# Hammer of Math: Quick Hits, 12/16/2019

We’ve been linking a questionnaire form for you fine readers to submit ideas for us to explore, and this week’s article will be the first of those Quick Hits. Get it? Hammer of Math? Quick Hits? We know it’s that kind of comedy that brings you back, reader. Thank you.

### Plague Surgeon Value

Our first question comes from Julian, who asks:

How many infantry models need to be in range of a Plague Surgeon for his re-rolls of Disgustingly Resilient to make his points back? Nurgle daemons can produce a similar effect with either a strat or Epidemius, so the calculation should work here as well.

For the purpose of this question I’ll interpret “make his points back” to mean that the Plague Surgeon preserves a quantity of wounds whose value equals the 60 point cost of the Plague Surgeon (or the 100 point cost of Epidemius, but he does a LOT of other cool things as well).Â Disgustingly Resilient is a 5+ Feel No Pain, which means it works against every wound (including mortal wounds). This isÂ extremelyÂ powerful, as every wound that is saved still has to be removed by a future attack. And a portion ofÂ those wounds are saved as well, repeating the process for countless iterations until finally the thing dies. The formula for calculating the effective number of wounds that particular save gives is:

Effective Wounds = Wounds * 1 / (1 – P(Save))

So a 6+ save effectively multiplies the wounds by 120%, a 5+ save 150%, 4+ save 200%, 3+ save 300%, and a 2+ save 600%. This is one of the reasons why things like Stratagems giving Knights a 3++ save is so imbalancing; the increase in effective wounds is as dramatic as going from no save to a 4+. The Plague Surgeon’sÂ Tainted Narthecium allows players to re-roll any Disgustingly Resilient rolls of 1 for Death Guard INFANTRY units within 3″. This is a flat 16.7% improvement to the probability since only 1 in 6 attempts will result in a re-roll. This changes the Death Guard roll from a 33.3% chance of success to 38.9%. In terms of effective wounds this changes the multiplier from 150% to 164%. That 14% difference is the influence of the Plague Surgeon. If we divide the 60 point value of the Plague Surgeon by that 14% we get the value of models that must be around him in order to make back his points. That value is 429 points, minus 60 for the Surgeon himself (since he boosts his own DR rolls), for a total of 369 points (nice), or 74 Poxwalkers.

When it comes to surrounding the Plague Surgeon with units that will actually make that value back, things can become a bit more complicated. We chose Poxwalkers here because, without an armor save (the Poxwalkers’ armor save is 7+), their effective wounds are entirely dependent on their Disgustingly Resilient ability, making them ideal for doing effective wounds/value earned back math. If you want to determine what other units to best surround your Plague Surgeon with, there are two schools of thought you could take:

1. Surround the Plague Surgeon with units that are more likely to be dependent on the boost from his DR bonus to survive. That means units with lower toughness and worse saves. This makes Poxwalkers an ideal target, but suggests that if you want to pare down unit counts, Plague Marines are your next best bet (or Foul Blightspawn) with their 3+ armor saves. This maximizes the number of times you’ll be likely to actually use the Tainted Narthecium’s re-roll.
2. Surround the Plague Surgeon with the biggest, baddest units you can – Typhus, Blightlord Terminators, and Deathshrouds, basically – in order to maximize the increase in effective wounds as a result of the Plague Surgeon’s ability. Over the course of the game you may see fewer re-rolls, but you’ve instead maximized the longevity of your army’s toughest infantry units, and it takes fewer models to recoup that Plague Surgeon’s cost.

There’s no “right” answer here, but in either case, the general guideline is that you need to keep your Plague Surgeon nearÂ a lot of points if you want him to earn his value using the Tainted Narthecium.

### Smash Tyrant Part Deux

Last week I discussed how Blood of Baal changed the math for some Tyranid options, and included a few “Smash Monsters” that took advantage of the Murderous Size Adaptive Physiology benefit. ReaderÂ Reaper asked me to follow up with what I agree was a significant omission:

What about the Reaper of Obliterax on a Flying Behemoth Hive Tyrant with Monstrous Size, Adrenal Glands, Toxin Sacs and a Heavy Venom Cannon? Chances for a successful charge and killing potential, please. đŸ™‚ Deep Strike in, shoot something with the HVC to boost itself with Hunter’s Drive for that sweet 9″ 90% charge probability. Buff up with Unstoppable Hunger, get in there. Drop Voracious Appetite to re-roll the wounds, for your S7 -3 AP Reaper, that will wound a Knight on 4+ thanks to Unstoppable Hunger for 4 damage, or for 9 damage on a wound roll of 5+! Rinse and repeat with Fight Again Stratagem if needed.

So the first question is what is the probability that the Hive Tyrant will get off his charge. A Hive Tyrant with wings is going to deep strike in for the typical >9″ distance, requiring a 9 or better on 2d6. The presence ofÂ Adrenal Glands adds +1 to the charge roll, and if the shooting attack by the Hive Tyrant kills a model thenÂ Hunter’s Drive allows the Hive Tyrant to get an extra die and drop the lowest value. And being Hive Behemoth the Hive Tyrant also gets to re-roll all failed charges.Â  We covered the probability of charges last week and Reaper is correct that the resulting probability is 90%. Without Hunter’s Drive it’s still a respectable 66%.

Next up is the attack portion. The Hive Tyrant in question is bolstered by several abilities and powers. TheÂ Reaper of Obliterax is an enhancement to the monstrous lash whip and bone sword weapon (User Strength, AP -2, 3 Damage, and even if the bearer dies it still gets to fight) which doubles the weapon’s damage on a wound roll of 6+.Â Toxin Sacs have a similar benefit, increasing the damage dealt by 1 on a wound roll of 6+.Â Murderous Size is an Adaptive Physiology which improves the Strength, AP, and Damage of a weapon by 1.Â Unstoppable HungerÂ is a new WC7 power from Blood of Baal which adds 1 to the wound rolls of melee attacks for a unit. AndÂ Voracious AppetiteÂ is a 1 CP Stratagem which allows a MONSTER or CHARACTER unit to re-roll wounds. The end result is 4 attacks which have the potential to do 9 damage on a wound roll of 5+. The previous iterations didn’t do so well against a Knight (especially compared to the Space Marine Smash Captain options), but let’s see how this version does.

Note that these curves are different from last week’s because they also include the use of Voracious Appetite and the Toxin Sacs. What’s interesting is that while on average the Reaper of Obliterax attack did more wounds (19.9 wounds versus 17.8 for the pair of monstrous scything talons), the Reaper of Obliterax was far more spread out with nearly twice the standard deviation (9.3 for the Reaper, 5.0 for the talons). The Reaper was able to one-shot a Knight nearly 40% of the time, whereas the pair of monstrous scything talons had roughly half the success rate. The talons were more reliable in the long run, but the Reaper can absolutely put out an insane amount of damage. It’s definitely worth considering.