This week’s Hammer of Math takes a look at some of the bonuses and features of the Adeptus Custodes.
The Codex: Adeptus Custodes book has been out for over a month now, and it’s already seen extensive success in several events. From a competitive standpoint it has an excellent blend of flexibility, lethality, and resilience. From a mathematical standpoint it’s… pretty boring. Just a lot of good things put together. We covered the walking blender that is the Blade Champion back in December, and this week we’re back to look at some other aspects.
Tanglefoot Grenades
Custodes have access to the Tanglefoot Grenades Stratagem for 1CP, which can be used once per turn at the start of the opponent’s Movement or Charge phase. You pick a unit within 12″ and visible to a Custodes INFANTRY unit, and subtract D6″ from their Movement characteristic or charge roll down to a minimum of 0″. Note that this occurs at the beginning of the phase, before any unit moves are declared, so the opponent at least knows how badly they’re screwed before they commit.
And the answer is that sure enough, they’re pretty screwed. A 9″ charge goes from being a not great but viable 27% (roughly 1 in 4) to 5% (1 in 20). If the Custodes player rolls a 4+ on their D6 roll then no number of re-rolls or “roll N pick 2 highest” abilities will enable a 9″ charge. Things are certainly better for units like Eversors (3d6″ charge range) or units under the Canticles of Hate for a +2″ charge bonus, but the Stratagem still puts them below the curve of an unmodified 2d6 charge roll. For scenarios in which the charge range is reduced but still feasible the chart below provides the numbers for a variety of charging scenarios.
Guardian Spears vs Castellan Axes
In addition to being excellent bodyguards for any <SHIELD HOST> CHARACTER model within 3″ thanks to their Watchmen ability, Custodian Wardens pay the same price when choosing between castellan axes and guardian spears. Both have identical shooting profiles and deal 2 damage in melee, but the castellan axe has +3 S and -2 AP while the Guardian Spear has +2 S and -3 AP. So which one is preferable for a variety of scenarios?
Since the number of attacks and damage are identical for these weapons, we can focus exclusively on the combination of gatekeeping rolls which produce the effective probability of wound. As a refresher, 40k is divided into a series of driving rolls and gatekeeping rolls. Driving rolls (attacks and damage) determine the raw output of the attack, while gatekeeping rolls serve as go/no-go probabilities which will end the attack when failed. By comparing these probabilities for combinations of target Toughness and Save characteristics we can determine which areas show superior performance
Overall we see that the guardian spear thrives across certain toughness bands where the target is saving o a 4+ or better. Both perform the same against Space Marines, while against Adeptus Sororitas, Gravis, and T6 opponents like a Talos the spear is more effective. T8 is a sweet spot for the axe, especially against Crusher Stampedes which will get an invulnerable save which makes the spear even less effective. Note that these probabilities do not include the effects of invulnerable saves, re-rolls, or the Rendax Marital Ka’tah.
Rendax Stance Comparison
One of the hallmarks of 9th Edition seems to be every faction getting a series of abilities that change over the course of the game and give unfamiliar players a headache trying to figure out what it all means. Space Marines have their doctrines, Mechanicus have their Canticles, Drukhari have their pain parties, and Custodes have their ka’tahs with various stances. One of those ka’tahs is Rendax, which is specifically designed for use against VEHICLE or MONSTER units. Stance 1 allows attacks with an unmodified hit roll of 6 to automatically wound the target, while Stance 2 is limited to melee attacks on the turn in which a unit charged, was charged, or performed a Heroic Intervention. When those requirements are met the unit adds 1 to the Strength characteristics of their attacks.
So which is better? We start with our friendly gatekeeper equation.
P(Damage) = P(Hit) * P(Wound) * (1 – P(Save))
Stance 1 provides an effect that goes off an average of 1 in every 6 attacks, allowing you to bypass the wound roll. Assuming a 2+ to hit this means that 1 in 6 attacks will skip the wound step, and 4 in 6 attacks will go through the original process.
P(Damage, Stance 1) = (1/6) * (1 – P(Save)) + (4/6) * P(Wound) * (1 – P(Save))
How much of an improvement is that? We can do some math to figure that out. We’ll start by incorporating a term X to indicate the difference in probability.
X * P(Damage) = P(Damage, Stance 1)
X * [(5/6) * P(Wound) * (1 – P(Save))] = (1/6) * (1 – P(Save)) + (4/6) * P(Wound) * (1 – P(Save))
We can drop the Save probability from both sides and multiply by 6 to eliminate the denominator.
5 * X * P(Wound) = 1 + 4 * P(Wound)
X = [1 + 4 * P(Wound)] / [5 * P(Wound)]
So the effect of Rendax Stance 1 depends on the probability of wounding. The higher the probability to wound, the less Rendax has an impact. Here, I made a chart so you don’t have to:
Stance 2 is better when the Strength bonus is enough to get you a +1 to wound and you are in melee. Stance 1 works in other circumstances, such as when shooting the target or when your attack is wounding a MONSTER or VEHICLE on a 2+ (in which case you probably don’t need the help). As with many of the Custodes abilities, this is fairly nuanced and requires a good understanding of how the battle will flow as well as when you will face the right targets.
Conclusions
Adeptus Custodes are characterized as the pinnacle of human ability, an elite fighting force armored in the best that the Imperium can produce. With the new book they certainly seem to reflect that, with a combination of Stratagems, weapons, and abilities which can be extremely deadly in the hands of a skilled player. Behind this book is a lot of nuance, and I’m very impressed with how well GW implemented it. Whether it’s the optimal time to deploy a Stratagem like Tanglefoot Grenades, how to best equip your Wardens, or predicting the best situation to apply your ka’tah and in what order, there’s a lot of depth to this army and we’re already seeing the results in tournaments.
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