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So I was recently playing in a tournament, and I brought 2 squads of imperial guard infantry and an officer off the board edge and proceeded to first rank second rank light up a squad of brimstones. After a few fists full of dice, I ended up killing 2. So as I hung my head I thought, what are the odds of that... The standard method of figuring averages or rolls would say I should have done 9 wounds. (72 shots, 50% hit 36, 50% wound 18, 50% save 9) While this falls way outside of what could be considered a normal range, it made me think. What are the odds of doing x number of wounds? So I did what I always do, and I made a spreadsheet. As you can see from the data below, the odds of me only killing 2 was about 0.4%, or just ever so slightly within 3 standard deviation, which is the standard for near certainty. I adjusted my sheet a bit to make it easy to use, so if you want to see what your odds are of doing so many wounds, feel free to check it out.

https://drive.google.com/file/d/0By2u1KlcD03aSENueV92SUJNMjg/view?usp=sharing

0.0% Chance of 0 Wounds
100.0% Chance of at least 1 wounds
99.9% Chance of at least 2 wounds
99.6% Chance of at least 3 wounds
98.4% Chance of at least 4 wounds
95.6% Chance of at least 5 wounds
90.0% Chance of at least 6 wounds
81.1% Chance of at least 7 wounds
69.2% Chance of at least 8 wounds
55.3% Chance of at least 9 wounds
41.2% Chance of at least 10 wounds
28.6% Chance of at least 11 wounds
18.4% Chance of at least 12 wounds
10.9% Chance of at least 13 wounds
6.1% Chance of at least 14 wounds
3.1% Chance of at least 15 wounds
1.5% Chance of at least 16 wounds
0.7% Chance of at least 17 wounds
0.3% Chance of at least 18 wounds
0.1% Chance of at least 19 wounds
0.0% Chance of at least 20 wounds



Automatically Appended Next Post:
I made a google docs version too. I noticed there was a difference in the syntax

https://docs.google.com/spreadsheets/d/1NBlgJB-oIohBg38w-7A28qh3Su4wE4eqSRfKJAs-ILY/edit?usp=drivesdk

So the point of this is that the average doesn't always happen every time? I fail to see what you're trying to prove here.

No one says an average happens every time you shoot, outliers are a thing. You should have contingencies going into a game for if you roll bad, but you can't base all your decisions on a 0.4% chance of something happening. We've all seen stuff like that before, and even more ridiculous things than that.

Heck I watched draigo go from full wounds to 0 in 5th edition by getting caught at the edge of a 6" hellhound explosion and then getting charged by a guardsman squad. I don't think any sane person wouldve been able to plan around that happening but there you go.

You're playing Guard, the most consistent faction on average because it rolls the most dice and doesn't get screwed by 1 or 2 bad rolls.

If you made 50 bad rolls, that's might be a curse on your family by a voodoo priest.

Or Chessex dice

Yes, factoring standard deviations into the battle plan reduces risk compared to working to averages. That's not always easy during the midst of war, so a general rule when an important job needs doing is to send twice as much force as you think you'll need. You've then got a 98% chance of doing at least the average damage that one unit should do and probably more, if that makes sense. However, OP sounds like your guard were unlucky in your example and there's nothing reasonable to be done about that.

 Insectum7 wrote:
Or Chessex dice

QFT. You have to 'train' chessex dice otherwise they misbehave.

I found that another helpful munition effectiveness meter is 'chance of doing at least one wound' on a per-unit basis; it sets nice and low expectations.

seems like there is some rounding involved in your original post, there is no way you have a 100% chance of getting at least 1 wound, or are your at least actually less than X wounds not less than or equal to.

Well with 1 decimal numbers obviously it's rounded. I would rate chances of all numbers being exactly 1 decimal as far lower than 20 wounds out of 20 lasgun shots

The reason averages are used in-game is because it's quick and fairly simple, while providing a "good enough" benchmark for performance. It can be useful to know what the chances of rolling slightly above and below that number are but I'm not sure what the point is of knowing you have a 0.4% chance to do 2 wounds in your situation is. Had you known this, would you have still fired? Almost certainly.

I do wish more people would understand what average means in this context, though. I get a bit tired of people moaning about getting 2 wounds below the average when the chances of that happening are often around 33% or higher.

Averages are useful, but only if you also consider the likelihood of total success and abject failure.

If I need to do say, 5 wounds, and I know that statistically I'll do 1, I may be able to find a better target.

But if I need to do 5 wounds, and I know that statistically I'd do 3....that's a risk I'm more willing to take.

Consider previous 40k as an example.

I need to take out your Rhino, and your Predator. Because I just have to. Now I'm down to one Lascannon, and both the Predator and Rhino are down to a single hull point. I've also got a 5 strong squad with S4 pistols in range and the rear arc of both vehicles.

Statistically, my S4 pistols should do nothing. I just don't have enough. But it doesn't take much of a spin off centre to get that precious 6 and take out your tank.

So in that situation, I figure the smart thing to do is shoot the Predator with the S4 pistols. It's no harder for them to take out either tank, but the Lascannon will have an easier time against the Rhino. And if the Predator survives, the Lascannon could still finish it on its own.

By understanding the raw statistical probability, I've still informed my decision, even though I know I need to break it. The risk is worth it there.

DeviationOfWar you make interesting observations, thanks for the data you show. This is something I've talked about frequently with the people I play with. Anyone who uses statistics to investigate data properly, understands an average is only one way to help describe a distribution of data. That is not to say it isn't useful, often its the most useful descriptor but its not the only one. The example I always give is the difference between the 2 handed sword and halberd in D&D 3rd Ed. 2d6 damage vs. 1d12. Similar average but a way different distribution.

The sword averages at 7 and the halberd 6.5 . Yet despite its average being 7 for the sword it will only roll that 1/6 times, its the most likely result but its not as common as people may immediately think. If you want to hit for max damage you'll be doing that 1/36 hits where with a halberd its 1/12. i.e. the Halberd has a flat distribution but the sword peaks at 7 and tapers away quickly around that 7.



I play orks most the time and I think the high price of our weapons despite low average expected outcomes is due to pricing based on the full distribution of outcomes rather than the average. Orks throw a lot of dice and often our average is about the same if not a bit lower than BS 3+ armies (from what I see on the table top, no stats to back it up). however, the damage potential of orks (albeit small) can be huge. I've not experienced it often but I've had these outliers happen to me. I've had the ork psychic power (I think it is called da krunch) do a strength 10 large blast hit a squad 3 times then followed by 1 strength 8. (in the power you would roll 2d6 for strength if the result was 10 or more then you would do it again) I've also lost 2 shokk attack guns in the first turn (double 1 on both of them) and it was the only time I played 2 of them heh.

Anyhow, people should keep one eye on the distribution of outcomes as well as the average, I think if we are picking 1 measure then then average is the best and its understandable why people gravitate towards it.


(btw I'd always take the halberd, you get so many more occasions doing max damage which is loads more fun than being 'slightly better on average', Besides the halberd had a x3 crit multiplier compared to the swords x2).

As others have said average gets used a lot because it is quick dirty math, vs trying to mentally calculate the percentage for each amount of possible wounds. IT is also of note that these types of things really only apply well if you have a ton of dice.

Averages are mostly intended to create a generalized impression of how a unit should perform - the problem is people construe what a unit can do 'on average' as an expectation. Aka, what a unit should do because 'on average it does X or Y' - often to the point of ignoring that it is just an average and your individual dice results can (and will) swing either way.

DeviationOfWar wrote:
So I was recently playing in a tournament, and I brought 2 squads of imperial guard infantry and an officer off the board edge and proceeded to first rank second rank light up a squad of brimstones. After a few fists full of dice, I ended up killing 2. So as I hung my head I thought, what are the odds of that... The standard method of figuring averages or rolls would say I should have done 9 wounds. (72 shots, 50% hit 36, 50% wound 18, 50% save 9) While this falls way outside of what could be considered a normal range, it made me think. What are the odds of doing x number of wounds? So I did what I always do, and I made a spreadsheet. As you can see from the data below, the odds of me only killing 2 was about 0.4%, or just ever so slightly within 3 standard deviation, which is the standard for near certainty. I adjusted my sheet a bit to make it easy to use, so if you want to see what your odds are of doing so many wounds, feel free to check it out.

https://drive.google.com/file/d/0By2u1KlcD03aSENueV92SUJNMjg/view?usp=sharing

0.0% Chance of 0 Wounds
100.0% Chance of at least 1 wounds
99.9% Chance of at least 2 wounds
99.6% Chance of at least 3 wounds
98.4% Chance of at least 4 wounds
95.6% Chance of at least 5 wounds
90.0% Chance of at least 6 wounds
81.1% Chance of at least 7 wounds
69.2% Chance of at least 8 wounds
55.3% Chance of at least 9 wounds
41.2% Chance of at least 10 wounds
28.6% Chance of at least 11 wounds
18.4% Chance of at least 12 wounds
10.9% Chance of at least 13 wounds
6.1% Chance of at least 14 wounds
3.1% Chance of at least 15 wounds
1.5% Chance of at least 16 wounds
0.7% Chance of at least 17 wounds
0.3% Chance of at least 18 wounds
0.1% Chance of at least 19 wounds
0.0% Chance of at least 20 wounds



Automatically Appended Next Post:
I made a google docs version too. I noticed there was a difference in the syntax

https://docs.google.com/spreadsheets/d/1NBlgJB-oIohBg38w-7A28qh3Su4wE4eqSRfKJAs-ILY/edit?usp=drivesdk

HAH, I take you 0.04% chance and raise by my current streak of:

10 +3 failed in a row followed by two failed 2+

All that coming together at around 1/ 2 500 000 chance. Heh the gods have conspired to break my 20+ win streak like that... , probably to punish me for playing loyalist scum after so much success with chaos

GhostRecon wrote:
Averages are mostly intended to create a generalized impression of how a unit should perform - the problem is people construe what a unit can do 'on average' as an expectation. Aka, what a unit should do because 'on average it does X or Y' - often to the point of ignoring that it is just an average and your individual dice results can (and will) swing either way.

Perhaps because it is called "expected value"

Jokes aside - humans as a species are not hardwired for probability and statistics - it is not intuitive for us. One common misconception about dice roll results is that rolling five fives when you need five sixes is somehow "closer" to desired roll than rolling five ones, or any other non-success roll. We also mix "scale of result" as a factor influencing "worth" of beting against low probabilities of such result - we do play Loteries with 10^-8 probabilities of winning yet we deem "unprobable outcome" of a lucky roll with 1/6th odds when we need it in a peak of a 40K battle... Other common misconception is that probability and statistics are connected by causality relation - i.e. that if we roll succesive 1, 2, 3, 4, 5 then the next roll is somehow more likely to be 6 because statistics...

Analysing averages and distributions in 40K is a great tool to fish for miscosted units/weapons, but it is not "an ultimate decision making tool" in-game. You can build your tournament strategies around averages, but tournaments are just few games, nowhere near statistically important number of samples. But on the other hand, it is more usefull in 8th ed (this is one of the reasons why 8th is percieved as "ballanced better than 7th") exactly because all that in-game dice rolling - if you roll 200-300 dice for Razorwing flock's single fight phase, then you are far more likely to do those 4 dead marines worth of statistically average damage than when you are rolling just 16 dice, fishing for sixes. In 8th, "overall results experienced in a single game" are closer to mathhammer averages - you simply need less games to achieve statistical distributions of your personal results because a single game is a bucket of dice instead of just a big mug of dice.

In-game, calculating average outcome or distribution of succes is meaningfull only if you are presented a meaningfull choice. As Mad Doc wrote - raw odds of succes don't really mean a thing if that's the only use for weapons you have at any given moment. If your only use of small arms fire is to throw them at tanks you are either doing awfully wrong in movement and anticipation department, playing a huge mismatch, or previous parts of the game had you made "then rational" decisions leading to current "relative uselesness" of your unit. Knowing your mathhammer by heart doesn't win you games, proper decision making, quick adaptation to unlucky rolls, redundancy and forward thinking does. Mathhammer is just an underlayer to those.

If you make a hundreds dice rolls in a game. You should have at least 1 dice probability with a 1% chance of occurring to occur. Statistics bro. Then also - murphies law - anything that can happen - will happen. Also something else to thing about - you might think you are an unlucky roller - I know I think that. When I really stand back and look at my rolls though - I roll some crazy amounts of 6's sometimes - they just seem to come at some stupid time when I am rolling bolters and not 5++ saves. The universe doesn't care what you are rolling for it seems!

 Xenomancers wrote:
If you make a hundreds dice rolls in a game. You should have at least 1 dice probability with a 1% chance of occurring to occur. Statistics bro. Then also - murphies law - anything that can happen - will happen. Also something else to thing about - you might think you are an unlucky roller - I know I think that. When I really stand back and look at my rolls though - I roll some crazy amounts of 6's sometimes - they just seem to come at some stupid time when I am rolling bolters and not 5++ saves. The universe doesn't care what you are rolling for it seems!

That is exactly what I wrote about above: statistics and probability are not connected by causality. Statistics is a post-factum analysis of data, it does not influence probabilities of future dice rolls. With increased number of those "hundreds of dice rolled in game" you aren't going to be "sure" that you roll those 1% odds single dice. You're always just increasing the correlation between your in-game results with statistical distribution of theoretical results. Nothing more - any unlikely deviations can and will happen. Any finite number of consecutively thrown tails is probable, it is just statistically unlikely - even if you have already thrown 100 tails, probability of next tail is still 50-50.

While the averages are quick and dirty, I think knowing the actual statistics would be better when you are taking a chance. Lets say there are 2 objectives, one with 4 marines on it, and one with 3 marines on it. You have an infantry squad with first rank second rank that can rapid fire either. Lets say you also have Celestine who can reach the 4 man squad with assault from an 8.5 in charge. If you overtake the one objective you can tie, but if you can kill the 4 with Celestine alone and the 3 with the infantry squad alone you can win. We assume Celestine makes her charge, because if not it wouldn't matter anyways.
Average wounds for 37 lasgun shots is 2.01, average wounds for Celestine is 2.78. Lets say the difference is between 1st 2nd and 5th in a tournament.
Do you
A) split your fire and go for the win? It is about 1 over with each, so it would take an above average round with both, but if your shooting fails, Celestine can still win it by herself.
B) Double down and play for the draw? Maybe more greater good than blood for the blood god.
Now if you are a grab your balls death or glory player you will go for it without a second though. But if you knew the odds would you? For option A, you have a 72% chance to lose, 18% chance to tie and a 9% chance to win. If you played it safe for second place, you would have a 76% chance of a draw, and a 24% chance to lose.

9% chance to win for an extra 48% chance to lose.

Now, I know this isn't practical to know every statistic, or to whip out a spreadsheet in the middle of a match, but having a rough idea of the rate at which they drop off is huge. Even if the table were reversed, you could do a little social engineering, "oh man, you could win if you clean them both up." And if you think this is rubbish, you are that person I can goad into making it so I have a 90% chance to not lose.

The failure was that you made the number one mistake when playing the Imperial Guard. You expected your lasguns to actually kill something! If I fire 150 lasgun shots at a single grot I assume he will survive and have a backup plan in place for when he inevitably does.

Deviationofwar has the right idea. Statistics help us know what the outcome should be if we could play it over and over again. It helps us make decisions in game. Whether to split fire with a big units shooting or if you should charge an assault unit with your 10 man guard squad. for example - if you could tie up your opponents best assault unit with a unit of 10 wimps you should make that play. Statistics say he should kill 9 or less on average - so go for it! He might kill all 10 and it seems like a waste but over 50% of the time he wont kill all 10 and you can burn 2 command points to auto pass your morale. These are the decisions that make a good player. Statistics help us make those decisions. Theres also times you should take a long shot - especially if you are behind in the game. just like in football when you throw a hail mary - when you aint got nothing you got nothing to lose.

This seems legit. I personally would go for the win, cause, feth tying. But, I am a big fan of this calculation. FYI, Brimstones are just that good.

Averages are a good way of judging where to apply your force. That being said, it is far from empirical or foretold.

When people expect to shoot a unit and do 6 wounds but come up with 3 or 4, they tend not to think too much about it. But instead, when firing at a vehicle, they figure they should do 9-10 wounds to a dreadnaught in one go. If they happen to do 6 instead, I regularly hear something along the lines of "It should have been killed".

In reality, doing the average number is usually on the order of 3-5% depending on the number of dice thrown. People should realize that the chances of rolling below that average are basically half.

True dat.
I've had *that* luck in my last few games, opened fire on a Dread with Long Fangs packing four Lascannons, got a grand total of four wounds on the damn thing.
One miss in spite of re-rolling one to-hit, one 6+ save, a three and one for damage, command point re-rolled the one to another one.
Thank goodness it wasn't a ven dread - they would have bucked the odds again and made at least one FnP save as well.

 Dakka Wolf wrote:
True dat.
I've had *that* luck in my last few games, opened fire on a Dread with Long Fangs packing four Lascannons, got a grand total of four wounds on the damn thing.
One miss in spite of re-rolling one to-hit, one 6+ save, a three and one for damage, command point re-rolled the one to another one.
Thank goodness it wasn't a ven dread - they would have bucked the odds again and made at least one FnP save as well.

That brings up another good point in this discussion:

When people calculate the damage, they just crunch the numbers and come up with x saves missed and so many wounds going through. One armor save saves all of the random wounds coming from a weapon. It doesn't take too much to show two sixes on saves from a vehicle and skew your numbers hard. In the case of multi wounds against vehicles, there's much more chance of scatter; FNP-like saves against each individual wound cause the distribution to be less dependent on the all or nothing type of saves from vehicles.

That's for characters too. Statistically speaking, a lascannon isn't going to kill your Chaos Lord. But when someone rolls that hit, rolls that wound, then rolls a 5 or 6 on their dmg and you failed your invuln save? That's a dead Chaos Lord. In such a case it's less important to know the average wounds it will deal versus the % chance of the Lord surviving.

Distributions are important in this edition. With up to five dice rolls rather than 3 there can be much more variation in the results.

This calculator does a great job:
http://mathhammer.thefieldsofblood.com/


Automatically Appended Next Post:
This is an example I posted in another thread.

Rapid Fire Battlecannon shooting at a Leman Russ:



Thermal Cannon (pre-codex) at a Leman Russ:



So the Thermal Cannon has a higher average and higher potential but it also has a higher chance of doing nothing. The RFBC has a substantial higher chance of getting a result close to it's average (less likely to be substantially worse or better).

The TC has a higher potential but the RFBC is more reliable. This is not apparent simply from looking at the average result which suggests that there is little difference.

DeviationOfWar wrote:
While the averages are quick and dirty, I think knowing the actual statistics would be better when you are taking a chance. Lets say there are 2 objectives, one with 4 marines on it, and one with 3 marines on it. You have an infantry squad with first rank second rank that can rapid fire either. Lets say you also have Celestine who can reach the 4 man squad with assault from an 8.5 in charge. If you overtake the one objective you can tie, but if you can kill the 4 with Celestine alone and the 3 with the infantry squad alone you can win. We assume Celestine makes her charge, because if not it wouldn't matter anyways.
Average wounds for 37 lasgun shots is 2.01, average wounds for Celestine is 2.78. Lets say the difference is between 1st 2nd and 5th in a tournament.
Do you
A) split your fire and go for the win? It is about 1 over with each, so it would take an above average round with both, but if your shooting fails, Celestine can still win it by herself.
B) Double down and play for the draw? Maybe more greater good than blood for the blood god.
Now if you are a grab your balls death or glory player you will go for it without a second though. But if you knew the odds would you? For option A, you have a 72% chance to lose, 18% chance to tie and a 9% chance to win. If you played it safe for second place, you would have a 76% chance of a draw, and a 24% chance to lose.

9% chance to win for an extra 48% chance to lose.

Now, I know this isn't practical to know every statistic, or to whip out a spreadsheet in the middle of a match, but having a rough idea of the rate at which they drop off is huge. Even if the table were reversed, you could do a little social engineering, "oh man, you could win if you clean them both up." And if you think this is rubbish, you are that person I can goad into making it so I have a 90% chance to not lose.

You see, you are so focused on calculating percentages, that you ommited one solution to your scenario... But first thing first: as you are presented with a meaningfull choice, knowing your averages is, of course, beneficial - I never opposed that. But knowing exact odds of wining/losing/drawing as a result of your choice in this particular scenario isn't - you pretty much can go with very rough and basic "guestimate". In this particular scenario, you KNOW, that spliting up is harder to pull off - you know that even if you don't know mathammer at all. Without mathhammer you simply don't know how much "overkill" double-tap is and how difficult going for both objectives is. With rough guestimate (estimating averages as "no higher than" is pretty much instant), you know that you have to perform above average to win, but have a margin for a draw. But if you DESIRE a win, you don't have any other options than go for two, so the real question here is "are you playing to be 1st or you'll be content with much more likely 2nd place". Psychology and attitude of player means a lot more than percentages, as you yourself noted.

Where your percentage approach comes somewhat meaningfull is with the inclusion of a third option: a "middle ground" play is to assault 3 man squad with Celestine and shoot 4 man squad with lasguns. You have lower chances of wining this way, but better chances of a draw than in your version of a "win play", as it is not indifferent which exact marines survive. But again, a question if you are willing to gamble comes first, how much of a gamble it will be comes second. And you still can "sort solutions by probability" without actually knowing exact probabilities. Then comes a matter on "how beneficial actual winning is" - does this tournament has prizes? Does 1st place prize is higher enough than 2nd place prize to actually compensate the odds? At this point you know your game inside out, even without knowing percentages, resolution lies with lucky/unlucky rolls. And in this case, one more important "feeling of making informed decision" comes to play - if you go for a "safe draw", then odds are in your favour, so if you lose it's "I've played optimal scenario, he was just lucky and I was unlucky". If you go for a win, odds are against you, so in case of failure you have only yourself to blame for gambler attitude.

My entire point is that while mathhammer is a useful tool, it is not "ultimate solution to in game decision making" - there are a lot of other factors to consider (I've pinpointed some of psychological nature above). And you presented us with a specific scenario, where those may matter for people focused on percentages, but just imagine, that involved in same case are not seven marines, but one objective is occupied by a squad just a bit larger than what Celestine can maximally kill with full damage output. In such case your only option for a (highly unlikely) win is to throw theoretically possible 37 kills at this squad and Celestine for the other one. Percentages are now so obvious, that there is hardly any choice involved really. And from my gaming experience, 40K is more often than not quite obvious in what decisions are better.

 heckler wrote:

 Dakka Wolf wrote:
True dat.
I've had *that* luck in my last few games, opened fire on a Dread with Long Fangs packing four Lascannons, got a grand total of four wounds on the damn thing.
One miss in spite of re-rolling one to-hit, one 6+ save, a three and one for damage, command point re-rolled the one to another one.
Thank goodness it wasn't a ven dread - they would have bucked the odds again and made at least one FnP save as well.

That brings up another good point in this discussion:

When people calculate the damage, they just crunch the numbers and come up with x saves missed and so many wounds going through. One armor save saves all of the random wounds coming from a weapon. It doesn't take too much to show two sixes on saves from a vehicle and skew your numbers hard. In the case of multi wounds against vehicles, there's much more chance of scatter; FNP-like saves against each individual wound cause the distribution to be less dependent on the all or nothing type of saves from vehicles.

I look at averages and swing the math-hammer but I also consider the best and worst possible outcomes, mostly the average and worst possibilities *call me a pessimist* because that's usually the numbers I'll be dealing with at the end of the rolls, based on their expression as they roll you can usually tell what side of the average your opponent usually lands on.
I tend to overkill because my luck tends to be average or below.

I saw a player painting his dice once. He was painting the pips black. They were already black. I asked him what he was doing and he said trying to redistribute the weight of the dice by adding more weight in the form of paint in the pip indentations. It's very hard to notice if done well apparently. People will do crazy things to not fall on the below average side of the seesaw.

If you ever played MtG the dice roll *must* be 2d6 because apparently some people can consistently get above ten on a rolldown d20 or a single d6.