How vulnerable is a land raider to a Deff Rolla?

[Bodacious2182]

I saw some other discussions elsewhere on the 'net and people were trying to do the math and coming up with different answers. Some of them were assuming that the average roll of a D6 is 3.5 :P Please show me a D6 that will roll 3.5!

 

Laughing aside, I am bad at math and coming up with formulas and algebra and whatnot, but I am good at statistics. Running a simulation for a Deff Rolla wasn't that hard. I used MS Excel and the RANDBETWEEN function to get everything done.

 

When a deff rolla rams a vehicle there are d6 hits against the vehicle. Given that I simulated this roll 1000 times. Given the result of the d6 I then simulated 1000 times the result of a d6 for armor penetration for the number of times the first d6 determined. For each result I then determined what was a glance and what was a penetration. I then simulated a roll on the damage chart for each glance or penetration.

 

I determined that of the 3534 dice rolled for armor penetration the number penetrations (5 or 6) rolled (1176), 33% (387) resulted in a destroyed or exploded result.

 

Please download my spreadsheet and review it if there are any errors or false assumptions. If there are any questions I ill be happy to answer them. Most of the calculations are at the bottom of sheet 2. If you don't have excel and still want to look at this, download the file and upload it to google docs.

 

 

Download my spreadsheet here.

[Chengar Qordath]

I saw some other discussions elsewhere on the 'net and people were trying to do the math and coming up with different answers. Some of them were assuming that the average roll of a D6 is 3.5 :P Please show me a D6 that will roll 3.5!

3.5 is the mathematical average of a D6 roll, even if it is not a result you can actually roll on the dice.

 

That matter aside, the rest of your math is solid, but it's not that hard to determine that a D6 has a 1-in-3 chance of rolling a five or a six, and I'm not sure why we would need a long, complicated spreadsheet to demostrate that.

[Brother_Kluft]

deff rolla does d6 str 10 hits

 

3.5 hits x 1/3 to pen x 1/3 to wreck/destroy = 0.38 = 38%

 

Pretty damn good really

[pingo]

Brother_Kluft has it nice and succinctly.

 

You don't need to run this scenario 1000 times. This isn't Deadliest Warrior :P

 

I expect you'll find that the mean of the random results for rolling a D6 in your spreadsheet is near as makes to difference 3.5. Although you can't roll 3.5 on a D6, it does make sense. After all, the mean result of rolling 2D6 is 7.

 

38%... is this therefore the Orks' best chance of destroying a Land Raider. I hope so; it's so terribly Orky! :P

[Bodacious2182]

I'm not sure why we would need a long, complicated spreadsheet to demostrate that.

 

Because, as Brother_Kluft proved, using a 3.5 as a mathematical average sets up a false premise when determining results. My simulation removes any false assumptions when rolling for number of hits. A 3.5 can never be rolled, only one of the 6 numbers. The difference between 3, 3.5, and 4 is significant in this scale and that significance can retard the results.

 

My simulation proves that 38% is incorrect. Sure there is a margin of error, but not+5%.

[JamesI]

I did a similiar simulation, and over 2000 times, I got an average of 3.48 for the number of hits caused by the deffrolla. Then I did it again and got 3.52. The average number of hits is 3.5 and over a large sample will be the result.

[Sparhawk]

I'm not sure why we would need a long, complicated spreadsheet to demostrate that.

 

Because, as Brother_Kluft proved, using a 3.5 as a mathematical average sets up a false premise when determining results. My simulation removes any false assumptions when rolling for number of hits. A 3.5 can never be rolled, only one of the 6 numbers. The difference between 3, 3.5, and 4 is significant in this scale and that significance can retard the results.

 

My simulation proves that 38% is incorrect. Sure there is a margin of error, but +5%.

 

Actually unless you set up a Confidence interval we have no way of knowing whether or not 38% is incorrect. With your simulation I don't know that you can say that you can assume with 95% certainty that the average destruction rate for a deffrolla is 33% +/- 4%.

 

I just wanted to point out that you can't say it isn't 5% without backing that statement up with some math.

[pingo]

using a 3.5 as a mathematical average sets up a false premise when determining results. My simulation removes any false assumptions when rolling for number of hits. A 3.5 can never be rolled, only one of the 6 numbers.

 

No. The assumption is 100% sound and mathematically provable.

 

There is a 1/6 chance of each number being rolled. Roll a dice 6 times and you would expect a 1, 2, 3, 4, 5, and 6. Add those together to get 21. Divide by 6 to get the mean gives 3.5.

 

This is just as true for 10 rolls, 100 rolls, 1000 rolls, 1,000,000 rolls, or infinite rolls.

 

In fact, what Brother_Kluft has done is effectively run a simulation an infinite number of times, which is much more accurate than 1000 times.

 

Try running yours more times. I'll bet you'll get nearer 38%.

 

Also: are Excel's random number generators really totally random?

 

When doing this kind of statistics, you need to be more abstract.

 

Here's a question: if the 'average' dice roll is not 3.5, what is it?

[Bodacious2182]

I am not disputing that the average roll of 1d6, mathematically is 3.5. Yah, I get 3.5 when I average the 1000 rolls, so what? That is not disputed here.

 

What is disputed is the results when basing the average of 1d6 and using it to determine results of an effect. 3.5 can never be rolled, only 1 of the 6 numbers. Using 3.5 as a basis for these kinds of mathematics, when a 3.5 is never going to be seen on the table, is a false premise. Using 3.5 as pointed out firmly sets the probably at 38%. That isn't true. I contend that it is much less than that and within a margin of error.

[JamesI]

To give Bodacious credit (I haven't looked at his simulation, but did my own) over 10000 trials, I get a 33% average kill rate. Now, you have to look at how random the random generator is in Excel, but I've done it several times and get a consistent number just less than 33%.

 

Now, this does not include the possibility of getting enough damage to immobilize/weapon destroy the land raider to death, just the odds of penetrating then getting a 5/6 to wreck/explode it.

[Bodacious2182]

I'm not sure why we would need a long, complicated spreadsheet to demostrate that.

 

Because, as Brother_Kluft proved, using a 3.5 as a mathematical average sets up a false premise when determining results. My simulation removes any false assumptions when rolling for number of hits. A 3.5 can never be rolled, only one of the 6 numbers. The difference between 3, 3.5, and 4 is significant in this scale and that significance can retard the results.

 

My simulation proves that 38% is incorrect. Sure there is a margin of error, but +5%.

 

Actually unless you set up a Confidence interval we have no way of knowing whether or not 38% is incorrect. With your simulation I don't know that you can say that you can assume with 95% certainty that the average destruction rate for a deffrolla is 33% +/- 4%.

 

I just wanted to point out that you can't say it isn't 5% without backing that statement up with some math.

 

 

i mean to say, "not +5%." Sorry.

 

Excel has a data analysis tool to determine descriptive statistics. On the result set for the number of penetrations the confidence is 11.6 and standard error of 4.5. So that is between 29.5% and 37.5% chance. So yah, it is close to +/- 5 % it seems. Unless I am just dead wrong about running that utility on those numbers.

[pingo]

Sorry, you've lost me.

 

50% of the time you'll get 1-3 hits. 50% of the time you'll get 4-6 hits.

 

This is surely exactly the same as getting 3.5 hits 100% of the time. Mathematically, it's the same.

 

I see what you're saying, but I don't see how it would make a difference to the end result.

[Koremu]

Because people don't understand how to use mathematics.

 

Working out the mathematics theoretically assuming perfect averages is a lot better than doing 1000 or 1000000 sets of dice rolls (and a LOT better than trusting to a computers RND function).

 

However, I would point out that you are all wrong, because none of you have tried to take into account the possibility of the Land Raider being destroyed by a succession of glancing hits, weapon loss and immobilisation. HINT: It's an incredibly minor chance, but it exists.

 

EDIT: Also, quit wittering on about "margin of error". The margin of error is a statistical artefact drawn around a confidence interval - when quoted in survey and polling reports the usually present either the 66% or 95% confidence interval - meaning that they are that sure that the real result lies within margins drawn.

 

We are dealing with raw probability mathematics. Unlike polling confidence, we don't have to worry about if our selection of pollees is accurately representative. In p-math we can work out a raw likelyhood by ensuring that our data selection is adequately representative.

 

Polling takes a small sample and attempts to extrapolate the whole from that sample.

What we are doing takes the whole (in the form of mathematical expression) and outputs the raw probability of the success of a single example.

 

Back on point: The most influential dice roll of the sequence is the one to determine # of hits. That has the biggest direct outcome on the result.

[Brother_Kluft]

Please reference http://en.wikipedia.org/wiki/Law_of_large_numbers to see for yourself the avg die roll is 3.5.

 

Yes you can never roll a 3.5, since a die represents a subset of positive integers. But operations on integers often create Real numbers. Dont hate on the maths, maths are your friend!

[Sparhawk]

Exactly! That's just like when I hear people say that if you pick up a dice showing a 1 it is less likely to roll 1 since it already has...People really hate how dice are memoryless....

[Koremu]

Exactly! That's just like when I hear people say that if you pick up a dice showing a 1 it is less likely to roll 1 since it already has...People really hate how dice are memoryless....

Ahhh, the gambler's fallacy! How many times have I seen it drawn upon.

[Frosty the Pyro]

Ignoring the chance to kill by imobalized+weapon striping (because that is a huge pain in the ass to calculate, though I CAN do it),

 

 

There is an average of 32.436% chance to destroy an AV 14 vehicle with a deffroller (also please note this is just the deffrollers 1d6 S10 hits, so it ignores the normal hit that comes from ramming)

 

More specificly on a roll/chance to kill

1/11.11%

2/20.99%

3/29.77%

4/37.57%

5/44.51%

6/50.67%

 

 

 

These are the exact values (but rounded to within .01% for ease of presentation) of getting a destroyed or wrecked result, there is no error, it takes into acount every posible dice combination, and their proabability of ocuring.

 

I could upload my spreadsheet for the calculations (which are actual calculations, not simulations) if you want, but someone will need to tell me how to upload files to the forum.

 

 

please note the signifigant diference between the actual 32.44% average, and the "quick and mess" average of 37.69% (3.5 hits*1/3=1.166 pens destroy chance = 1-(4/6)^pens=.3760

[bystrom]

What Koremu said, and that 38% isn't percent, its the average number of land raider kills a deffrolla will inflict. Easiest way of seeing this is by, for example having 10 deffrollas, which would give 3.8 (as its not between 0 and 1 its not a probability).

 

My calculations give it about 32.5% (including weapon destroyed and immobilised kills, that is 3 weapons).

 

My method was calculating the probability to get a destroyed result for 1 to 6 hits by summing the probability for different binomial results. Then adding these together and dividing by 6 (weighing each probability with a sixth chance). Then Did the same but for glance and pen. resulting in 4 wep. destr./immobilised results and weighing them. Then adding all probabilities together.

 

EDIT: Pyro got before me, as can be seen, 4 weapon destroyed/immobilised results isn't very probable.

[Frosty the Pyro]

weapon strip destruction actualy requires 5 results, 3 weapons, 1 imobilized, and one aditional for the destroyed. 6 results if you have a extra weapon (storm bolter, multi melta, or hunter killer)

[bystrom]

Doh! forgot that. It just means getting such results are neglible (not that I didn't calculate it, just that it ends up being 32.438...% instead of 32.436...%)

[Koremu]

please note the signifigant diference between the actual 32.44% average, and the "quick and mess" average of 37.69% (3.5 hits*1/3=1.166 pens destroy chance = 1-(4/6)^pens=.3760

Most of the difference can probably be attributed to the chance that the Deff Rolla can cause multiple kill results. I don't care to do the math, but if you've rolled 6 hits from the Deff Rolla, the chance of 2 or more kills coming up must be relatively high.

 

In that light it is worth considering Vehicle Squadrons in light of the Deff Rolla.

[Top Secret]

deff rolla does d6 str 10 hits

 

3.5 hits x 1/3 to pen x 1/3 to wreck/destroy = 0.38 = 38%

 

Pretty damn good really

 

Being the mathematical idiot that I am, this equation satisfies me completely. How often will a Deff Rolla kill a Landraider?

 

Answer: about 1/3 of the time. I am sure that will make every statician in the room cringe with my logic, but honestly, I don't really care about the exact numbers. I just know now that I need to take out that Battlewagon before it gets close.

[Frosty the Pyro]

please note the signifigant diference between the actual 32.44% average, and the "quick and mess" average of 37.69% (3.5 hits*1/3=1.166 pens destroy chance = 1-(4/6)^pens=.3760

Most of the difference can probably be attributed to the chance that the Deff Rolla can cause multiple kill results. I don't care to do the math, but if you've rolled 6 hits from the Deff Rolla, the chance of 2 or more kills coming up must be relatively high.

 

In that light it is worth considering Vehicle Squadrons in light of the Deff Rolla.

Actualy by using 1-(4/6)^pens removes the counting multiple kills from one result. There error is more into the fact using a fraction instead of using multiple whole numbers and taking the wieghted average, due to the fact that ((1-(4/6)^1)+(1-(4/6)^2))/2 does not equal 1-(4/6)^1.5

[JamesI]

please note the signifigant diference between the actual 32.44% average, and the "quick and mess" average of 37.69% (3.5 hits*1/3=1.166 pens destroy chance = 1-(4/6)^pens=.3760

Most of the difference can probably be attributed to the chance that the Deff Rolla can cause multiple kill results. I don't care to do the math, but if you've rolled 6 hits from the Deff Rolla, the chance of 2 or more kills coming up must be relatively high.

 

In that light it is worth considering Vehicle Squadrons in light of the Deff Rolla.

When I calculated 32% I set up my spreadsheet to look at the end to see if any wrecked/exploded occured. In some instances the vehicle died 4 times, others just once but it counted as 1 kill either way.

[waaanial00]

Ignoring the maths for a minute the answer is fairly simple assuming the question is "How Vulnerable is a land raider to a Deff Rolla".

 

Considering the question in no way suggests that the vulnerability is for destruction then I would say "fairly". As this is not quantifiable its probably irrelevant to most people but in terms of a tactical thread it should be considered.

 

A landraider, whose primary task is to deploy units is very vulnerable to being immobilised as it destroys its greatest tactical application. A landraider used for fire support is not.

 

Just being thorough really, if people are worried about getting destroyed by a Deff Rolla only then I fear they are missing the whole point about vehicle damage. A vehicle does not need to be destroyed to render it no longer a threat.

 

Also this string of maths has not considered other situations, the battlewagon is a transport and therefore can have a bunch of Power Klaw wielding Nobs in it. Simply getting immobilised would greatly increase the chances that said vehicle is destroyed in the assault phase.

 

Again not disputing the maths but this is a very one dimensional view of the impact of the Deff Rolla on a landraider, which sadly is what I find with Mathammer threads like this. They tell you a lot without telling you much of use.

 

Wan