rapid-fire antipersonnel weapon that can also take out very light vehicles when necessary, but is ineffective against heavily-armoured targets and entirely useless against tanks. Secondly, because the weapon is handed out like a party favour and requires no effort whatsoever to obtain, and is one of the few weapons whose effectiveness not only increases with a good attack roll but does so linearly and does all this at extreme range, there is rarely any point taking any other weapon whatsoever in any circumstances. If this mechanic were to truly represent the in-game universe, the entire Adeptus Astartes should be walking around with Heavy Bolters out of sheer tactical pragmatism.

A possible solution

After some reflection, I am still inclined to think the solution is one I briefly outlined on Dan's blog: firmly embracing the canon. According to everything I have ever read on the subject, bolt shells work like this (nicked from a random online description):

The bolter fires self-propelled, armour-piercing, mass-reactive explosive missiles called bolts. They are constructed to detonate a split-second after penetration, to optimize damage.

A significant part of the damage from a bolt shell comes from detonation after penetrating the target's armour. If the shell does not penetrate the armour, there is no secondary damage from the explosion.

We run into a slight problem here, because Tabletop and RPG model things in substantially different ways despite largely sharing terminology. Thanks for that.

In tabletop, there is (depending on edition) a 1/3 or 2/3 chance that a heavy bolter shell will simply ping ineffectually off armour, even before the ability of Marines to simply shrug off damage comes into play. However, if the shell gets through Armour (with a failed armour save) and Toughness (with a successful wound roll), it will take out the Marine every time because they have only one Wound. So will any weapon.

In the RPG, it is literally impossible for a heavy bolter shell not to penetrate power armour. They have Penetration 6 and a minimum damage of 12, while power armour is at most 10, half the required amount to shrug off a bolt shell. Moreover, only a minimum roll against a hit location of Torso will fail to wound the average Marine (2d10+10 Pen 6 versus Armour 10 and Toughness 8) which is about a 0.1% chance. However, thanks to having 20-odd Wounds the Marine can survive a single full-strength hit from a heavy bolter, although two will almost certainly be fatal. On average each shell will inflict (11.5 + 10 Pen 6 - Armour 2 [8-6] - Toughness 8 =... ) 11.5 Wounds. Against a Terminator this would be 5.5 Wounds.

Whether we can implement a canonical version of bolt weapons depends substantially on how we're prepared to interpret Toughness. If Toughness represents the likelihood that a weapon will not cause injury, thanks to very tough tissue and so on, then we can reasonably argue that a bolt shell failing to overcome Toughness + Armour does not penetrate enough to explode effectively. If Toughness represents the target's resilience to pain or ability to endure damage, however, then we can't fairly argue that a bolt shell that has overcome Armour has not penetrated to a point where full damage from the detonation should be inflicted. Unfortunately, while this might just about be acceptable against mid-heavy infantry like the Space Marines, it's nonsensical against most heavier targets. Terminator armour is only Armour 14, still automatically penetrated by a heavy bolter shell; so is a Carnifex, the toughest Tyranid you're ever likely to encounter. Only the absolutely most armoured entities around - most of them semi-mechanical things - have Armour getting above 16.

But it's not impossible. My mechanical suggestion is that all bolt weapons have their damage split into two parts. Only the first half is inflicted automatically. If the initial damage overcomes Armour, the secondary damage is inflicted; otherwise it has no effect.

Implementing Mass Reactive Bolt Shells

With a heavy bolter, the combination of fixed bonus (+10), Penetration (6) and dice makes a very powerful combination, starting at 16 - more armour than virtually anything we'd encounter. Halving the damage seems the most logical step, but because of the weighty Pen 6 this still leaves us with 12 minimum penetration. If we were to accept the Toughness-as-defence model, then this isn't too bad. Space Marines have A+T of 16 and occasionally a little more; rolling 1d10+5 Pen 6 would leave us with about a 50% chance of a heavy bolter breaking through their defences to inflict additional damage (another 1d10+5). Sadly, even I am sceptical about that interpretation of Toughness for anything other than pure mechanical balance against heavy bolters.

So noting that Armour is typically 8 for a Space Marine, and only 14 for a frikkin' Terminator, we need the minimum damage + Pen for a heavy bolter to be less than 8 if we want this to be any damn use, and ideally for a 14 to be a rare and special thing. Exactly what kind of odds we're looking for depend on how closely we want to adhere to tabletop and which version of tabletop at that.

In the most recent version I played, the chance of a heavy bolter shell taking out a Space Marine are 1/3 (to fail Armour) * 2/3 (to inflict a Wound), giving 2/9. I don't think we should go any earlier than that for examples, and I haven't played any more recent version so I can't use those (and besides, frankly the chances of Space Marines getting any less resilient are slim to none). Bearing in mind that Wounds work differently, I think it's reasonable to work on the odds of a Space Marine running out of Wounds in Deathwatch as the comparator. Let's also note that a tabletop heavy bolter in that iteration fired three shots a round, of which two would hit on average. I believe that means the chance of taking out a Space Marine in any given round were 1-(chance of not taking out, to the power of number of attempts), which means 1-(7/9²) = 1-(49/81) = 1-0.6 = 0.4

The same iteration of the rules would have odds against a Terminator of 1/6 to fail armour and 2/3 to wound, giving 1/9. The chance for a heavy bolter to take one out is about 0.2 per round. In earlier, crunchier iterations, it was vastly less.

Against a Space Marine, I suspect a Deathwatch heavy bolter is also liable to inflict about two hits. Someone using a heavy bolter will likely be competent with it and have equipment or skills that increase their chance of success, meaning an average 50% roll will be a little way under their target number. It could be a lot under, but let's be conservative for now and assume one additional hit.

Working backwards, a Space Marine has about 20 Wounds, so we're looking for heavy bolters to have a 0.4 chance of taking out a Space Marine with two hits; or more broadly, for one bolt shell to inflict about 10 Wounds on average. At present, it inflicts about 15. Ideally, to fit with the canon, I would like there to be a slim chance of the shells glancing uselessly off power armour. I also want this system to be generalisable to other bolt weapons, such that a boltgun has a much larger chance of bouncing off harmlessly.

I get the feeling I probably shouldn't mess with the Pen. That means Damage is all we have to play with for now. I'll begin by maintaining the same overall damage, but that may not last.

First attempt

What if we cut things right down and have the initial damage be only 1d10 Pen 6? Under this scheme, there's a 1/10 chance of a heavy bolter shell glancing off a Marine. Otherwise, it'll go through and inflict the additional 1d10+10 from the explosion. There's also a 3/10 chance of wounding a Terminator. In both cases the additional damage will automatically overcome Toughness, but it's virtually impossible to take down a Marine in a single hit. The average damage will be 21.5 Pen 6.

Damage is (0.9 * (21.5 - 8 - [8-6] = 11.5)), which is 10.35 against a Marine.

Extra added bonus maths!

As noted below I forgot about variable armour, and had to go back, rather against my better judgement.

There's a 40% chance of hitting Torso armour, which is 10 rather than 8. I thought this was a measly difference to begin with, but it actually isn't. Against Armour 10, the shell has a far greater 3/10 chance of failing to penetrate and causes less damage overall.

Average damage to a Marine is therefore the weighted average of (0.9*11.5=10.35) and (0.7*9.5=6.65), giving (6.65*0.4)+(10.35*0.6) for a final average of 8.87.

Overall and accounting for Armour, average damage per hit is 10.35 8.87 against a Marine or 1.65 against a Terminator. This means that, pleasingly, it will take an average of two three hits to fell a Marine and twelve to fell a Terminator.

The heavy bolter remains more or less equally effective against the Marine, and anything less armoured (almost everything) but is now vastly less impressive against a more heavily armoured target.

In contrast, the heavy plasma gun would do an average of 18 damage to the Terminator and annihilate the Marine instantly, the lascannon would do vaporise both, and an assault cannon would finally be a better option for anti-Terminator operations.

Oh, and I should probably rule that the Tearing special rule is applied to the secondary damage, not the initial impact. Allowing a reroll on that would substantially boost the chances of penetrating armour - again, I can't be bothered to do the maths, but it would largely eliminate the chance of a Marine escaping injury from a shell.

That's surprisingly pleasing for a first attempt! What if we apply this principle to the humble bolter? The bolt pistol has identical damage, so we only need do this once.

Bolter

With the bolter (2d10+5 Pen 5), we'd be looking at 1d10 Pen 5 - almost the same. Well, again, if we assume most of the damage comes from the mass reactive charge (as we are repeatedly told by canon) then it makes sense the initial impact of the actual shell is only slightly more dangerous because it's a little bigger.

Here, we have a 1/5 chance of not penetrating power armour - actually, slightly less accounting for Armour 10 on torso, which is a 40% chance hit location... gah.

No, no, I can do this. If we hit non-Torso, there's a 4/5 chance of penetrating power armour, at which point we do an average of (16 Pen 5 vs. Armour 8 and Toughness 8 =...) 5 damage, so overall 4 average. If we hit Torso, there's only a 3/5 chance of penetrating and we do only 3 damage through A+T 18, so 1.8 average. So the final average damage is ((4*0.6) + (1.8 * 0.4) = 2.4 + 0.72 =...) 3.12 damage on a hit. I hope. Maybe? Oh, whatever. It's low, okay? It's low.

Currently, I note, the average damage is ((5*0.6) + (3*0.4)) = 4.2, so it's really not a huge difference. The maximum damage is unchanged. Worth noting, it is now possible to do zero damage to a Space Marine with a bolter, which was not previously the case, but given that this happens all the time in the vast array of Marines vs. Chaos Marines literature out there, this does not bother me one tiny jot. I also think that's far less of a problem mechanically than the opposite - things crossing the "possible to Wound" boundary. The difference between "invulnerable to this" and "1% chance of injury" is far more significant from a game management POV than the difference between "always injured by this" and "95% chance of injury".


Suggested bolt weapon fix

So here's a summary of the important bits from all that guff...

All bolt weapons gain the Mass Reactive quality.

Mass Reactive

Designed to detonate moments after impact, Mass Reactive shells must penetrate armour to achieve their full potential. Initial damage from a Mass Reactive weapon is 1d10, applying Penetration as normal. If the result is less than the target's Armour, the attack is deflected. Otherwise, determine the remaining damage and apply the total against Armour and Toughness as normal.

The Tearing property applies to secondary damage only. Righteous Fury applies to initial and secondary damage.

Example

Brother Genericus fires his bolter (2d10+5 Pen 5) at a Tyranid Warrior. His first hit rolls 1d10 initial damage and scores a 2. With the bolter's Penetration, this penetrates 7 Armour, against the Tyranid's 8, and spangs off its armour.

His second shot rolls 1d10 and scores a 7, piercing 12 points of Armour in total. The shell pierces the Tyranid's carapace and explodes, and the remaining 1d10+5 damage kicks in. With the Tearing property Genericus rolls an additional die and chooses the best; he rolls a 3 and a 1 and chooses the 3, giving 8, which is added to the initial roll. The final damage is 7+3+5=15 Pen 5 against the Tyranid's Armour 8 and Toughness 10. This does 2 Wounds.

A third shot rolls an initial 9 and easily penetrates. Genericus rolls 6 and 8 and chooses the 8 for a final damage of 22 Pen 5. Deducting 3 points for Armour and 10 for Toughness, the hit does 9 Wounds to the Tyranid.


I was expecting to expend more brainpower on this (but not more time, I spent several hours on this, which time I'm sure will be roundly appreciated by a vast horde of admiring oh who am I kidding...) and probably end inconclusively, but then my second idea kind of worked pretty much exactly how I wanted, so... yeah, bye.

8 comments:

  1. FWIW, next time we do Deathwatch I intend to implement my own house rule on autofire weapons: you get to use the bonus only if each shot is targeting a different target (or you're targeting a horde), otherwise it's a penalty instead (as it is all the time in Only War/Black Crusade).

    This will mean that the heavy bolter is still very good against hordes and groups of lightly-armoured foes, decent enough against groups of heavily armoured foes if they're not that tough beneath that armour, but much less good against vehicles, big gribbly monsters, and foes with heavy armour and decent toughness (like Chaos Space Marines, tyranid abominations, and Chaos Demons), which is more or less how it should be. Equally, missile weapons remain just as good because (off the top of my head) I don't think you actually have autofiring missile weapons. I'd also be inclined to rule that you can't spin around and fire in a big circle so you'd have to target the foes you are directly facing.

    The thing that's really devastating about the heavy bolter isn't the damage a single shot does, it's the fact that in the hands of someone like Dan's character you could well be dealing with 5-8 hits per burst, which grinds down even big monsters very rapidly. If you turn that +20 into a -20, however, suddenly the expected hits-per-burst shoots down. (You can still get a sick number of you roll low, but you can't count on it, which means that there's still a tactical consideration to be had.)

    If you didn't have so many hits-per-burst in the last adventure, the tomb-spider would have actually managed to get off a shot itself, and those gauss weapons it had could conceivably have killed you in one shot. And if combats are slowed down a little (because Dan can't shoot everyone to bits in a round or two) then that'll mean there's more opportunity for you to shine.

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    Replies
    1. Blogger completely ignores comment! Try again, probably forgetting my original points...

      Interesting idea. It seems like it should do what you're aiming for, it makes a fair amount of sense, and it's quite simple, which is always nice.

      This was mostly an intellectual exercise for my own satisfaction, because Dan's comment prodded me. I'm not sure I'd actually implement it if I were running a game; apart from anything else I'd want to cross-check it against a number of different targets and compare to several other weapons, just to make sure there's no weirdness creeping in elsewhere.

      Incidentally, I might have missed it and don't have the rulebook with me to check again, but it seems like there's no standing benefit for DoS with single-shot weapons. That seems like it'd be inclined to skew high-BS characters towards autofire weapons, since they gain additional benefit on top of the basic chance of hitting, whereas single-shots don't offer that. Is that right?

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    2. Single shot weapons get the slightly sucky benefit that *one* damage die is capped below at your DoS - so you have one die that cannot be less than 4 if you roll 4DoS, for example.

      This sucks out loud compared to one additional hit per DoS, or even one per two DoS for semi-auto.

      I agree something needs to be done to tame the heavy bolter (I suspect that it's actually better than a heavy flamer for hordes as well - remember we misread the rules first time around so our heavy flamers were twice as effective as they should have been).

      I think if I wanted to implement mass-reactive shells I'd probably go for something simple like rolling 1D10 for damage and only applying the remaining 1D10 + 10 if the initial roll penetrated armour (including the bonus for Pen).

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    3. I think if I wanted to implement mass-reactive shells I'd probably go for something simple like rolling 1D10 for damage and only applying the remaining 1D10 + 10 if the initial roll penetrated armour (including the bonus for Pen). I honestly can't tell, were you deliberately rephrasing my post there? Sorry, it's been a long week.

      Single shot weapons get the slightly sucky benefit that *one* damage die is capped below at your DoS - so you have one die that cannot be less than 4 if you roll 4DoS, for example.

      Ah yes, I remember now.

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    4. I honestly can't tell, were you deliberately rephrasing my post there? Sorry, it's been a long week.

      Oh, not deliberately (I confess I got a bit muddled in all the maths), I just looked for the least faffy way to do it, which involved keeping Pen and taking the most convenient part of the damage (which would be one of the two D10s).

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    5. I got the same idea by a slightly different route, basically. I've added a summary at the bottom now to make things a bit clearer.

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