This week’s Hammer of Math looks at how the presence of Wards and Armour Saves changes the resiliency of units.
The new Battletome: Nighthaunt has been released and with it come some very cool abilities for the ghostly boys (and gals) of Nagash. One of the more terrifying ones is Ethereal, which combines a 6+ ward (which can be further improved) and ignores all modifiers (positive or negative) to save rolls. The ability also allows units to retreat and charge (which makes sense for the incorporeal), but our focus will be on the impact of saves.
The challenge with understanding how saves (especially wards) impact the battlefield is that their effect is cumulative; every wound that is saved forces another attack which can also potentially be saved. One way to examine this is to look at effective wounds, which can roughly be considered the average amount of damage that has to be inflicted on a target in order to get past all of its saves. This is something I have covered extensively in previous articles on the Warhammer 40k side, but the AoS system for rending and wards makes it easily translated.
The formula for effective wounds in AoS is as follows:
Effective Wounds = Wounds * (1/[1 – P(Save)]) * (1/[1 – P(Ward)])
In other words the effective wounds of a model is equal to the product of the Wounds characteristic of the model, the reciprocal of the probability that the model will fail the armour save, and the reciprocal of the probability that the model will fail the ward1. Since AoS uses a D6 system for saves we can calculate the values for the reciprocal.
What this means is that a model with a 2+ save is roughly six times harder to kill than a model with no save at all, and that 2+ save makes a model twice as resilient as a model with a 3+ save. And since the effect is multiplicative ward can be particularly nasty. A model with a 4+ armour save and a 5+ ward is equivalent to a 3+ armour save, only the 5+ also works against mortal wounds.
Impact of Rending
While Rending won’t affect wards (or anything with the Ethereal trait), against most units the the impact of Rending is significant. When you think in terms of effective wounds even reducing an armour save by 1 can be the equivalent of doubling the number of attacks when you’re reducing a 2+ down to a 3+. The inverse is also true given that Ethereal prevents modifiers from affecting the save. A model with a 4+ save against a -2 Rend would only have an effective wounds of 120% given the 6+ save. Apply Ethereal and the effective wounds is now 240%, or twice as hard to kill as the unit would otherwise be.
The fact that saves are applied against every attack makes them a major component of the resiliency of units in AoS. When looked at from the perspective of effective wounds, seemingly small effects like small Rending modifiers or a 6+ ward can have a huge impact depending on the value being modified. What makes things particularly interesting for AoS is how the hit and wound rolls are (generally) unaffected by the target, which makes effective wounds calculations even more useful and relevant.
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1 I’m fully aware of how unhelpful that probably was for most of you and regret nothing.