Monday, February 20, 2012

Vampire Infantry Meta-analysis

When the new book came out, a good friend of mine did a unit meta analysis to calculate the cost of each point of Combat Resolution for the different Vampire Count infantry units. Today I was thinking about it some more, and wanted to expand on what he'd found...

warning: wall of text incoming!

My friend's summary was that Ghouls were the least cost-efficient infantry choice. This was based on  "math-hammer" to calculate the expected number of wounds caused, compared to the cost per model.

For example, a unit of zombies 5-wide fighting a WS3 T3 enemy with 5+ armour save and Parry can be expected to do just under 1 wound total. With 3 ranks and a Standard, that's about 5 points of Combat Resultion. 3 points / 5 CR = .61 points per Combat Resultion

Skeletons with HW and Shield do a little better, causing 1.4 wounds, but due to increased cost come out to .93 points / CR

Skeletons with Spears and Shields do a bit better thanks to the extra rank of attacks, getting just over 2 wounds with a cost of .82 per CR.

The the poor Ghoul goes in, and despite doing the most damange (2.8 wounds), he has a staggeringly high cost of 1.7/CR

For comparison, I figured up Grave Guard too..they do a healthy 3.5 wounds and have a 2.36/CR cost. Not too impressive.

I saw two things I wanted to expand the evaluation to include: first, do these fictional combats result in wins or losses; and what happens when the frontage is changed.

So with our purely hypothetical WS3 S3 T3 LtArm/Shld opponent now fighting back, with both sides 5-wide and ranked up for 3 ranks, we find the following:

*Assumptions: I didn't care about Initiative, assuming both sides have enough bodies to step-up and keep swinging. I also assumed no magical "bonuses" to either side, as the permutations there become unthinkable...we get this and that buff, they get this buff and that thanks! Also, for the Grave Guard, I did not factor in the BoB...this greatly increases the effectiveness of the unit, but I'm really just doing them to see how they compare to the core choices. In other words, I know the Grave Guard are awesome, I want to see how un-awesome Zombies are!*
The Zombies, who do just under 1 wound, take 3 1/3 wounds back, losing combat by a healthy 2.5 (this is assuming the enemy is also ranked 3-deep with a standard). This means they'll lose almost 6 models total.

The HW/Sh Skeletons did 1.4 wounds, but take just under 2 back, losing combat by a wee bit, less than .5.

The Spear Skeletons do 2 wounds, and take just over 2 back, only losing combat by a small margin of .14.

Now the Ghouls, who look unattractive at first, dish out there 2.8 wounds, and only take 1 2/3 wounds back, winning combat by a small amount (.1)!

And the Grave Guard take just over 1 casualty, winning combat by a healthy 2 1/3!

The moral here? Ghouls and Grave Guard are more expensive, but win fights. Zombies and Skeletons are less expensive, making decent "anvils", but...I don't think Hammer/Anvil tactics work too well with Unstable. If you want a 'tarpit' that will not crumble too horribly, Skeletons with Spears don't look too unattractive. While the HW/S guys take less damage, the Spear guy's extra attacks seem to make up for it. At least against these weedy opponents!

But what happens if we expand the frontage? I run my Ghouls and Grave Guard in a horde formation usually, and the above math was for 5-wide vs. 5-wide.

If we go 7-wide vs. 7-wide, things don't change too much. The Zombies still lose by about 2.5; the HW/SH Skeletons still lose by about .5; the Spear Skeletons lose by about .2...

but interestingly the Ghouls go up to winning by over .5; and the Grave Guard up to a very nice 3 1/3!
So what happens if we go in to a Horde formation, and the enemy stays 5-wide? Being easy on myself, I'm assuming 20mm enemy bases here, so 5 of theirs fight 7 of ours.

The Zombies dish out almost 2 wounds, but still lose combat by almost 1.

The HW/SH Skeletons dish out almost 3 wounds, and actually win combat by 1! (Note, this assumes we're a Horde AND get three ranks for Combat Resolution)

The Spear Skeletons are even better, doing almost 4 unsaved wounds and winning the combat by 1 2/3!

Now the Ghouls really start to shine, as they do over 5 unsaved wounds, and win combat by 2 1/2.

And our expensive Grave Guard really enjoy the extra rank's attacks, dishing out 7.3 wounds and winning by 6.

And last, what if it's horde vs. horde? Despite looking pretty cool on the table, it also generates the maximum amount of dead things!

The Zombies kill 2.8, and lose 8.3, losing combat by 5.5 for a total amount of 14 dead zombies...

The HW/Sh Skeletons kill 4.2, lose 5.6 bodies, lose combat by 1.4 for a total 7 dead skeletons...

The Spear Skeletons kill 5.6, 6 2/3 are killed and they lose combat by 1.1 for almost 8 dead skeletons...

The Ghouls, on the other hand, continue to win, killing 7.4, losing 5, and winning combat by 1.4.

And as expected, the Grave Guard clean house, killing 10 of the enemy, losing 3.3 of their own, and winning combat by a lot.

Here's a chart that I'm hoping will format properly to show us the combat result:
5-wide7-wideHorde vs. 5-wideHordes
Skel (HW/S)-0.46-0.651.06-1.39
Skel (Spear)-0.14-0.191.67-1.11
GG (GW)2.363.316.187.08

Ghouls consistently win, doing better as they "horde". This is what I expected to see. The Graveguard the same. What I'd hoped to find was that Skeletons (in either configuration) could consistently win fights, but what we find is that they consistently lose. Yes, they are cheaper. You can take twice as many of them, actually...but to my way of thinking, that just means they sit there losing for a long time! Moreover, this is against a weedy WS3 S3 T3 opponent with only one attack. What I expect to find as we go against tougher meanies is that things will get more pronounced...the Zombies will lose by more, the Grave Guard will win by less, but I expect the 'curve' to look the same.

So I make up another hypothetical opponent, this one WS4, S4, T4 with the same 5+ save and 6++ Parry.

5-wide7-wideHorde vs. 5-wideHordes
.62 / 4.44.86 / 6.221.3 / 4.441.85 / 13.33
Skel (HW/S)-2.16-3.02-1.14-6.48
.93 / 3.091.3 / 4.321.94 / 3.092.78 / 9.26
Skel (Spear)-2.31-3.24-1.11-7.41
1.39 / 3.701.94 / 5.192.59 / 3.73.7 / 11.11
2.31 / 3.333.24 / 4.674.32 / 3.336.17 / 10
GG (GW)0.690.974.512.08
3.47 / 2.784.86 / 3.897.29 / 2.7810.42 / 8.33
This time I've added in the expected number of casualties, the first (left) number is how many the Vampire unit causes, the second how many casualties it takes.

So it's disappointing to me to see the Ghouls consistently losing, but compared to the Skeletons they're losing by far less. Still, only the Grave Guard can compete here "toe-to-toe". The "Hordes" column shows us that the Ghouls dish out a lot of damage, killing 6 while losing 10...but with Unstable that turns in to almost 15 dead. This is attrition that we don't really want to get in to. Can Invocation bring back that many? What about the HW/S Skeleton "Tarpit"...can Invocation make up for over 15 dead per combat round? Or 25 dead Zombies?

Well, it depends really. How many Invocation spammers do you have? What level are they? Do you have an Unholy Lodestone? Most important of all, what did you roll for winds of magic? Will your opponent be accomodating and not dispel your Invocations?

So the root of this excercise was a comparison of Ghouls vs. Skeletons and see if I can come up with a use for them. More on that, as well as my thoughts on the effectiveness of Invocation and Hammer/Anvil in Unstable army, tomorrow...

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