Mathhammer - Dark Lances vs. Splinter Cannons

Roboute Guilliman takes on the Drukhari Army

I've always been interested in the math behind Warhammer and how to use probability to influence your decisions during game play and list construction. I think the general consensus is that more volume outweighs higher quality weaponry. I wanted to see how this worked so I built a spreadsheet that would calculate 10,000 shots and compare something like a Dark Lance vs. a Splinter Cannon.

I used Roboute Guilliman as the defending model.

Roboute Guilliman
Toughness	Save	Invulnerable
6	2+	3+

I ran 10,000 shots through him with a Dark Lance - Heavy 1 / Strength 8 / AP -4 / D6 Damage.

Dark Lance x3 (63 Points)
Hit %	Wound %	Damage Rolls	Damage
65% - 72%	41% - 47%	30% - 37%	1.22 - 1.88

Damage Rolls is the percentage of wounds that were not saved.

I also ran 10,000 Splinter Cannon (6 shots per Weapon because of Rapid Fire) - Rapid Fire 3 / Strength: Always wounds on 4's  / AP 0 / 1.

Splinter Cannon x4 (64 Points)
Hit %	Wound %	Damage Rolls	Damage
65% - 72%	30% - 36.5%	15% - 18.5%	.68 - 1.72

It seems like the Dark Lance edges it out in this situation with a higher average damage.

Next, I wanted to try this vs. a Primaris Marine. Excess wounds don't matter as much since they don't spill over so I'm only calculating the average number of Primaris killed.

Primaris Marines
Toughness	Save	Wounds
4	3+	2

Again, I ran 10,000 Dark Lance shots through the unit.

Dark Lance x3 (63 Points)
Hit %	Wound %	Damage Rolls	Primaris Kills
65% - 72%	53% - 60.5%	100%	1.42 - 1.62

It looks like 3 Dark Lances kill 1 Primaris and do 1 damage to another on average.

Splinter Cannon x4 (64 Points)
WS 3	Strength 8	Damage Rolls	Primaris Kills
65% - 72%	30% - 36.5%	30.5% - 37.5%	1.02 - 1.60

This was pretty close as well but the Dark Lance, point for point, seems like a better choice. The Poison Weapon attribute that the Splinter Cannon has that allows wounds on 4+ works much better against models like the Plague Marines with Toughness 5.

I think I will try running 10,000 shots against them next but it requires another addition the formula because of their 5+ Disgustingly Resilient. I'll post that result tomorrow.