Welcome back! Last time we talked a little bit about how we define “good”. Be sure to follow and subscribe through the sidebar of the blog and twitter to stay up to date with all of our good posts.

Today we are going to take a look at how to compare the lethality of two different units. This is a building block along the path to being able to compare two lists to each other. In this post and in general on the blog, I’m going to be speaking in terms of points because power levels are a more general way of building lists. Due to the fact that we are going to be talking about the nitty gritty of “should I take four weapons on a Tau commander or three with Advanced Targeting System?”, discussing power levels would be moot as you can take upgrades and weapon substitutions for free.

The real goal of all of this is to determine what is the most efficient use of your points. If you have a 1500 point list and you need a dedicated anti-tank unit, is a Broadside with a Heavy Rail Rifle and Smart Missile Systems or a Hammerhead with a Railgun and Smart Missile Systems a more efficient use of your points? While there are many factors to consider (mobility, degrading stats, “Fly”, number of total units, etc.) the lethality and average lifespan of both units are the two factors that are both easy to calculate and are fairly universally consistent (meaning that they are not situational). As a list-builder and general, you must be the one to determine when things like mobility, degrading statistics, “Fly”, etc. bring more value to a unit selection than the quantifiable metric of lethality. If you have questions about how to do that, or how to consider making lists in general, here’s a great guide.

So if we have decided that we want a dedicated anti-tank unit and decided that the general properties of both a Hammerhead and Broadside would both work with the rest of our army, we now need to see which is more cost-efficient by comparing their lethality per points that they cost. While I can’t post the root costs or stats here, I will detail the formulas I’m using and the final result so that you can follow along (if you have the Xenos 2 Index) or apply to any other unit comparison you wish to make.

Let’s get some assumptions out of the way:

- We will compare one Broadside to one Hammerhead
- The Broadside will be equipped with Heavy Rail Rifle and two Smart Missile Systems
- The Hammerhead will be equipped with a Railgun and two Smart Missile Systems
- What we are shooting at will be Toughness 8 and have a 3+ Save value
- Both Broadside and Hammerhead will be in range to fire both of their weapons
- No markerlight support or any other benefits or bonuses

Let’s first take a look at how many hits, on average (remember, all of these numbers will be “on average”), each unit makes each turn. To calculate this we can use the following equation, for each weapon that the unit has:

N is the number of shots that a weapon has and BS is the ballistic skill of the unit doing the shooting. 7 minus the BS, all over 6, gives us the probability of that unit hitting their target for a single shot. Because both the Broadside and the Hammerhead have weapons with multiple shots, we need to then multiply the probability of hitting with one shot by the total number of shots for that weapon, which is what the above formula accomplishes. Because both units have multiple weapons, we need to use Formula #1 three times for the Broadside (three weapons) and three times for the Hammerhead (also three weapons) and then add up the results for each unit to get the sum for that unit’s expected average hits per turn. In our case, the Broadside is expected to get five hits a turn, considering all three weapons, and the Hammerhead is expected to get six.

But hits don’t always translate into wounds. So let’s see how many unsaved wounds we can expect to cause versus our Toughness 8, 3+ Save target. This is another calculation that we must make on a per-weapon basis and then add up the results.

Here, we take the result for each unit from Formula #1 and multiply it by the probability to cause a wound and then multiply that by the probability for the target to fail a save. Defining the probability to wound and the probability to fail a save in Formula #2, we get:

The Wound Roll is defined in the Advanced Rule Book on page 181 and is the roll needed to wound a target, comparing the shooting weapon’s strength to the target’s toughness. The Sv is the target’s Sv value (3+ in our case) and the AP is the AP statistic of the weapon being fired at the target. It’s important to note: (1 – the probability of saving the wound) is equivalent to the probability that the wound is not saved. **Footnote 1**

Because different weapons can have different AP values, you should use Formula #2, detailed, once for each weapon for each unit. In our example, the Broadside with a HRR and two SMS’s is expected to cause 0.944 unsaved wounds a turn. A Hammerhead with a Railgun and two SMS’s is expected to cause 1.037 unsaved wounds per turn.

Typically, targets with Toughness’ of 8 will have more than one wound, so it is probably more beneficial to look at the Damage/turn/point, rather than Unsaved Wounds/turn/point. Luckily, it is easy to calculate the average damage per turn for each unit. For multiple damage weapons, those that roll D3’s or D6’s, I will be taking the average dice roll (2 damage and 3.5 damage, respectively for the D3 and D6 damage roll cases).

For each weapon, multiply the Formula #2 number of unsaved wounds by it’s average damage. Then add up the results for each weapon to get that unit’s average damage per turn. In our example, the Broadside does 2.194 average damage per turn while the Hammerhead does 2.148 average damage per turn.

Lastly, we divide their point cost by their average damage per turn to get the metric we started out to calculate: the lethality (or damage) per point. The **Broadside comes in at about 83 points per damage** while the **Hammerhead comes in second at about 91**. So if all you cared about was maximum point efficiency then, you’d pick the Broadside every time. However, as we already discussed, there is a lot to consider apart from raw point efficiency. One interesting point is that if the Hammerhead is with Longstrike (or the Hammerhead **IS** Longstrike), who gives nearby Hammerheads +1 to their To Hit roll, the Hammerhead becomes more point efficient than the Broadside. Math is fun kids.

### Summary

It’s valuable to take a look at the the amount of damage that a unit can do per point that the unit costs, in order to be able to differentiate the point-efficiency of each unit. That way, we can be sure that the units we take are likely to pull their own weight. Which unit will you be taking: Broadsides or Hammerheads? Tell us in the comments below.

Next time, we will take a look at another important metric: average lifespan. After all, it’s not only important how much you can shoot, but also how long you can keep shooting while under fire. Happy dice rolls!

###### Footnotes:

- In cases where the target’s Sv value is such that the expression ((Sv – AP) – 1)/6 would result in a value greater than or equal to one, the target does not get a save. This is a complicated way of stating that the AP of the weapon exceeds the save value of the target, which we all know results in the target not getting a save. For example, a humble Guardsman has a 5+ save. If he was shot at by a weapon that had -2AP or greater, he would not get a save roll – he would just die in a flash of light and red mist for the god-emperor. In this case of a -3AP weapon, ((Sv – AP) -1)/6 would result in ((5 – (-3) – 1)/6, or 7/6, so no save roll.

Nice math-hammering! Great blog quality btw!

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Thank you!

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Can you math hammer the validity of using the over charge on an ion cannon (for a hammerhead). Because by my math there is almost no likely scenario it is worth risking the mortal wounds from overheating on a hit roll of 1.

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That’s been my result as well 😦

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