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dark Elf Odds and statistics 
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DarkElfOddsofVictory.pdf


this may be worth a serious read for you all....!!

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Wed Nov 05, 2008 6:40 pm
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Averages mean nothing.

Warhammer is not just based on statistics. You can roll higher/lower than these idealised cases and they don't take prior turns (i.e. shooting/magic phases) or player strategy into account.

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Wed Nov 05, 2008 6:51 pm
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so me studying statistics in detail then planning my army around them and winning 2 gt's means nothing? LOL

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Wed Nov 05, 2008 7:00 pm
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no, you dont expect them to happen, but you SHOULD base a competetive game strategy on what should happen. so it is worth a look.

ps, ant uve got far far too much time on ur hands mate :lol:

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Wed Nov 05, 2008 7:02 pm
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Yes knowing the statistics help but it's not everything. There will be games that you'll go against the odds and these games are the most important ones.

Also, who knows the trick that the opponent could take out of their sleeves, statistics don't take this in consideration, yes it's interesting, but not really useful.

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Wed Nov 05, 2008 8:49 pm
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silentdeath wrote:
so me studying statistics in detail then planning my army around them and winning 2 gt's means nothing? LOL


Well, your study obviously didn't teach you anything about making the statistics relevant or meaningful. What are you trying to illustrate with them? That 100pts of core DE shooting are worse than 175pts of rare daemonic shooting? That there are plenty of dumb targets for DE to shoot at? Why didn't the rxb-men shoot at the keeper?

That 240+ pts of black guard can beat 175pts of flesh hounds? Why was there no herald in the hounds? Or skulltaker?

200+ pts of witches and an assassin can beat a 175pt flesh hound unit... big whoopie.

Good for you that you play tournaments and well done that you win them but your presentation skills need a bit of aid. In this case, you've gone for information overload... too many stats telling too many tales and many of them simply not being relevant to the majority of gamers.


Wed Nov 05, 2008 9:13 pm
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Statistically I got 1st place in heat 2 (yeah, if my opponents in 2nd and 6th game knew what statistics are and rolled average I'd win those games <.<). Realistically I was 12th.

So as far as statistics do matter in deciding if the charge has a chance of success or which spell to cast for most effect, you still have to take into account that:

It may all just go to hell with series of bad rolls.

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Wed Nov 05, 2008 9:24 pm
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I don't get why are you bashing him. There's nothing wrong with statistics, even if some of them are pointless.


Wed Nov 05, 2008 9:28 pm
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riker666 wrote:
I don't get why are you bashing him. There's nothing wrong with statistics, even if some of them are pointless.


You take better units, you stand a better chance of winning...up to a point.

You don't win warhammer based on statistics, you win it based on skill and luck. Sometimes you're lucky, sometimes your opponent is. I've seen my bloodcrushers (for example) beat the odds two games in a row to save 5 S5 hits and 3 toughness tests from plague censer bearers after they had charged me.

Saving that many wounds on 6+ armour and 5+ wards is not that likely, doing it twice is just freaky. Statistics are just the average case with this type of analysis.

The ability of Black Guard to do their stuff doesn't mean too much in the front of Tzeentchian flamers (who can easily get away) or even Dark Elf shades.

You encounter so many variables in a game of warhammer, let alone a tournament, that statistical analysis is futile. You know certain units and tactics will work and that some or all have the right rules to create a strong army. 2 WS5 S4 ASF attacks are always going to be mean - what really matters is the points you pay to do it.

Statistical analysis just gives you a 'What if?' picture. Unfortunately the game is rarely kind enough to play to your numbers.

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Wed Nov 05, 2008 10:51 pm
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Quote:
You take better units, you stand a better chance of winning...up to a point.

You don't win warhammer based on statistics, you win it based on skill and luck.


And you make your tactical decisions based on the statistics of winning a combat/shooting a unit. You may have the best tactics in the world, but you need the right units to pull off the tactical decisions. Then after these tactical decisions have been made luck will alter the events of the combat/shooting/psychology tests, so in essence, all of these things affect a warhammer game, but you cannot win a game without luck and skill. (unless your daemons lol)


Wed Nov 05, 2008 11:06 pm
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Rork wrote:
riker666 wrote:
I don't get why are you bashing him. There's nothing wrong with statistics, even if some of them are pointless.


You take better units, you stand a better chance of winning...up to a point.

You don't win warhammer based on statistics, you win it based on skill and luck. Sometimes you're lucky, sometimes your opponent is. I've seen my bloodcrushers (for example) beat the odds two games in a row to save 5 S5 hits and 3 toughness tests from plague censer bearers after they had charged me.


Yeah, it's just like how we don't use statistics and probability models to determine where and how to engage forces and where to bomb and how best to utilize artillery in real life... Oh wait, we do, because it works.

A lack of understanding what probability is makes probability useless or misleading. If you understand that probability tells you the chance of a given outcome, or set of outcomes, then they are incredibly useful, because they can tell you with a high degree of accuracy where your resources are more effectively deployed. It's a huge difference between having a vague sense that Executioners are good can openers and witch elves are infantry killers. But, if you have a real statistical model, you can know with certainty what the odds are of each set of possibilities when engaging units. Averages are not the end of statistics for christ sake. When a person says "I should get 2 kills", they aren't doing statistics in any meaningful way. They are generating a poorly derived average, without understanding the likelyhood that the average result even occurs, which is a pretty key part of statistics. Most statistics occur on a curve, and take into account the actual likelyhood of any given result occuring. People around here, with the exception of Lakissov, almost never ever do that. Thus, most people's statistics here are reallly crappy. Don't confuse other people's use of poor math with statistics as a field.

For example, you can, if you take the time, determine the likelyhood of getting any given set of kills in a combat. For example, you may be fighting a group of knights, do the math, and then determine that you have a 50% chance of getting 0 kills, a 25% chance of getting one kill, a 10% chance of getting two kills, a 7.5% chance of getting 3 kills, and a 7.5% chance of getting 4 or more kill. That encompasses all possible outcomes. It tells you the odds of any discrete set of outcomes. If you want or need between two and four kills to get enough CR to win the combat, you look at your chart, and you can see that you have a 25% chance of achieving this outcome. Thus, if you feel you can only afford to comit this unit to a winning battle, you can look at such information, weigh it against your plans, and determine if the 75% chance of not meeting your objectives is outweighed by the benefit. No single outcome is guaranteed, but you can determine if a given set of outcomes is more likely or less likely than any other set. And that knowledge is extremely useful, because it helps you plan much more accurately. More accurate information is always better for a general so long as they know how to properly utilize it. The problem here is just that most people either don't know how to get accurate statistical information, or don't know how to utilize it. That is their fault, not statistics' fault. It's like blaming multiplication for crappy gas mileage when you didn't carry a zero.

Now, is statistics all there is to Warhammer? No, but frankly, I don't think almost anyone would promote such a viewpoint. There is no use in knowing the odds of an outcome if you can't secure the positioning to get favorable engagements. If you don't know how to move your troops, or have a grasp of strategy, numbers aren't going to help overcome that. But, if you have two otherwise equal generals, and one has a good grasp of how to do statistics and employs that knowledge, and the other doesn't, the general who uses statistics has a definite advantage.

The funny thing is, you probably use the poor brother of statistics, past experience, to make your decisions about these kinds of things. The difference is, statistics is based on universal mathematical truth, and experience is always anecdotal and general in scope. Good statistics will always trump "gut feeling" because it is simply more accurate.

Are

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Thu Nov 06, 2008 6:39 am
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Archdukechocula wrote:
For example, you can, if you take the time, determine the likelyhood of getting any given set of kills in a combat. For example, you may be fighting a group of knights, do the math, and then determine that you have a 50% chance of getting 0 kills, a 25% chance of getting one kill, a 10% chance of getting two kills, a 7.5% chance of getting 3 kills, and a 7.5% chance of getting 4 or more kill. That encompasses all possible outcomes. It tells you the odds of any discrete set of outcomes. If you want or need between two and four kills to get enough CR to win the combat, you look at your chart, and you can see that you have a 25% chance of achieving this outcome.

The best summary I have so far seen of how to apply statistics to WH.
I'd also clarify it a bit, and say that it's not just 'sets of kills' that should be calculated but the difference in Active CR that you generate and Active CR that the opponent generates (so if your knights have 10 attacks and the opponent has 5 attacks, then you calculate the probability of each outcome from -5 to +10, and then use the results in the way you described, e.g. calculating the cumulative probability of getting Active CR of +2 or more)


Thu Nov 06, 2008 4:22 pm
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silentdeath wrote:
DarkElfOddsofVictory.pdf


this may be worth a serious read for you all....!!



I do much the same for 40K with my nids, which did contribute to my 19 to 1 win loss ratio. I've not reduced everything to tables though, I mostly do thm in my head as required.

I haven't done the same in War Hammer yet because I simply don't know the stats of the opposing armies well enough.

Knowing that a fight will come down to CR and that your unit's moral may be the critical factor is important to winning melees. Time to use that flank charge or bring the Boss/BSB within range of the unit. Likewise calculating the effect of Word of Pain or Doom and Darkness on a combat is critical to winningthe major combats.

There are a lot of dice rolled during a game so the staticstical average will have a bearing on the outcome. It won't allow you to predict the outcome of any given combat, but will help with the control, location and comitment of resources during the game.

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Thu Nov 06, 2008 8:13 pm
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Quote:
determine the likelyhood of getting any given set of kills in a combat
Archdukechocula explained perfectly what help could bring the good quality statistics he describes.

Now it seems to me overwhelmingly difficult to develop an Excel spreadsheet to give that information for generic combats, especially complex combats (involving several units, or units with heroes, or mounted units, not forgetting chariots or monsters and riders with magic items) taking into account the many aspects of GW psychology.

If anyone has it, it oculd be an outstanding help for theorical studies in order to complement the experimental way we all have to evaluate different units. I tried to develop it myself but I am wasting too much time.

Quote:
you probably use the poor brother of statistics, past experience
On the other hand, Druchii.net is an excellent way to multiply the experiences. I feel much more experienced after browsing D.net for a couple of month than from the few battles I fought so far.

It is also a mine of interesting ideas. Pure statistics can tell you whether an idea is sound or not, but someone has to bring up the idea first.

If I can get good statistical analysis for the D.R.A.I.C.H., I'll be very pleased to include them.
Thank you silentdeath for your sheets. I did not include them because it lacks some analysis, as sulla somehow expressed it.
The kind of analysis I am looking for is what benefit is brought by adding a champion, or an hero with such or such equipment, to such or such troop? Of course it is better, but the cost raises, so it may become less efficient (kills per points).
It has to be analysed also taking into account the role of the unit. For a babysitting unit, I is important to resist shooting; for a hammer unit, it is important to kill many ordinary models; for a monster-hunter, it is important to kill a single tough monster on a single charge; for a tar pit, it is important not to loose much...

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Thu Nov 06, 2008 10:26 pm
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Rork wrote:
Averages mean nothing.

Warhammer is not just based on statistics. You can roll higher/lower than these idealised cases and they don't take prior turns (i.e. shooting/magic phases) or player strategy into account.


Sorry Rork, but that's a completely ridiculous assertion. Statistics are *extremely* useful. In fact, one of the most important ways statistics ARE useful is when you have multiple possible outcomes, and need to formulate reasonable set of expectations. Every time you decide not to charge a Bloodthrister with your hero on a dark pegasus, it's because you know he's going to get his clock cleaned. And you know that because you're doing elementary calculations in your head every time you move a unit, and size it up against possible targets.

Statistics tell us what to expect. Luck may, of course, deviate that result one way or the other, but if you play 100 games, and take note of the roles you make during every single one, those averages will begin to mean something to you. Statistical Analysis gives us the tools we need to stack the luck in our favor.


"The general who wins a battle makes many calculations in his temple ere the battle is fought. The general who loses a battle makes but few calculations beforehand. Thus do many calculations lead to victory, and few calculations to defeat: how much more no calculation at all! It is by attention to this point that I can foresee who is likely to win or lose." - Sun Tzu, the Art of War

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Fri Nov 07, 2008 1:09 am
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I follow that your sheets, SilentDeath, could probably use a bit of polishing; however, the general idea of statistical analysis is very useful. Of course, you have to combine them, to a degree, with empirical data. Prime example that I can give is the broadth of the ranks needed to achieve the highest possible combat resolution combined with the factor of manoeverability of a unit - i.e. how many models can I take into the front rank to get the best possible CR before the whole unit gets too unwieldy? Does it pay to have six models in the front rank or is the average number of kills too low for it to be useful? Is firing double shots with the Rxbow always better? Or are there times when the decreased to-hit value pays off? This is where statistics are really useful and SilentDeath gave a first example of that.

By the way, Dyvim Tvar's excellent articles on Magic where heavily based on statistics and I didn't hear anybody complain about that. Don't knock it till you try it, I crunch numbers myself before a battle, and even during it. I'm sure most of you do it, as well, even you, Rork. Maybe you don't even realize it since you got all the formulas memorized due to long experience (and that's where I want to be some day, myself). But don't you calculate something like "Well, if I sent my assassin against this unit of Blood Knights, he will have such and such a chance to kill this and this many of them based on his WS, their WS, Manbane, RoKhaine..."?

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Fri Nov 07, 2008 1:58 am
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Statistics are great and undeniably helpful, but they are certainly not everything. It would be great if you could crunch numbers and predict the outcome of any given combat accurately, but it doesn't work that way. I have lost many engagements that statistically speaking I should have won, relying on numbers to win combats may work part of the time but not all of the time. And besides luck aside, there are far to many unseen variables that can effect the outcome of CC, shooting and magic to ever make statistical calculations rock solid. For example HE sword masters charge a block of corsairs, by rights the sword masters will most likely annihilate the corsairs and then the assassin hops out and turns the tables. You can't tell me statistics could prepare the HE player for the ultimate outcome and if you can your thinking about warhammer way to much.

IMO games are won by knowing how to advance your own troop's, while avoiding magic and ranged attacks and at the same time drawing your opponents forces into handicapped positions so your own troops can capitalize. It's great knowing that unit A can destroy unit B with relative ease, but situations are seldom so simple.


Fri Nov 07, 2008 2:30 am
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dread_knight666 wrote:
Statistics are great and undeniably helpful, but they are certainly not everything. It would be great if you could crunch numbers and predict the outcome of any given combat accurately, but it doesn't work that way. I have lost many engagements that statistically speaking I should have won, relying on numbers to win combats may work part of the time but not all of the time.


This is a great example of someone misunderstanding statistics. There are no combats that you should win. There are combats that you are likely or unlikely to win, and usually that margin is actually much slimmer than people imagine (again, because they either do crappy math, or no math at all). Likelihood should never be confused with certainty. The whole point is to weight the cost of a failure and its likelihood of happening against the gains of a success and the likelihood of it happening.

This is, in many ways, like poker and pot odds (calculating pot odds, as another example, is something that literally all professional poker players do). You may have pocket queens on the draw in Texas Hold'em, but if you don't know how to calculate pot odds (i.e. the likelihood that your hand plays out to be the winning hand versus the cost of staying in the game due to betting), then you can very easily lost a lot of money on many occasions with that kind of hand. Yeah, pocket queens are a "good hand" and they "should win", but they aren't guaranteed, and the has cost of theoretical loss has to be weighed against the likelihood of the loss occurring, and the potential winnings of victory versus the likelihood of victory happening. So it is with Warhammer. You have to compare the cost of your engagement against the likelihood of certain outcomes and the potential benefit. And, of course, likelihood is not certainty, but is rather just the most common outcome. Just as in poker, you have to be prepared to lose a few even when the odds are in your favor. But in the long game, the person who does the math will do better by a substantial margin than the person who doesn't.

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Fri Nov 07, 2008 3:50 am
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@ slientdeath,

Yeah to summarize the charts need a standard deviation, or range of possiblities within 60 and 95%.

Thanks for the contribution, however.

A good lecture would be on how to properly apply statistics to table-top games, I think.

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Fri Nov 07, 2008 4:34 am
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langmann wrote:
@ slientdeath,

Yeah to summarize the charts need a standard deviation, or range of possiblities within 60 and 95%.

Thanks for the contribution, however.

A good lecture would be on how to properly apply statistics to table-top games, I think.


Actually, you don't need to use standard deviation with dice, because the range of possibilities are discrete in nature, which means all possibilities can be calculated with effectively 100% accuracy. Standard deviation is meant for use on things like surveys, to adjust for how representative a population is. A dice, however, has effectively an equal chance of rolling any given number, which allows you to determine all possible outcomes to a precise degree.

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Fri Nov 07, 2008 6:11 am
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Good work Ant.


Fri Nov 07, 2008 11:24 am
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Statistics may not be the absolute be-all-and-end-all but they definitely help. If you know the numbers then you know what to attack with what, what the risk/reward ratio looks like for different courses of action, when to back away and when to dive in, etc.

Sometimes experience means you don't need them, fair enough - but sometimes you can do the numbers and realise that super-kill-unit bearing down on you is actually very unlikely to vercome your static CR or vice versa, and it changes the whole look of a game.

Numbers don't make good decisions but they certainly help.

Cheers for taking the time to do these up.


Sat Nov 08, 2008 2:08 pm
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I find stats hugely important in a game. You need to calculate what your chances are of casting a spell with x dice (thanks to the excellent magic article on this site that's easy) then you have to figure out if the target is worthwhile (whether or not you are likely to achieve your goal of say, causing a panic test). Same for shooting. For combat you have to see if you can generate enough CR to win or avoid enough damage. But like everyone has been saying, odds don't tell the whole story (I gave up on heavy cav for a while because amost every time I charged I managed to get no hits with actual knights, a quite unlikely outcome), but you still have to realize that if you play without taking into consideration the chances of a favourable outcome you just aren't going to be a very solid and efficient player.

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Sat Nov 08, 2008 4:17 pm
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Sigh! You're looking at the stats the wrong way.
Quick stats lesson, so bear with me here.
let p be the probability of an event happening.
let q be the probability of said event not happening which is equivalent to 1-p.
let N be the number of events.
Right. Now for dice we have normal distribution so the mean is defined by Np and variance is Npq and standard deviation is the square root of variance.

using the following abbreviation: H: Chance to hit; M: Chance to miss; W: Chance to wound; F: Ward/Armour Save failed
so for the BSB attacking Flamers
p(Causing a wound)=(H+M*H)*W*F=40/81
thus q=1-40/81=41/81
so mean=3*40/81=1.48
and the variance=3*40/81*41/81=0.75
Hence you should expect to do between .73 and 2.23 wounds
so at best you expect to kill 1 flamer (flamers have 2 wounds BTW), at worst you do no wounds.
the steed is even worse off with p=4/27 and q=23/27. The mean=0.15 and the variance=0.13. so the steed doesn't do much.
So assume 1 wound done.
The Flamers strike back with p=H*W*F=5/36 and q=31/36.
So the mean is 6*5/36=0.83 and the variance is 6*31/36*5/36=0.72. Thus you would expect the flamers to get between 0.12 and 1.55 wounds.
So you would win by one on very few occassions.

The important lesson here is that the mean/average is not what you should be looking at. The range is.

Also the best way to look at Warhammer stats is to roll dice and record the results, and the best way to do this is to write programs to roll lots of dice. You would then get a percentage for win/draw/lose.

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Sun Nov 09, 2008 2:58 pm
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Azimyth, you don't use mean and variance when doing discrete statistics. Standard deviation is meant for populations and large groups in order to attempt to achieve a representative sample of distributions. The point of standard deviation is to help determine an approximate range of probable results for strictly yes or no answers, such as "will you vote for Barack Obama?". We don't need that with dice, because we know there are exactly six possible outcomes on a dice, and that the likelihood of any given outcome is precisely 1 in 6. Standard deviation, which it looks as if you are using, is meant to determine a set of ranges with a strictly yes or no answer. It is not really meant to be applied to a range of results, although admittedly you adapted it about as well as possible to the application, and the method is probably serviceable enough, and I give you credit for managing that. Still, standard deviation is a sloppy way of doing the math for dice, since you can never actually do .7 wounds for example, and we can calculate the exact probabilities of achieving the real discrete outcomes of a contest (i.e. 1 wound, 2 wounds, 3 wounds, etc, rather than .7 wounds). Basically, we can determine exactly all possible outcomes in a set with basic math. .7 wounds is not a possible outcome, and in that way standard deviation is misleading.

Also, when you say you can expect to get between .73 and 2.23 wounds, you forget to mention the probability of that expectation (95% chance of getting within that range based on the formula you used I think, if I remember my old statistics class correctly), and the probabilities of narrower sets (Like the 90% range, the 65% range, etc).

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Sun Nov 09, 2008 4:22 pm
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