MathHammer is worth doing before you lock in an army list, but only if you look at the spread of results and not just the average. The average tells you what a unit does on a typical day. The spread tells you how often it lets you down, and a unit that lets you down is the one that costs you games.
Here's how I'd use it, which tools are worth the time, and where the numbers will quietly lie to you.
What MathHammer actually is
UnitCrunch puts it simply: MathHammer is "the use of probability and statistics to make more informed decisions." That's all it is. You don't need a stats degree, just the attack sequence and some patience.
It's useful in two places. Before the game, it checks whether a unit can do the job you're paying points for, and it lets you compare two weapon options side by side. During the game, it helps with target priority, splitting fire, whether a Stratagem is worth the CP, and charges. For example, a 9" charge on 2D6 comes off about 28% of the time. That's worth knowing before you build a turn around it.
The basic sum
Every attack goes through the same four steps: hit, wound, save, damage. Multiply the odds at each step and you get the expected damage.
UnitCrunch's worked example goes like this. Say you have 10 shots that hit on 3+, at Strength 4 into Toughness 5, AP-1, Damage 2, against a 3+ save:
- Hits: 10 × 4/6 = 6.67
- Wounds (S4 vs T5 wounds on 5+): 6.67 × 2/6 = 2.22
- Unsaved (the 3+ save becomes 4+ after AP-1, so half get through): 1.11
- Damage: 1.11 × 2 = 2.22
So the unit does 2.22 damage on average. Fine. Now the important part.
The average is the least useful number
That 2.22 almost never happens. According to UnitCrunch, about 31% of the time all ten shots do nothing at all, and about 9% of the time they deal 6 or more. So nearly a third of the time you've spent a whole shooting phase for zero.
Frontline Gaming's "Great Expectations" makes the same point with ten Space Marines shooting ten Space Marines. The average is 1.11 kills, but the chance of killing exactly one is only 38%. "Average" and "likely" are different words for a reason.
Building on that, the gap gets brutal when you need a threshold. In the same article, 28 plasma shots at a Plagueburst Crawler have about a 79% chance of doing 6+ wounds, which sounds great, but only about a 17% chance of actually killing it. Take away Disgustingly Resilient and the kill chance jumps to about 61%. One defensive rule turns a reasonable plan into a long shot. If your list depends on that unit removing that target, the average isn't going to tell you.
A quick conservative rule of thumb
If you don't want to run a full distribution every time, Frontline's "The Law of Averages" (maths credited to Adam Lane) suggests subtracting one standard deviation from the average. That gives you a roughly "1-in-6 bad day" figure.
Their example: Vanguard Veterans with 41 attacks average 20.5 wounds. You need 20 to wipe the target, so the average says yes. The conservative figure is about 17, which says you'll fall short more often than you'd like.
That's a decent gut check. But a commenter on that piece makes a fair point: binomial probability lets you choose your confidence level directly ("I want 80% odds of 20+ wounds") instead of guessing how conservative to be. I think that's the better habit, and the tools below do it for you anyway.
The tools
You don't need to do any of this by hand.
UnitCrunch runs Monte Carlo simulations, which means rolling the attack thousands of times and showing what comes up. It reports quartiles and the interquartile range, so you see the middle 50% of outcomes, not just one number. It's the one I'd open first, because it puts the spread in front of you by default.
Adept Roll, covered by Wargamer, is an unofficial app with a free tier and a subscription of roughly $5 a year. It imports fan-maintained BattleScribe data, so you're not typing in every profile. The catch, as Wargamer says, is that this data "may contain errors." At $5 a year it's cheap, but you still need to check the profiles against your codex. Treat it as a planning aid, not a guaranteed win.
A spreadsheet works if you like building things. Just make sure it shows a distribution and not only expected damage per point, or you'll be optimizing for the wrong number.
Where the maths misleads
This is the part people skip, and it's where bad lists come from.
It ignores the board. UnitCrunch says it plainly: the maths doesn't know about board position, objectives or activation order. A gun that does 30% more damage is worth nothing if it never gets line of sight.
Damage per point leaves out most of what a unit costs. Commenters on "Great Expectations" list range, mobility, resilience, synergy, opportunity cost and whether your buffs actually apply. For example, a unit that only looks great with a character's reroll aura is really two units' worth of points, and it falls apart once that character dies. Spreadsheets make some units look better than they are and others worse.
A wrong input still gives a confident answer. Forget a -1 to hit, or that the target has a 5+ invulnerable save, and the calculator will still hand you a precise number to two decimal places. Precise and right aren't the same thing. Calculators don't come with doubt built in.
UnitCrunch's own line sums it up: MathHammer is "an input to a decision, not the decision."
What I'd actually do
- Run the unit's main job, not its best case. Pick the target it's meant to kill and check the chance of killing it, not the average damage.
- Look at the bad-day number. Check the 25th percentile in UnitCrunch, or subtract a standard deviation if you're doing it in your head. If the plan fails one game in three, change the plan.
- Double-check special rules on both sides. Damage reduction, Feel No Pain-style rules and invulnerable saves move the numbers more than almost anything else.
- Use damage per point to make a shortlist, not to decide. Once you're down to two options, the board, range and synergy pick the winner.
- Skip paying for anything until the free tools stop being enough. UnitCrunch and Adept Roll's free tier cover most list-building questions.
Do the maths, then trust the spread over the average.