So.. Wych Cults are kinda rare now

wyches have 1, maybe 2 places in my lists ALWAYS. Foremost, vehicle hunters. 2, scoring if I am desperate and its convenient. I have given up on wyches in boats. Theyre always the first to get shot down because my opponents know that half the damn unit, maybe more will die in the explosion. Wracks and grots are really the only 2 units I use in boats. Wracks are so much more efficient with points anyway. They can wound monstrous creatures and tie them up, the T4 makes all the difference in the world, with a 50 point haemy they get FC making them better in CC with those nice re-rolls (obviously abiding by the poison weapon special rules). grots, wracks, HW wyches, and beast packs all the way.

Barking Agatha wrote:

Devilogical wrote:

Oh, please. Stop it already. Overwatch isn`t THAT scary. Only flamers and tau squads can be dangerous.

Really? Even without a flamer, if a squad of wyches charges 10 space meringues, they will overwatch with 20 bolter shots, hitting on 6s. Every 6 rolled is practically a dead wych.

At this point, maths crunchers will often say that 'statistically, that's only 3.33 hits'. Well, no. Statistically, it's actually 3.33 +/- 1.66 hits, because there is such a thing as Standard Deviation. Since there is no such thing as a dice roll of 1.6, that means that you should expect anywhere between 2 hits (if you're really lucky) and 5 hits (if your opponent is). It's as likely to be 4 hits as it is to be 3.

The chances that any one wych will survive a hit are 0.33 (the mean) +/- 0.47 (the standard deviation). Since there is no such thing as a dice roll of '0', the standard deviation is not on the wych's side.

So, if a squad of wyches charges 10 space meringues, how many will die to Overwatch? 2.22 +/- 5.8 wyches. That means anywhere from: they might all survive (if you're lucky), or 8 wyches dead (if you're unlucky). Most often it will be between 1 and 4. This will happen every time, unless your opponent gets a particularly unlucky roll.

That isn't scary? Of course it is. That is why no one ever charges 10 space meringues with wyches any more.

Edit: For comparison, if genestealers charge the same space meringues, you get 1.66 +/- 2.0 dead genestealers; that is, between 1 and 4, usually 2 or 3.

If other space meringues charge the same space meringues, you get 0.027 +/- 0.97 dead space meringues; that is, maybe one, usually none!

THIS

im not in to mathhammer at all, but I agree Overwatch really grinds my gimpsuit gears...

Because math makes me hard!

The Binomial distribution is indeed the right distribution for this sort of thing as it handles the probability of k successes in a series of n yes/no experiements (in our case, did the wych die yes/no).

The probability of k dead wyches from n boltershots fired is given by,



where p is the chance of a wych dying, i.e (1/6)*(2/3) 6's to hit, 3's to wound for overwatch when the wyches have no cover or FNP.

So here are some plots for the chance of wyches dying from 10 bolters overwatching (so 20 shots)!



The x-axis is number of wyches killed from overwatch and the y-axis is the probability of that many wyches dying. The calculations were for 20 shots (i.e 20 dead wyches), but I only plotted up to 7 because as you can see the probabilities are pretty much 0 after 7 (although not exactly 0, there is a very, very, VERY small chance of 20 shots killing 20 wyches). The different colours are for different situations as follows;

red - normal overwatch, p = (1/6)*(2/3)
blue - overwatch when the wyches have FNP, p = (1/6)*(2/3)*(2/3)
yellow - overwatch when the wyches have 4+ coversave, p = (1/6)*(2/3)*(1/2)
green - overwatch when the wyches have 4+ coversave AND FNP,  p = (1/6)*(2/3)*(1/2)*(2/3)

As I'm sure anyone can see the chance of you not loosing any wyches to overwatch is pretty small, <50% even at the best of times. I really think overwatch hurt wyches really bad. For a discrete distribution like this you can for super(-duper-ultra)-simplicity sake (sorry if there are any mathematician here) you can view the highest probability and expected value to coincide (so 2 for red, 1 for blue etc.).

EDIT: I forgot my point; If you have a small squad (5) wyches charging 10 bolters the chance of loosing the ENTIRE SQUAD is higher than not loosing any...

Comparing this to what happens when marines charge into those 10 bolters,



you can easily see there is quite a big discrepancy there, you MIGHT loose 1, but most of the time you wont... I personally think overwatch hurts DE more than any other army as we have relativily few (as compared to say ork boyz or gants) fairly squishy (compared to say assault marines) dudes trying to charge stuff.

This is what entertains me on a slow friday evening!

Tl;dr OVERWATCH HURTS IF YOU'RE WEARING SKINTIGHT SPANDEX

Nice maths! Now all we have to is figure out why those wyches are chargeing those marines. If they make it on to combat they are most likely to die quite soon. After the calculations above, I don't put Anu Numbers here