The Biophagus can enhance the musculature, aggression or resilience of his test-subjects. When we have the option, which should we go for?
The Biophagus is an out-and-out buffing piece, but a very unpredictable one. When his Genomic Enhancement ability affects Core units (acolytes, neophytes, metamorphs, jackals), any bonuses he confers are randomised between AP+1, exploding 6s and 5+ FNP. They’re all potentially useful in the right situations, but we can’t reliably apply them anywhere. The important exception is aberrants, where the enhancement can be chosen (with 5+ FNP seemingly the most popular option).
So the question here is this: which of the three enhancements is the most useful? In exploring this one, we’ll focus on aberrants (because they have a choice of enhancement, rather than having one imposed on them), but we’ll also have a broader look at how buffs affect probability and damage outcomes, and how that might affect our choices across the wider game.
[Sidebar point: for our purposes in this particular corner of maths, exploding 6s (when they generate exactly one additional hit each time) are functionally the same as +1 to hit. You can find a fuller explanation of why this is (and also where they’re different) over here. But for now, we can treat it as the same thing.]
PERCENTAGES: IT’S ALL RELATIVE
Percentages can be an awkward thing to discuss in terms of dice-rolling, because we can use very different numbers to talk about the exact same thing.
For example, if I have a unit that hits on 6s, and then give them +1 to hit, how much better are they? At 6s, each attack has a 16.7% chance of hitting (16-and-two-thirds, if we’re being really picky). Going to 5s means that unit now has a 33.3% chance of hitting, so we’ve improved by 16.7% (ignoring the rounding error). This is consistent for each step – every time we gain +1 to a roll, no matter what number we need, we gain an additional 16.7%.
However, we’ve also doubled our chance to hit, from just 6s to 5s and 6s. That’s a 100% increase in hit rate. The difference here is that this figure is relative; it varies depending on the numbers we start with (unlike the 16.7% increase, which remains fixed). Take aberrants, for example: they usually hit on 3s, and a +1 to hit would move that to 2s – a 16.7% increase. But the jump from 3s to 2s (or 4/6 to 5/6) is also a 25% increase – we’re now getting an extra 25% hits relative to a non-buffed aberrant.
Here's how the relative increase changes as we work through different WS scores. (The same would also be true for BS, the wound roll, saves (gaining light cover, for example) and any other similar roll.)
[WS2+ gains no benefit here, as 1s always miss. Otherwise, it would have been a 20% increase. That said, the exploding 6s of enhanced aggression would still work here, if we could get the aberrants up to WS2+ some other way.]
We can see that the worse our initial WS (or BS, AP, or even our chance to wound), the more we benefit from an increase, because the relative increase is greater. This doesn’t often matter when comparing different units – your WS6+ models might get a greater relative gain, but my WS3+ unit will still get more hits overall. But it does matter within a single attack sequence where we could potentially modify either the hit roll or the save roll. Now we’re competing against ourselves, and making the right choice will directly affect the outcome.
And this is where the difference between an absolute percentage increase (the flat 16.7% for gaining an extra pip on the dice) and the relative increase (the variable percentage score based on the relative change) really matters, especially when it comes to calculating things like damage outcomes. Here’s why.
MULTIPLIERS
Within a given sequence, a multiplier at any point affects the whole outcome by the value of the multiplier. When we calculate a predicted damage outcome, we multiply the chances of a successful hit, successful wound and failed save together to give the chances of causing damage. For example, a WS6+ attack, wounding on 4s against a save of 3+ looks like this: 1/6 x 3/6 x 2/6, which comes to 6/216 or 1/36. Now, imagine that we can double the chances of hitting (by going to WS5+, a 100% relative increase). That would give us 2/6 x 3/6 x 2/6, or 12/216, or 2/36 – doubling the chance to hit doubles our final result. In absolute terms, it’s not a big increase, at just an extra 1/36; but in relative terms, it’s twice the damage. If our attack sequence would have killed one enemy, now it kills two.
We could achieve the same thing by modifying AP instead of WS. In this example, we’d need to jump to AP-2, forcing a 5+ save, which doubles the chance of a failed save from 2/6 to 4/6. Now our sequence looks like this: 1/6 x 3/6 x 4/6, which is 12/216 or 2/36 again. Doubling any single element of the sequence doubles the outcome. Great. But you’ll notice that it was easier to double the chance to hit (via +1 to WS), than it was to double the chance of a failed save (where we had to find an extra 2AP).
This is where we finally get back to the original question: which genomic enhancement is most effective? And the answer is: the one that gives the greatest relative increase. Sadly, this isn’t ever going to be completely clear-cut, because only two of the three options affect the damage sequence. The third, enhanced resilience, affects our survivability instead. However, we can still apply the broad principles here, even though the relative increase doesn’t mean much – resilience moves us from no FNP roll to 5+ (which is effectively an infinite increase). Ultimately, this one is a preference call – if you want your aberrants to be more survivable, go with resilience; if you prefer to live fast, die young and do as much damage as you can on the way out, then musculature or aggression may be for you.
MUSCULATURE OR AGGRESSION?
Because aberrants almost always hit at WS3+, enhanced aggression has a fairly stable effect, offering a 25% increase in damage output. In the event that we find ourselves hitting on 4s, the relative increase rises to 33% - as we touched on earlier, the less accurate you are, the more a WS bonus matters. But generally, we’re looking at a 25% increase (meaning that for every 4 dead enemies, we’d now be looking at 5).
Enhanced musculature is more variable, because the relative increase depends on the target’s save. Given that aberrants have a base AP-2, let’s see how that pans out.
To maximse our overall damage output, we’re looking for the greatest relative increase from either the hit roll or the save roll. Given that the hit roll will usually be a 25% increase, that’s the better option against a save of 4+ or worse (the extra AP is wasted against 5+ or worse anyway). There’s parity against a 3+ save, but most 3+ saves come from power armour, which now has Armour of Contempt – where that’s the case, we get a better outcome from modifying AP rather than WS.
Let’s try that out. Assuming a mathematically helpful 36 attacks, how do things play out against marines?
As we predicted, modifying AP is more useful here, producing 33% more failed saves (compared to the 25% increase in damage output from aggression). Modifying the hit roll feels like the more obvious choice, because of the extra hits and subsequent extra wounds, but in this particular case, the saving throw matters more, and those extra wounds count for little when they bounce off the armour.
CONCLUSIONS
In short, between enhanced musculature and aggression, musculature (AP+1) is the better option against anything with a 3+ or better save. Against lighter targets, where the AP-2 of the heavy power weapon is already removing most (or all) of the save, we’re better off taking the extra hits offered by aggression.
More broadly, the lesson here is that we gain more from boosting our weaknesses than our strengths. That feels slightly counter-intuitive. After all, who doesn’t want to see WS3+ pushed up to WS2+. But relatively speaking, it’s a waste – if we’re already pretty good at hitting things accurately, we don’t gain much for being just a bit better. Instead, we’ll get much more efficiency from boosting a poor AP or a low chance to wound.
Just to demonstrate that, one last example. Here, our unit has WS3+, wounds on 4s, and the enemy saves on 2s (we have AP0). So we start with a 67% chance of hitting (which is good), and a 16.7% chance of beating the save (which is less good). Again, we’ll use 36 attacks.
We gain a 100% relative increase by boosting our weakness (beating the save), but only a 25% relative increase boosting our stronger attribute (the hit roll). And that plays out in the final outcomes.
All that said, there aren’t necessarily many opportunities to decide between various buffs in the way that the Biophagus offers. So this may not come up all that often. But at least we know what to do when it does. In the meantime, keep those vials bubbling, and may all your experiments go to plan.