This week’s Hammer of Math looks at the numerical impact of some of the rules changes associated with the 40k Balance Dataslate released for April.
I’m a huge fan of how Games Workshop is making the 40k ruleset more flexible and responsive. I remember years ago when the idea of even getting a FAQ was laughable, and now GW is releasing quarterly updates which contain significant alterations to game balance. While it sucks to have your favorite army nerfed, it sucks even more to have an army that is so weak that it’s just not fun to play. It’s nice to see major changes outside of a new book release, and I feel it goes a long way towards maintaining the health of the game.
For an insight about how the Balance Dataslate will impact things from a competitive point of view, I highly recommend checking out our Roundtable article.
Armour of Contempt
First up is a major addition that applies to any ADEPTUS ASTARTES, SANCTIC ASTARTES, HERETIC ASTARTES, or ADEPTA SORORITAS model. Assuming your model doesn’t have certain wargear, abilities, or is already under an affect that worsens/reduces Armour Penetration then the Armour of Contempt ability will now “worsen” the Armour Penetration of all incoming attacks by 1. Basically what this means is that the ability will shift the AP of an incoming attack one step closer to 0, but it can’t make it become AP +1.
From a mathematical point of view, the effect of altering a gatekeeping roll like an armour save is that can significantly affect the number of attempts required to ensure a successful result. The higher the initial probability, the greater the effect of increasing the probability. One way to look at things is the effective number of rolls required on average to bypass a particular probability. Attacks that are saved require a follow on attack, and those attacks may also be saved, and so forth. The formula is below, along with a chart showing the impact.
Effective Wounds= 1 / [1 – P(Save)]
This is not the first time we’ve brought this up, and I even emphasized how minor changes can lead to massive imbalances in a previous article. So how does Armour of Contempt impact things? What we can do is look at the delta in effective wounds caused by increasing the save for a particular combination of AP and Save characteristic. For example let’s say we have a 3+ save getting hit by AP -2 for an effective save of 5+ and an effective wounds of 150%. With Armour of Contempt the save is now a 4+ and the effective wounds is 200%, which is a 33% increase relative to the original value. In other words you’ll need 33% more attacks to get the same effect as before.
The effect is considerable, with AP -1 weapons being 20% less effective (at best) and 50% less effective against the most common 3+ save in these armies. The change also affects high AP weapons against their preferred targets (assuming no invulnerable save), which can be particularly unpleasant given that these weapons typically only get a few shots.
Indirect Fire Weapons
Any weapon that can target units that are not visible to the bearer are considered Indirect Fire weapons, and if no targets are visible to the bearer then the attack reduces the Ballistic Skill characteristic and increases the armour save of the target by 1. ASTRA MILITARUM units are not affected, but things like T’au airburst launchers and Hive Guard impaler cannons are. And because this new rule directly affects the characteristic of the target and firer it stacks with other effects like Dense Cover or Armour of Contempt above.
We can analyze the effect of this rule change through a similar method as above, with two changes. First we need to examine the cumulative probability of the hit and save rolls. Because the two rolls are generally independent (meaning that the hit roll usually does not affect the save), the probability of the attack getting through the hit roll and save roll is the product of each probabilities. In other words if you’re hitting on a 3+ and your opponent is saving on a 3+ then the probability of hitting and getting past the save is (2/3) * (1/3) or (2/9). The second change that we need to make is that we need to look at the effective save of the target instead of the Save characteristic. This way we can incorporate AP without needing to worry about creating a bunch of charts for each scenario. The effective save is just the AP (a negative number) subtracted from the Save characteristic. So for example a 2+ save against an AP of -2 has an effective save of 4+.
This change is brutal. For example, Hive Guard impaler cannons (BS 3+, AP -2) firing into something with a 3+ save need 78% more shots to be as effective as they were before the update (though note that the Hive Guard have a way around this in the new Codex). If that something happens to have the new Armour of Contempt rule then the Hive Guard need twice as many shots as before. Toss in the damage of Dense Cover or Light Cover and things get even more unpleasant. It’s pretty clear that Games Workshop is fully aware of how effective it is to hide units out of Line of Sight and attack with impunity, and there is now a price to pay for doing so.
Both Adepta Sororitas and Salamanders received a modification to their faction abilities, gaining the ability to deny units the ability to re-roll wound rolls against them. This was done because Armour of Contempt made their original abilities superfluous. The impact of this ability depends on the original re-roll. In the case of re-rolling 1s the effect is a flat 17% reduction in effectiveness. Against abilities that allow you to re-roll any value the impact increases as the original probability decreases, going all the way up to an 83% reduction versus a target number of 6+. Against Transhuman Physiology the effect is a 50% decrease in effectiveness assuming the attacker intended to re-roll any value of 3 or less.
Having played 40k on and off since 2nd Edition, I feel like we’re entering a new era of competitive balance and responsiveness on the part of Games Workshop. While there are a lot of players who are unhappy about the changes (particularly Custodes), these kinds of adjustments will do a lot to keep the game fresh. All of these changes are significant alterations to the state of the game, and I’m excited to see how things shake up because of them.
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