Which chaos icon is statistically the best? Following on from my Lord of the Raptors posting, I now want to know which chaos mark (i.e. icon) would be optimal to give to my unit of chaos raptors? More generally, I'd also like to know which icon would work best as the armament of the aspiring champion varies? In this series of two postings, I'll be looking at some mathematical analysis!
In passing, it's worth noting that much of this article can be mathematically translated to ordinary troop selections, but I wanted to know especially about raptors as they can be a significant investment of points in a chaos space marine army and I don't want them to go to waste. I'll also point out that this text was written down in note format over 6 months ago when 4th edition was current, but the conclusions are still valid.
Assumptions.
We need to start somewhere, so let's assume that we've got a 10 strong squad of raptors. In this article, I want to consider the differences between equipping this squad with the various icons (Chaos Glory, Slaanesh, Khorne, Tzeentch & Nurgle) and arming the aspiring champion with no upgrades, a power fist, and a pair of lightning claws. My naive assumption is that a power fist should be paired with a Khornate icon and lightning claws with a Slanneshi one.
To evaluate the impact of this squad, let's have it go up against some Imperial counterparts: a 10 man assault squad with a sergeant who has two close combat weapons. I'll state from the outset that these assumptions are limited in scope and concentrate only on the close combat phase.
Baseline.
The first lesson is to make sure that our raptors are the ones doing the charging. This should be readily engineered against a pure tactical squad who move slower than the raptors, but some thought might want to be applied when looking to charge an assault squad with jet packs.
Let's look at what happens when the raptors charge their Imperial cousins. Without any upgrades, all marines will strike simultaneously and will hit 50% of the time and wound 50% of the time -- this means we have an expectation of 0.25 wounds being caused for every attack. On the charge, our squad of 10 raptors has 31 attacks (9 lots of 2+1 attacks and 1 lot of 3+1 attack from the champion -- the +1 representing the charge and the base 2 attacks sourced from using two close combat weapons). This means it'll cause 7.750 wounds on average. With power armour, the opposition will save two thirds of those wounds, resulting in an average 2.583 unsaved wounds.
If they don't get the charge, then the raptors will be reduced to 21 attacks, which we expect to cause an average of 5.250 wounds, of which 1.750 will remain unsaved. Therefore by charging, the 10 strong squad of raptors stand to cause just under 1 extra unsaved wound. The self-same argument can be applied to Imperial Assault Marines and the lesson is the same: be the one charging!
Power Fist.
How many more unsaved wounds above 2.583 on the charge will our raptors inflict if the aspiring champion is equipped with a power fist?
The only change in the dynamic now is that the power fist champion attacks last (and must avoid being removed when all other combatants strike) and now causes unsavable instant-kill wounds on 2+.
Of the 31 attacks on the charge, 27 will take place with "normal" weapons. They inflict an average of 6.750 wounds which we expect 2.250 will go unsaved. The four attacks from the champion will be expected to have 2 hits and inflict 1.667 unsaved wounds. That adds up to 3.917 unsaved wounds -- an increase of 1.334 compared to without the power fist.
Following similar logic, but without the charge, they're causing 2.750 unsaved wounds (an increase of 1.000 compared to without the power fist).
Lightning Claws.
No save and re-roll failing to-wound rolls -- not a bad prospect! But how does it pan out in game terms?
On the charge, the 9 ordinary members of the squad are still inflicting 2.250 unsaved wounds. The aspiring champion with 4 attacks will hit twice on average. One of those two hits will wound (no save). The second is expected to miss, but be successfully re-rolled half of the time. So the expectation is that the aspiring champion will cause 1.500 unsaved wounds. That adds up to a total of 3.750 unsaved wounds -- an increase of 1.167 compared to the baseline. Not quite as good as a power fist (by 0.167 unsaved wounds), but that shouldn't be surprising.
Following similar logic, but without the charge, they're causing 2.625 unsaved wounds (an increase of 0.875 compared to without the lightning claws).
The first conclusion to be drawn is that points could be saved on a power fist by purchasing lightning claws if our raptors are purely an anti-infantry unit. Take the power fist for a dual anti-armour role.
Margins.
We'll now define the margin of victory as the difference in the number of wounds caused. This'll be referred to as dW herein.
Let's summarize what we have so far:
dW=0.000 for baseline raptors vs. baseline assault marines (or indeed, for similarly equipped units against each other).
dW=0.833 for baseline raptors charging baseline assault marines (the inverse is also true).
dW=2.167 for power fist aspiring champion raptor charging baseline assault marines.
dW=2.000 for lightning claws aspiring champion raptor charging baseline assault marines.
In Part II, coming soon, we'll get to the heart of the matter: how does dW change for different icons?
In passing, it's worth noting that much of this article can be mathematically translated to ordinary troop selections, but I wanted to know especially about raptors as they can be a significant investment of points in a chaos space marine army and I don't want them to go to waste. I'll also point out that this text was written down in note format over 6 months ago when 4th edition was current, but the conclusions are still valid.
Assumptions.
We need to start somewhere, so let's assume that we've got a 10 strong squad of raptors. In this article, I want to consider the differences between equipping this squad with the various icons (Chaos Glory, Slaanesh, Khorne, Tzeentch & Nurgle) and arming the aspiring champion with no upgrades, a power fist, and a pair of lightning claws. My naive assumption is that a power fist should be paired with a Khornate icon and lightning claws with a Slanneshi one.
To evaluate the impact of this squad, let's have it go up against some Imperial counterparts: a 10 man assault squad with a sergeant who has two close combat weapons. I'll state from the outset that these assumptions are limited in scope and concentrate only on the close combat phase.
Baseline.
The first lesson is to make sure that our raptors are the ones doing the charging. This should be readily engineered against a pure tactical squad who move slower than the raptors, but some thought might want to be applied when looking to charge an assault squad with jet packs.
Let's look at what happens when the raptors charge their Imperial cousins. Without any upgrades, all marines will strike simultaneously and will hit 50% of the time and wound 50% of the time -- this means we have an expectation of 0.25 wounds being caused for every attack. On the charge, our squad of 10 raptors has 31 attacks (9 lots of 2+1 attacks and 1 lot of 3+1 attack from the champion -- the +1 representing the charge and the base 2 attacks sourced from using two close combat weapons). This means it'll cause 7.750 wounds on average. With power armour, the opposition will save two thirds of those wounds, resulting in an average 2.583 unsaved wounds.
If they don't get the charge, then the raptors will be reduced to 21 attacks, which we expect to cause an average of 5.250 wounds, of which 1.750 will remain unsaved. Therefore by charging, the 10 strong squad of raptors stand to cause just under 1 extra unsaved wound. The self-same argument can be applied to Imperial Assault Marines and the lesson is the same: be the one charging!
Power Fist.
How many more unsaved wounds above 2.583 on the charge will our raptors inflict if the aspiring champion is equipped with a power fist?
The only change in the dynamic now is that the power fist champion attacks last (and must avoid being removed when all other combatants strike) and now causes unsavable instant-kill wounds on 2+.
Of the 31 attacks on the charge, 27 will take place with "normal" weapons. They inflict an average of 6.750 wounds which we expect 2.250 will go unsaved. The four attacks from the champion will be expected to have 2 hits and inflict 1.667 unsaved wounds. That adds up to 3.917 unsaved wounds -- an increase of 1.334 compared to without the power fist.
Following similar logic, but without the charge, they're causing 2.750 unsaved wounds (an increase of 1.000 compared to without the power fist).
Lightning Claws.
No save and re-roll failing to-wound rolls -- not a bad prospect! But how does it pan out in game terms?
On the charge, the 9 ordinary members of the squad are still inflicting 2.250 unsaved wounds. The aspiring champion with 4 attacks will hit twice on average. One of those two hits will wound (no save). The second is expected to miss, but be successfully re-rolled half of the time. So the expectation is that the aspiring champion will cause 1.500 unsaved wounds. That adds up to a total of 3.750 unsaved wounds -- an increase of 1.167 compared to the baseline. Not quite as good as a power fist (by 0.167 unsaved wounds), but that shouldn't be surprising.
Following similar logic, but without the charge, they're causing 2.625 unsaved wounds (an increase of 0.875 compared to without the lightning claws).
The first conclusion to be drawn is that points could be saved on a power fist by purchasing lightning claws if our raptors are purely an anti-infantry unit. Take the power fist for a dual anti-armour role.
Margins.
We'll now define the margin of victory as the difference in the number of wounds caused. This'll be referred to as dW herein.
Let's summarize what we have so far:
dW=0.000 for baseline raptors vs. baseline assault marines (or indeed, for similarly equipped units against each other).
dW=0.833 for baseline raptors charging baseline assault marines (the inverse is also true).
dW=2.167 for power fist aspiring champion raptor charging baseline assault marines.
dW=2.000 for lightning claws aspiring champion raptor charging baseline assault marines.
In Part II, coming soon, we'll get to the heart of the matter: how does dW change for different icons?
1 comment:
lord vampyre - you are correct. This text was written a long time ago (long before 5th edition).
So, the text should be altered to read:
"Of the 30 attacks on the charge, 27 will take place with "normal" weapons. They inflict an average of 6.750 wounds which we expect 2.250 will go unsaved. The three attacks from the champion will be expected to have 1.5 hits and inflict 1.25 unsaved wounds. That adds up to 3.500 unsaved wounds -- an increase of 0.917 compared to without the power fist."
...A little less than before.
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