# Hammer of Math: Numbah Krumpin’

In honor of what I’m preemptively calling Ork Week out of respect for my favorite faction, this week’s Hammer of Math is going to cover the much beloved (just not by GW) Stompa in the context of points efficiency. One of the most difficult things to quantify is just how effective a unit given its price, particularly when you consider the vast number of variables and circumstances that surround 40K. In this article we’re going to take a stab at a comparative approach.

The Ork approach to warfare is one of my favorite bits of 40K lore. Everything about Ork Kultur is about fighting, to the point where warfare is so ingrained into the Ork way of life that the notion of peace is incomprehensible. Where other species build works of art, Orks build works of war. The Stompa is the perfect example of this. Take a walking effigy to Mork (or Gork, we here at Goonhammer are strictly non-denominational), give it an adamantium muumuu, cover it in guns and vehicle-sized chainsaws, and point it towards the enemy.

Unfortunately the ideal displayed in the lore doesn’t necessarily match up to the reality of 8th Edition. Clocking in at a whopping 870 points, the Stompa comes with 40 T8 wounds, a 3+ save, and a regrettably limited number of weapons that are hamstrung by the Ork BS of 5+ and GW’s seeming obsession with giving Orks guns with a high variance of shots. In the case of the Stompa it’s several big shootas (27 shots worth), a supa-rokit that gets 1d6 shots each turn (for three turns), a deffkannon which can do 3d6 S10 shots, and a supa-gatler which gets 3d6 S7 shots off can be fired a few extra times at the risk of being rendered completely useless if you fail a roll. It’s a little nastier in melee, getting up to 6 attacks that can hit at S20 and 6 damage or up to 18 attacks that hit at S10 and 1d3 damage. With a Move characteristic of up to 12″ there’s a good chance it will get into combat. All of that and a transport capacity of 20 sounds like a nasty threat until you remember that you’re paying 870 points for a massive level of variance.

So how do we figure out if all of those points are worth it? We stack it up against other peer competitors.

### Relative Efficiency Value

Nearly a year ago Rob put together an article cover the basics of probability, and I expanded on that article in the very first Hammer of Math. In both of those articles we discuss the concept of “expected value”, which simply represents the average outcome that will be produced on a long enough timeline. For example the expected value of a 1d3 roll is 2; 33% of the time the result will be 1, 33% of the time the result will be 2, and 33% of the result will be three. Sum up the product of the probability and result and you get the expected value.

(1/3 * 1) + (1/3 * 2) + (1/3 * 3) = 2

We can expand that concept to the entire sequence of an attack. For gatekeeping rolls (hit, wound, save, ignore wounds) the expected value is simply the probability of success. For driving rolls (number of shots, damage) the expected value will a number greater than or equal to one. Take the product of each individual value and the result is the cumulative relative value for that attack. For example an Intercessor rapid firing at a Deathskull Ork boy has 2 shots, a hit roll of 3+, a wound roll of 4+, a save of 6+ (Deathskulls get a 6+ invulnerable save), and deals 1 damage which will kill 1 Ork.

2 * (4/6) * (3/6) * (5/6) * 1 =  0.56 Dead Orks

Meanwhile the Ork boy shooting back with a slugga gets 1 shot, a hit roll of 5+ that gets an additional attack on a 6, a wound roll of 4+, a save of 3+, and deals 1 point of damage which is half the wounds of an Intercessor.

(1 + (1/6)) * (2/6) * (3/6) * (2/6) * 0.5 = .032 Dead Primaris Marines

So obviously an Intercessor is better at shooting Orks than an Ork is at shooting Marines. But how much better? The Intercessor costs 17 points, while the Ork boy costs 7. So multiply the expected value by the number of points of the unit and divide by each other to get the relative efficiency at killing:

REK = Value Killed / Value Lost = (0.56 * 7) / (0.032 * 17) = 7.2

So the REK for a Primaris Marine shooting an Ork Boy is 7.2, meaning at ranged combat the Primaris Marine will deal 7.2 times more points worth of damage than they will receive. But that’s only part of the equation; it doesn’t take into account the disparity in cost between the two units. You have a 17 point Intercessor firing at a 7 point boy. So to get the efficiency, divide the REK by the ratio of the point values:

REV = REK / (PointsAttacker/PointsTarget) = 7.2 / (17 / 7) = 7.2 / (2.43) = 2.96

So the REV for the Intercessor against an Ork Boy is 2.96, meaning that in shooting they will take out nearly three times as many points as they lose against an equivalent force.

We can do the same thing for assault, assuming charging for both parties and that the Ork Boy is in a unit of 20 models.

Primaris Marine: 3 * (4/6) * (3/6) * (4/6) * 1 * 7 =  0.83 Dead Orks = 5.83 Ork Points

Ork Boy: 4 * (4/6) * (3/6) * (2/6) * 0.5 = 0.22 Dead Intercessors = 3.78 Intercessor Points

So in assault the REK for an Intercessor against an Ork Boy in assault is 1.54, which when divided by 2.34 is 0.66. In assault Intercessors are expected to only inflict 66% of the points the take against an equivalent force.

### Stompa vs Knight Castellan

We can use the approach above to examine the REV of the Stompa against a variety of targets. First up we’ll look at another Lord of War that’s nearly the same number of points; the Knight Castellan. While they have obviously fallen out of favor in competitive play thanks to the significant nerfs of last year’s FAQ, one would expect that a massive lumbering war walker would represent a good point of comparison for another massive lumbering war walker.

The Stompa has four weapons that can deal damage at range, and the Castellan does as well. For the purpose of this analysis we’ll assume that the Stompa is a Deathskull and gets a 6+ invulnerable save, while the Knight Castellan has a 4+ invulnerable save from a Warlord trait or the Rotate Ion Shields Stratagem.

The Stompa only inflicts 51% of the damage it receives but costs 124% of what a Castellan makes, meaning it’s only 42% efficient in Shooting. This isn’t going to surprise anyone who has a Stompa; it’s not very good at shooting given how much it costs. Against a dedicated ranged platform like a Knight Castellan it’s taking twice as much damage as it receives when you include the relative value of the units, and that doesn’t include the significant variance that could occur when the main weapons all roll low. Since the Stompa is a hybrid platform that’s intended for both shooting and melee, while the Castellan is a purely ranged platform, it seems reasonable to think about what happens in the Fight phase if the Stompa ever reaches the Castellan.

Obviously the Stompa, with its dedicated vehicle-slaughtering weapon and six attacks, is going to do a lot more damage. While the expected value is high, note that it’s not high enough to actually kill the Castellan. In other words on average the Stompa will take away around 71% of the wounds that a Castellan has.

### Stompa vs Astraeus

The Astraeus is an interesting vehicle. It looks like it should be a transport, but it’s a giant floating tank that exists to shoot. It moves fast, flies everywhere, and yet seems to be surprisingly undergunned for 628 points with only five heavy guns dealing out a total of 18 shots. Given that the Stompa seems to be in a similar situation as overpriced and under-gunned it might be worth comparing the two.

In most games a 628 point or 870 point model is going to be a centerpiece of that army, so one might expect them to go after each other. In this case neither has the offensive capability to reliably take out the other, but point for point the Stompa is outclassed by the Astraeus.

### Stompa vs Lord of Skulls

At 479 points the Lord of Skulls is a lot cheaper than the Stompa, but it’s surprisingly comparable. The Lord of Skulls has both melee and shooting capability, either devastating the enemy with a Knight-sized cleaver that does six damage per hit or shooting a gorestorm cannon and hades gatling cannon that seem perfect for killing Primaris units. It’s also very resilient with 28 T8 wounds and a 5+ invulnerable save.

The Stompa is outclassed by the Lord of Skulls in both shooting and melee, dealing equivalent levels of damage but costing significantly more.

### Wrapping Up

Hopefully this approach has merit and will be worth further consideration. Obviously it’s not perfect (for example comparing units that might not necessarily attack each other), but it’s a starting point that I hope can be expanded further. Since 40K is also strictly back and forth it’s difficult to pit two units against each other in a vacuum; on the table it’s more likely that one unit will get significantly degraded or wiped out completely before it has a chance to respond. That said I hope this is of sufficient interest to generate some feedback and see if there’s a path forward. If you think there are other units which might be fun to analyze in this fashion, let us know! We’ll need to know the unit and a representative suite of threats so I can do a comparison.

As for the Stompa, it clearly needs a boost. 870 points is a massive portion of any army outside of an Apocalypse level game (and if you’re doing that you should use the vastly superior Apocalypse rules, which are completely different), but what you seem to be paying for is wounds more than anything else. The lack of offensive firepower, high variability in attacks and damage, and lack of a FNP or invulnerable save make it more of a target than the centerpiece of an army that it should be. Perhaps Ork Week will deliver something good to Stompa players who want their big lumbering walkers to be as nasty as they look.

If you have any feedback, feel free to drop a note in the comments below or email us at contact@goonhammer.com. If you have any questions that you would like answered in a future Hammer of Math, please submit them here.