There isn't quite as much to this math as the other, but it hurts my brain more to do. You have to think about recipricals and it just seems counter-intuitive to what I usually want to do with gaming math.
For example, a BS3 S3 weapon shooting at a T3 target with a 3+ armor save would be:
2 X 2 X 2 = 8 shots expected to wound
Basically, 3 out of 6 shots will hit thanks to BS3 (aka: 1 in every 2), so the number of shots before we can expect* one to hit would be 2. The same can be said for wounding and armor save. 3 out of 6 that do hit, wound, and 3 out of 6 that wound aren't saved by the armor.
When we figure it out from an offensive point of view, we usually take those numbers and do something like:
(3/6) X (3/6) X (3/6) => (1/2) X (1/2) X (1/2) => (1/8) = 0.125 chance to cause a wound
But when we want to know how many shots I can take before I am expected to take a wound, we use the recipricals of the fractions. (reciprical, meaning the opposite, like 6/3 instead of 3/6)
(6/3) X (6/3) X (6/3) => 2 X 2 X 2 = 8
(the canny individual might observe that 8 = 1/0.125, which is exactly what we're doing by using all the recipricals, except where 2x2x2 isn't a big deal, fractions can get a bit trickier to do in your head)
Meaning, I can tank 7 shots and then expect the 8th to be a wound. Of course, this is all averages and expected values, etc. Just because math says 24 lasgun shots should kill 3 (24/8=3) of my T3/3+ guys, it doesn't mean it will happen that way every time. The average over every game we ever play will be 3, but we might never see exactly 3 deaths. Again, expected value is what we're working with here. It isn't perfect, but it's as good as we can get. And besides, if math could tell us the exact outcomes for everything, then there wouldn't be any point in playing the game. Where would the fun be in that?
So, to the table:
| Warriors v Wracks: Ranged Wounds | ||
| 10 Warriors | 5 Wracks | |
| MEq S4 | MEq S4 | |
| 1 W | 2.25 | 6 |
| 25% | 4.5 | 12 |
| All W | 22.5 | 30 |
| MEq S6 | MEq S6 | |
| 1 W | 1.8 | 3.6 |
| 25% | 3.6 | 7.2 |
| All W | 18 | 18 |
| Warriors v Wracks: CC Wounds | ||
| MEq S4 | MEq S4 | |
| 1 W | 4.5 | 9.6 |
| 25% | 9 | 19.2 |
| All W | 45 | 48 |
| 5's | 5's | |
| 1 W | 2.7 | 5.4 |
| 25% | 5.4 | 10.8 |
| All W | 27 | 27 |
And there we have it. Wracks are significantly more durable, but because there are less of them the required attacks to wipe out the whole squad are about even.
Now comes the tricky part. The part I don't like as much. The part that isn't about numbers...
Our math shows us that neither unit is enormously more desirable than the other, so now we have to look at all the other factors. Ugh, subjectivity.
Well, for starters, all the wrack math was including FNP, but none of the warrior stuff was. So if the warriors can get a pain token, they'll be far more survivable than the wracks against most things. At S6 and S7, the wracks will still be better per model but the number of attacks to wipe the squad will be the same.
Hmm, warriors come with 3 raiders with dark lances, and the option of taking a blaster. That's nice. The wracks have literally nothing that can touch armor. Anti-infantry is nice to have, but dedicated anti-infantry is dangerous.
Venoms are more durable than raiders, sort of. Taking nightshields makes them the same point cost and leaves the 3 warrior squads 5 points under the cost of the 4 wracks. Alternatively taking 5++ shields puts the warriors 10 points over the 4 wracks. Sort of a wash there.
What about less quantifiable things? Like, threat level. What's a higher priority target? 10 warriors in a raider? Or 5 wracks in a venom? I'm thinking the warriors, mostly for psychological reasons. Who was it, Fritz, I think, that had the 100% fool-proof video tactica where he basically said "people suck at target priority, so put whatever you want them to shoot in front and 90% of the time they will". I think, given the choice between shooting at 4 x 5 guys with T4 and FNP or 3 x 10 guys with T3 and nothing, most people would take aim at the 10. Whether or not this is tactically sound depends on the situation, obviously, but people like to feel like they're doing something. Killing 2 or 3 warriors is more satisfying than rolling a bunch of FNP saves and only killing 1, even though they represent the same percentage of the original squad size. Also, there are 4 of them? I'll never be able to kill them all.
It's human nature, I think. When faced with a lot of things to do (small tasks, or otherwise) we tend to get overwhelmed and do nothing. This weekend I need to do the laundry, clean the house, do the dishes, go grocery shopping, and change the oil. Ugh, there's so much to do I'll never get it all done. I guess I'll just watch TV instead. If doing what we deem an acceptably easy piece of the whole makes little appreciable difference in what still needs to be done yet, then we shut down and do nothing. That is why I feel like wracks won't get targeted quite as much.
I thought we were using math to figure this out, not psychology. What happened? Eh, it is what it is. Math failed me so now I'm ranting.
At the end of the day, I think it's going to come down to personal preference and how I feel about the units. I prefer the warriors, but I feel like using them exclusively isn't good.
This is what I want in my troops: 3 units warriors, 2 units wracks, 1 unit wyches. That gives me the shooty-death awesomeness of the warriors, a couple of units that are tough to move and have some decent output, and a squad of wyches to do whatever; hold an objective in cover daring someone to charge, tarpit PWs or other big scary CC units, go get into CC of their own, whatever is necessary.**
I feel like that would be a great mix. I also feel like it's too much. I haven't done the points yet, but it feels like too much. I'd still like a useful HQ (either an archon, useful character, or possibly more haemonculi) and some heavy infantry. Don't know how much I could fit in with my core + 3+2+1. I'm still liking the Baron+5 too. Does he force you to take hellions as troops? Or does he just make it an option?
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* - Probability is all about expected values. It doesn't mean that is what is going to happen, but it's the best approximation we can get when trying to do the math.
Sometimes it doesn't even make sense. What is the expected outcome if I roll a D6? 3.5, which, as it turns out, isn't even an option.
** - Wyches really are awfully versatile. I wonder if a full on wych cult would be any good. I can see it going either way, really. Eh, it doesn't especially interest me, but it's an interesting thought.
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