In Hammer of Math we take a weekly look at different statistics questions in Warhammer, run the numbers, and come up with the answers.
Grotmas saw Games Workshop dropping thirty different, all-new detachments on us with new rules and interesting new stats questions. Of these some of the most interesting are those posed by the Creations of Bile Detachment. In this detachment, players can get one of six bonuses that improve the datasheets of their Infantry units, each with different upsides and downsides. Of course, these aren’t created equal and so it’s worth diving into these to understand which ones are better than others – and by how much.
Let’s start by looking at the Detachment rule:
Detachment Rule: Experimental Augmentations
At the start of the battle, pick an augmentation to be active for your non-DAMNED INFANTRY models for the rest of the game. You can either choose one from the list below or roll for two, with duplicates doing nothing for you. If you have Fabius Bile as your Warlord, you can re-roll one or both of the dice in this process.
- Cholinergic Accelerants: +1 Attacks to melee weapons
- Hyperadrenal Infusion: +2” Movement
- Paraneural Reactions: +1 WS on melee attacks
- Subcutaneous Chitination: +1 Toughness
- Macrotensile Sinews: +1 Strength on melee attacks
- Opthalmic Enhancement: +1 BS on ranged attacks
At the start of the game you’ll have the option to either choose one of these or roll for two, and if you roll for two, you’ll get no benefit (nor a re-roll option) if you manage to roll doubles. This will happen 1/6th of the time, or around 18%.
If Bile is your Warlord, you’ll then have the chance to re-roll one or both results. Every time you roll, you have a 1/6 chance to match a given result, or 18%. While dice rolls are independent events – any given roll does not affect the probability of another – your odds of getting two doubles in a row are about 1/36.
Note that if you’re rolling this, the process is:
- Roll your 2D6
- Decide whether to re-roll one or both
- Make all rolls
Which unfortunately locks you out of the more preferable option of “re-roll one, then opt to re-roll the other,” but your odds are still pretty OK for avoiding a duplicate roll. Unfortunately there’s no magical way to avoid doubles – your odds are always going to be 1 in 6 for that (there are six outcomes where this happens out of 36 possible outcomes rolling 2D6).
Now let’s talk about the enhancements themselves.
The Enhancements
When we get to the enhancements you can get, they basically fall into two categories: Melee buffs and the other stuff. For melee buffs, you’ll often want to double up on these but if you can only get one, it’s worth having an idea of which of the three – +1 Attack, Strength, or Weapon Skill – will actually give you the most bang for your buck. Unfortunately, this kind of depends on your units, your weapons, and the targets. +1 Weapon Skill is meaningless on your Chaos Lords, who already hit on a 2+, and +1 Strength will only matter against some targets and with some weapons. So we’ll look at a few different units and situations and examine how different buffs affect their output. Specifically we’re going to look at:
- Astartes Chainswords
- Accursed Weapons
- Power Fists and Heavy Melee Weapons
- Hideous Mutations
As a quick note, we’re not going to assume any re-rolls for these. While you can have paired accursed weapons and legionaries get re-rolls, it’s not uniform across every unit and it complicates things in ways that aren’t helpful. The math here is otherwise pretty simple. We’ll take the number of attacks a weapon gets and multiply it by the probability of a hit, a wound, the probability of an attack going unsaved after applying AP, and the damage value.
Astartes Chainswords
The humble Astartes chainsword. Most of the models wielding one will have 4 attacks hitting on a 3+ with S4 and AP-1. Against Marine-equivalent targets – that is, models with T4 and a 3+ save, one model with four attacks will do an average of 0.67 damage per activation. That jumps to 0.83 with +1 Attack or Weapon Skill and 0.89 with +1 Strength, where the wound roll suddenly becomes a 3+. That’s because going from a 0.5 to a 0.67 (+34%) on wound probability is a bigger increase than going from 4 attacks to 5 (+20%) or from a 3+ to a 2+ to hit.
If we up the target durability to a TEQ – Terminator Equivalent, i.e. T5, 2+ save, then +1 Attack and WS will still have the same effective value (0.37). It turns out that whenever you start with 4 attacks and a 3+ to hit, getting +1 WS or +1 Attack will always have the same value, as 4 * (5/6) = 5 * (2/3). And +1 to wound is the clear winner here again, giving us 0.67 expected damage per activation.
Accursed Weapons and Hideous Mutations
Next up are the Accursed weapons wielded by Chosen, Terminators, and, by proxy, Warp Talons. These typically throw out 4 attacks at S5, AP-2 with 1 damage. And this is basically where our equilibrium point is for MEQ targets – with weapons that throw out 4 attacks wounding on a 2+ we get exactly the same expected outcome regardless of buff. This means that Chosen and Warp Talons benefit pretty much equally from all three, though it’s worth noting that +1 Attack has marginally more value by virtue of a higher variance – you can spike your initial results and get more damage through with extra attacks, and your chances of rolling more Sustained Hits is higher – more on that in a bit.
If we up the target again to a Terminator Equivalent, we again get more value out of Strength +1, where moving to 3+ to wound takes us from 1.11 expected damage to 1.85.
Hideous Mutations, with their somewhat sad 4 attack, S5 AP-1 profile, are in the same boat here, though it’s worth noting that +1 Strength will have no effect on their Devastating Wounds output, and you’ll typically want to get more hits (WS and Attacks are both good for this) in order to get more chances at Dev Wounds.
Power Fists
When we get to power fists and heavy melee weapons, we get to the first weapon for which +1 Strength doesn’t really matter, at least for smaller targets. You’ll be wounding MEQ targets on a 2+ and +1 Strength won’t help you get there against TEQ targets, where you’ll be on 3+ even at S9. The exception here is Obliterator fists, which hit at S9 normally and will go up to 10. Here +1 Attack has an edge over WS+1, and that’ll be true against TEQ targets as well.
The big difference here comes against heavy targets – if you’re going up against T8 or T9 threats, then going from 4+ to 3+ to wound or 5+ to 4+ is a much bigger deal, but those thresholds aren’t all that common or important – most of the real vehicle and monster threats you’ll encounter will be T10 or higher, making the jump from S8 to 9 less important.
Dark Pacts and Other Considerations
That’s the basic math, and outside of taking lots of chainswords into marine targets, you’ll generally want +1 Attack or +1 WS over +1 Strength. It’s just a lot harder to make the case for +1 Strength since it’s heavily reliant on passing key breakpoints both with your strength and the target’s toughness. And that’s before you consider that +1 Strength doesn’t impact or work with your Dark Pacts at all.
On that note, it’s worth pointing out that once you factor in Dark Pacts to gain Sustained Hits or Lethal Hits, +1 Attack gets the clear edge over both other effects. On average a unit of 5 Legionaries with Chainswords will generate more hits with sustained hits from +1 Attack than with +1 WS (20.8 vs. 20), while generating more wounds from Lethal Wounds as well.
From a unit-specific standpoint, it can depend a bit. I already mentioned that Obliterators really like going to S10 on their melee attacks, but they also don’t really want to be in melee. Plague Marines on the other hand, do like to be in melee and they benefit more than any other unit from +1 WS as their heavy plague weapons are WS 4+; moving to 3+ makes them much more reliable. And while Strength +1 isn’t good in that many situations, moving to S6 with Chosen, Warp Talons, and Possessed can lead to situations where they’re wounding tougher targets on a 5+ instead of a 6+.
Final Thoughts
So if you have to pick – and you aren’t going with +2″ Movement – take +1 Attack. It’s the only ability that’s flat-out always useful on every unit, in every situation, and it’s the only ability that combines with and gets you more value out of Dark Pacts. On the other hand, +1 Strength has the least value for most targets and can be bypassed by the ability to give your units Lethal Hits in situations where you need extra wounds. If I roll double 5s on my results, there’s a good chance I’m re-rolling both dice. If I roll +1 Attack, I’m always keeping it.
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