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| What are the odds!; Calculations & Probabilities | ||
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| Tweet Topic Started: 13th October 2014 - 06:54 PM (728 Views) | ||
| Dazzle | 13th October 2014 - 06:54 PM Post #1 | |
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Clanrat
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Hey everyone, In another thread I said that I'd someday do some calculations to see how important it is to run Gutter Runners in units larger than 5. Well that they has come and I thought I'd share with you! ![]() Allow me to explain what you can see there. The graph shows what the odds are of killing: -3 war machine crew members, T7 + light armor. -5 wounds to fast cav, t3 + light armor + shield + mount. -2 wounds to fast cav, t3 + light armor + shield + mount. In one turn with X number of Gutter runners, assuming that they have poison and are shooting at long range with slings. (so hitting on a 5+) So they didn't move that turn!!! (But still, as far as war machines go, I wouldn't put any money of hit on a 5 actually inflicting a wound) Now my idea for this thread is to get a nice collection of charts/graphs/tables like I just posted. I find that they can help with decision making sometimes. This one is particularly helpful in showing whether or not it is wise to free up some points by bringing less gutter runners. I was actually quite surprised to see that their odds of killing a war machine go up quite steady when adding numbers to the unit (I expected the line to be steeper at the start and to start going horizontal earlier). Ok now I'm going to explain the math a bit for people who would like to contribute (or verify/understand what I posted): The "formula" used to calculate probabilities like this is called a "Bernoulli trail" and it kinda looks exactly like this: (n! / ((n-k)! * k!) * ((Ps)^k) * ((1-Ps)^(n-k)) = Result N = number of shots. (number of gutter runners * 2) K = the number of wounds we want to inflict. Ps = the probability of a single shot inflicting a wound. Let me explain how that works, for poison its 1/6 * (5/6) (odds of hitting a 6 to hit and them rolling less than 6 on their armor save). For the normal hit on the 5 it is 1/6 * 1/6 * 5/6 (odds of rolling 5 on to hit, odds of rolling 6 on to wound and odds of them rolling less than 6 on their armor save). and we add these two probabilities up. (if we'd be firing at close range we'd have two "normal" hits and the first 1/6 would be a 2/6 (odds of rolling a 4 or a 5)). Result = (example) the probability of inflicting exactly 3 wounds when firing 10 shots. So if we want to know the probability of inflicting at least 3 wounds when firing 10 shots, We just "simply" add up the probabilities of inflicting exactly 3,4,5,6,7,8,9,10 wounds. Now for those that would like to contribute but think OMG that is a shitload of work, just use this site: http://stattrek.com/online-calculator/binomial.aspx (we're interested in the output shown in the P(X >= x) box as that is the "at least" probability) and just make a table in excel and post it here!! (after finding that site making that table took me about 5min)I'm curious to see where this thread will go, I think I'll add another graph someday that shows gutter runners really must have poison for war machine hunting =P -Dazzle Edited by Dazzle, 14th October 2014 - 05:43 PM.
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| Nurglitch IX | 13th October 2014 - 10:13 PM Post #2 | |
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Avatar by count zero
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Wouldn't it also be useful to know how many shots you need to be 99%, 95%, 90%, 75%, and 50% sure of killing it? | |
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| SkavenDan | 13th October 2014 - 10:19 PM Post #3 | |
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Doomwheel Fanatic
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5 gutter runners can kill any 6 wound monster easily I laugh in the face of probability
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| Dazzle | 14th October 2014 - 09:38 AM Post #4 | |
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Clanrat
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Yes and No, I don't think it's realistic to field units of gutter runners of that size. (as it would be higher than 13) I think if you want to bring more than 13 you're better of putting them in units of 3x5 so that if you can kill it with 20 shots you can aim the last 10 at something else. So yes it is interesting to know, but I don't think you'll ever field enough gutter runners to get 90%+. I thought it was quite interesting to see that the tip over point (50%) is at 9 GR, I thought it would be at 8 or 7, too optimistic it seems =P I am curious though how GR would perform on tasks other than war machine hunting, and if the points spend on poison would be better spend extra models when shooting at infantry units for example. -Dazzle |
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| Littlewicked | 14th October 2014 - 12:38 PM Post #5 | |
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Chieftain
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Thanks for all the hard work to get the formula and graph for this. I have a question below the graph you state that it is for long range and having moved which would be hitting on 5+. In your formula you use N as the number of shots equaling number of gutter runners *2 so this would be an additional negative for hitting making it so you are hitting on 6 if I am reading this correctly. Assuming I am correct for the graph to be accurate it would have to be either moving or shooting at long range. | |
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| Dazzle | 14th October 2014 - 05:38 PM Post #6 | |
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Clanrat
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Damn you're right! yeah That's my bad =/ Forgot the penalty for the use of slings. Well I guess it's still accurate when assuming short range or not having marched. I'll edit the post to remove the having marched part ^^ the quickest, most correct, fix. Thanks for pointing it out =) And about the hard work, It's not that bad if you've ever studied statistics (although It took me a while to refresh my memory I have to admit =P ). I hope someone else is also going to make an attempt to make a graph or table like that sometime. (if anyone has any questions just send me a PM, I wont bite ^^) -Dazzle |
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| Didimus | 14th October 2014 - 07:20 PM Post #7 | |
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Stormvermin
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Very nice! I did something like this for myself awhile ago, but it is great to see someone using statistics, not just dice-rolling simulators! Not sure how you did the math, but with higher number of Gutter Runners on lower number of wounds, it may be easier to calculate 1 - P(not killing) than P(killing). For example, for a killing a war-machine with 9 GRs with double shots), you could either calculate P(kill) = P(3 wounds) + P(4 wounds) + P(5 wounds) + ... + P(18 wounds) OR P(kill) = 1 - (P(0 wounds) + P(1 wound) + P(2 wounds)). |
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| Dazzle | 14th October 2014 - 08:50 PM Post #8 | |
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Clanrat
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Yeah I think you're right, but if you have a easy probability calculator (like the one I posted the link of) this is also a 100% correct way (And fastest!!) to do it. Your method works as well and might be faster to enter on a normal calculator, but lets face it, that would still take forever =P (I didn't believe that calculator that I found at first so I did the math to verify and it's spot on.) I'd like to get into dice rolling simulators for stuff that is close to impossible to calculate (like a swiftstride charge being about 8.4 inches on average). Anyway, any chance you can share what you did yourself Didimus? =D -Dazzle |
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| Dune-rats | 14th October 2014 - 09:03 PM Post #9 | |
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Clanrat
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Can you also do the chances of one shotting nagash with a fellblade, I've been trying to write a computer program but I'm lazy and it's a bit hard for someone as inexperienced as me | |
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W/L/D Vs WoC 2/2/1 | ||
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| Nurglitch IX | 14th October 2014 - 10:24 PM Post #10 | |
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Avatar by count zero
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Dice roll simulators are problematic. If they work they just trend to the pure math, and as my buddy likes to point out - dice aren't fair. GW dice are actually the worst, studies show they roll 1s closer to 21% than the statistical expectation of 16.7%. In any case, here's Swift stride vs. Normal charge - pure math hammer
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| Dune-rats | 15th October 2014 - 01:02 AM Post #11 | |
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Clanrat
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Wait it doesn't peak at 7? | |
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W/L/D Vs WoC 2/2/1 | ||
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| Nurglitch IX | 15th October 2014 - 03:06 AM Post #12 | |
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Avatar by count zero
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Nope. The difference between the two lines is greatest about there, but the SwiftStride is always a bit better. Edited by Nurglitch IX, 15th October 2014 - 03:07 AM.
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| Dazzle | 15th October 2014 - 07:40 AM Post #13 | |
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Clanrat
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Nurglitch that is a pretty awesome graph =D thanks for contributing! And about those GW dice, that is interesting, wouldn't expect that for a game that is all about dice! Dune-rats, if you reply to my PM I'll help you workout the math and you can post the results here yourself ![]() -Dazzle |
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| Didimus | 15th October 2014 - 04:24 PM Post #14 | |
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Stormvermin
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Here is one that I did. This calculates the probability of passing a Leadership Test based on different things. Since my main opponent is Lizardmen, I added some lines for passing cold-blooded leadership as well. The last few things are our Banner that is like a reverse BSB with a Ld modifier and the Carnosaur's bloodroar (basically reverse cold-blooded...roll 3 dice and pick the highest 2).![]() If the pic is too small, look at the attachment! MUTATE: As for Nagash...I have to double-check the stat-lines later, but I here are my initial results: After 1 round of Combat
MUTATE-2: Explanation of Chart - LM stands for Lizardmen. Their Cold-Blooded rule lets them take Leadership tests with 3 dice and use the lowest 2. The x-axis is generic for all Ld tests. If you want to factor in SiN, just use the # that you would be testing on (say base 2 + 3 for SiN = 5, which is just shy of 30% normally, higher if within range of the BSB and lower if coping with Bloodroar) Edited by Didimus, 15th October 2014 - 09:43 PM.
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| Dazzle | 15th October 2014 - 07:29 PM Post #15 | |
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Clanrat
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Few questions, do you account for SiN? and what does LM stand for? As for that fellblade battle, I don't know any of the stats, I know what the calculation should look like but can't do much before I know more! I can see how its a bit tricky to do the math as I had to think about for a bit before I was sure how to do it =P -Dazzle |
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and post it here!! (after finding that site making that table took me about 5min)
Runners.png (14.08 KB)





