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Well, this is my system for finding out how likely X is to wound Y. It works awesomely for me, and doesn't even require a calculator if you're decent at math. So, here's how it's done:
Creatures:
As we all should know, when you are shooting or assaulting an enemy non-vehicle model, you need to roll to hit, to wound, and then your opponent rolls to save. Thus, on any given attack, there will be (up to) 3 dice rolls. Each of these rolls have 6 possibilities, and this is where we get our perfect number:
216
216 is 6x6x6, or six times six times six, representing all three dice rolls. You start with your basic roll to hit, divide, roll to wound, divide, and roll to save, divide, and you get your fraction. That might've been hard to understand, so I'll do an example:
Tau Pulse Rifle fire versus Tactical Space Marines:
216 shots... Tau Fire Warriors roll a 4+ to hit, which is essentially a 50%. So, divide your number of shots in half, thus, reducing your 216 to...
108
Tau Pulse Rifles have one more point of Strength than Tactical Space Marines have Toughness. Thus, Pulse Rifles get a 3+ to wound. 3+ is 2/3 of a d6, so, divide your number by 3 and multiply by two... 108/3=36... times 2=...
72
Pulse Rifle AP does not beat Tactical Space Marine armour saves, so the Marine will get to roll his save. With the saves, your numbers are inverted. So, for your purposes, a 3+ is a 5+, and a 2+ is a 6+, and vice versa. 1's are the nonexistant save, and thus, don't come into effect. Okay, so, the Marine gets his 3+ save, meaning that 1/3 of your 72 wounds inflicted will be deflected by his armour. 72/3=...
24
So, now you have your final fraction. 24/216. This fraction can, and should, be reduced. 216 will always be divisible by any factor of the smaller number, so go by the smaller number's factors. Let's start with 2. 24/2=12. 216/2=108, as we already know. These numbers can be divided by 2 again, so... 12/2=6. 108/2=54. We can divide by 2 again... 6/2=3. 54/2=27. Now we can divide both of these numbers by 3. So... 3/3=1. 27/3=9. And thus, your final fraction is...
1/9
1/9 pulse rifle shots will successfully hit, wound and kill a space marine. This system can be applied with any attacks, shooting or close combat, against any unit.
Vehicles:
Against vehicles, you need to use a slightly different system. Since the Armour Penetration Table has 6 different effects in each section (glancing, penetrating, ordnance), you need to multiply your perfect number by 6, which can start to give you a headache. The Vehicle perfect number is 1200+60+36=1296. Big, scary number, but you may find it useful. So, I'll do a more brief example with the armour values. In this situation, I'll use two popular items: The Krak Missle (available to most races), and the Space Marine Dreadnought (front/side armour).
So, we start with our Vehicle perfect number. 1296. Let's say I'm shooting with and Eldar Dark Reaper Exarch, who has a 2+ to hit. For the 2+, I prefer to find the number and subtract it from my perfect number, rather than multiply the number by 5. So, 1296/6=216. 1296-216=1080. Now, things get a touch complicated. A krak missle will damage a vehicle on a 4+, but one of these will be a Glancing hit, where two are Penetrating hits. So, 1/6 will be glances, and 1/3 will be Pen.s. 1080/6=180. 1080/3=360. So, out of our initial 1296 Krak Missiles, 180 will glance, and 360 will penetrate. Then, we divide this number by 6 again, for each of the effects. 180/6=30, 360/6=60. Thus, each glance will have 30 occurences of each damage, and each pen will have 60. So, now it is time to reduce.
30/2=15, 60/2=30, and 1296(your base number)/2=648.
15/3=5, 30/3=10, and 648/3=216(hey!)
Now, understanding 5/216 and 10/216 will be a bit tough, let's reduce 10/216:
10/2=5, 216/2=108.
So, after all is said and done, out of 216 shots from an Eldar Dark Reaper Exarch Krak Missle, you will get 5 of each glance damage, and 10 of each pen. This seems like a small number, but it really isnt. If do not include the damage charts, you will have 30/216 glances, and 60/216 Penetrates, making 90/216 shots effective after rolling to hit and to "wound". 90/216=45/108=15/36=5/12. 5/12 doesn't seem too bad, does it? To find the fine specifics, you will probably need a calculator and a codex or two. I would cite all the occurences that would happen, but I am currently in Japan and separated from my books, so I am unable to do this.
So, for a wrap-up, when rolling against infantry, make a fraction out of 216 and reduce, and against vehicles, use the same if you want to know how often you will damage, or use 1296 if you want to know the rate of occurrence of each individual effect. I hope this has been useful/interesting for all of you who have read, and I hope I will see people using this system in the forums to compare units and the like. Thanks for reading.
My gaming group's new motto: That army you're using is overpowered because it hurts my guys, codex is broken and needs a rewrite.
Amazing Job. This is a great way to figure out statistics.
Or you could just do it the actual way--it's not really any harder.
It also keeps separate probabilities and averages. One of the worst problems I see gamers run into with statistics is confusing probabilities and averages, simply because in instances like the one you just mentioned, the two calculations produce the same results. Refraining from looking at it in a way that allows you to distinguish the two is just asking for trouble when you get into situations where the two don't produce the same results.
Just remember that the probability of an event happening is easy (hitting with a shot, for instance).
The probability of multiple events all happening (hitting, wounding, and killing with a shot, for instance) is simply the probability of each of those events times the probability of each other of those events.
The probability of an event happening at least once over a given number of trials is one minus the probability of it not happening in each of the trials. (or 1-(1-P)^N where P is the probability and N is the number of trials.
The average number of times an event will happen over a given number of trials is the probability of the event times the number of trials.
The math isn't any harder to do in your head (especially if you can remember than 6^3 is 216) and it much more useful when you approach it properly.
Last edited by Bean; December 26th, 2005 at 03:37.
Yeah, you just restated my equation without being thorough inexplanation/examples. This system serves to give you a ratio of attacks/successful attacks. The whole point of this is to find out how effective X weapon/attack is against Y model/tank. It helps to know whether it would be more effective to take a Railgun or Ion cannon to kill a wraithlord. Having this basic sort of knowledge can be helpful when planning out your army. And remember, after you have done all of the math and reductions, you can divide the top number by the bottom number, giving you a percent success rate. Some players may find this to be useless, but other players, such as myself, take comfort in knowing that they are using the right weapons against the right army, and knowing why they are the right weapons.
My gaming group's new motto: That army you're using is overpowered because it hurts my guys, codex is broken and needs a rewrite.
Fair enough--I'm just pointing out that your system is unnecessarily roundabout and tends to lead to erroneous assumptions when the numbers get more complicated.
I agree completely that using statistical analysis is the proper way to value units and weapons and design armies--I'd just like you to show more exacting math with better explanations so that people don't take what you're saying and misapply it in other situations.
The main issue I have is your first statement:
"Well, this is my system for finding out how likely X is to wound Y"
While a fire warrior will kill a space marine 1/9 of the time (a probability of 1/9) the math you show is not the proper way to generate probabilities. It's the proper way to generate averages. On average, a fire warrior will kill 1/9 of a space marine (or nine fire warriors will kill, on average, one space marine would be a better way of putting it.)
Though the probability and the average happen to be the same in this instance, they won't always be the same, and using this system to find probabilities is simply misinforming them--making it more likely that they'll make a mistake and find average resulst instead of probabilities in situations where the two aren't the same.
Last edited by Bean; December 26th, 2005 at 23:22.
For example, with your system, can you tell me the probability of killing a land raider with 18 rapid firing necron warriors? (this is a question that was asked on a quiz at a tourney I went to. Everyone there got it wrong, even me (the answer is actually really tough) but no one besides me even came close).
Actually, since neither of us have given the math necessary to actually do that (though I'd be happy to if anyone wanted it) just calculate the probability of getting a vehicle destroyed result on the chart.
Oh, and for referrence, I've got a spreadsheet that calculates averages results over several rounds of combat/shooting between two units if anyone wants it .
Last edited by Bean; December 26th, 2005 at 23:47.
Please, explain how probability, chance and average are different. The dictionary website gave these three definitions, which, in my understanding, are more or less the same.
AVERAGE:
Approximating the statistical norm
CHANCE:
The likelihood of something happening.
PROBABILITY:
Number expressing the likelihood that a specific event will occur.
My gaming group's new motto: That army you're using is overpowered because it hurts my guys, codex is broken and needs a rewrite.
Well, there's your answer. Probability expresses the likelihood of something happening. The Average is the statistical norm of a set of events. You find average occurance rates based on the probabilities of the events you're looking at, but the two aren't the same.
Since you didn't deign to accept my challenge, I'll use my example to illustrate the difference for you.
The probability of getting a Vehicle Destroyed result on a Land Raider with 18 rapid-firing Necron Warriors is 1-(1-(2/3*1/6*1/6))^36 or about .490 (49.0%)
This gained by findingn the probability of any given shot hitting, glancing, and gaining the desired result (P=2/3*1/6*1/6), then finding the probability of that not happening (1-o) then finding the probability of it not happening in all of thirty six cases ((1-P)^36) then finding the probability of that entire series of events being unsuccessful in all cases (1-(1-P)^36).
The averge result would simply be P times the number of shots, or (1/6*1/6*2/3)*36, or approximately .667 vehicle destroyed results (or two vehicle destroyed results for every three warriors, if you prefer to look at it in whole numbers).
As you can see, the two are not the same. Though the math you give does allow people to find average results, you begin your description by saying that you use it to find probability--and you can, in some cases, find probabilities with your system. My objection was that the math you provide is insufficient to find probabilities in a significant number of other important cases, and that by failing to deliniate between the two, you merely enhance an existing lack of understanding about statistics.
P.S.
Finding the actual probability of a land raider being destroyed by 36 necrons involves adding in the slim possibility of them generating sufficient weapon destroyed/immobilized results, and that math I can't remember off the top of my head (and I don't really want to go look it up, again, unless someone really wants to know).
bah...
i firmly believe that if you're using Statistics and Numerical Analysis on the game to build the better army, you, sir, are taking the game too dam seriously.
step outside,
get some fresh air,
and come back when you want to play a GAME
and not treat every battle like your life depends on it.
Pictures of the Smigs Army for your amusement....
http://photobucket.com/albums/b390/Holy_Smigs/
Eagles may soar, but weasels don't get sucked into jet engines.
"Crush your enemies, see them driven before you, and hear the lamentations of their women"
"JESUS SAVES! the rest of your models each take a wound."