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The graph is a good generalization for each unit.

You can write a page on every unit, it's role and how to use them, and the best tactics for it, etc.

But the graph could be a good snapshot of the unit.

Well, to address your point, yes, it is simplistic - it's meant to be a quick snapshot, not a detailed view of an army. It's also not static.

The graphs change every turn of every game. This, too, is what separates the good player from the merely average.

Consider drop-pod marines. Until the pods have landed, their mobility is quite high - you have to play against them (in the early parts of the game) like you would play against an extremely mobile force, by castling.

But, once those pods have landed, they're actually rather static. The good player knows to try and take advantage of the lack of mobility once the pods are down.

I don't think that there is any tactical advantage to be gained from these considerations, the advantage gained is strategic, and that does, in fact, take into account things like flank rushes.

What I really like about it is that if you go through the mental exercise of answering the questions - which army is better at assault, who is more mobile, etc... each turn (and especially on turn 1) you can make strategic decisions about how you want to address the game, prior to actually doing anything.

As an example... say I'm running a mech tau list. Normally, I like to deploy in such a way that I can pull a refused flank on the first turn, and because I'm more mobile than 90% of the other armies out there, this tends to work. But, when I run into a more mobile army, I have to change my overall approach to the game. That doesn't mean that my FoF maneuvers won't work - it does mean that I need to be the one to take care not to leave any units sitting around for my opponent to isolate and destroy.

P.S. - As to jet packs counting as mobility- maybe a little, but I think that jump-shoot-jump falls more into the durability camp.

Blackmoor wrote:The graph is a good generalization for each unit.

You can write a page on every unit, it's role and how to use them, and the best tactics for it, etc.

But the graph could be a good snapshot of the unit.

Or you can complete a list of the specific roles units might perform in a game, it could probably be completed in a page. Then write a few pages on how useful each role is, how the different roles relate, and the the factors that might lead to different things being needed from game to game.

For each unit you can then have three or so lines on which roles the unit can achieve, and which it can't.

Redbeard wrote:What I really like about it is that if you go through the mental exercise of answering the questions - which army is better at assault, who is more mobile, etc... each turn (and especially on turn 1) you can make strategic decisions about how you want to address the game, prior to actually doing anything.

As an example... say I'm running a mech tau list. Normally, I like to deploy in such a way that I can pull a refused flank on the first turn, and because I'm more mobile than 90% of the other armies out there, this tends to work. But, when I run into a more mobile army, I have to change my overall approach to the game. That doesn't mean that my FoF maneuvers won't work - it does mean that I need to be the one to take care not to leave any units sitting around for my opponent to isolate and destroy.

But if you're sufficiently skilled in the game to make a correct assessment of the relative mobility, assault, durability and shooting scores of the two armies, then you're sufficiently skilled to make a more detailed, more meaningful assessment of the best way to approach the game.

I'm sorry, but I think the model has a lot of vagueness in determining the relative scores, without producing any great insight at the end of the process. Ultimately, all you're doing is identifying that you're better at shooting, so you should try and stay at range, and that your mobility makes that easier to achieve. That's a very crude level of analysis at the end of the day.

The average player is probably capable of making the assessment, but doesn't necessarily think about it that way. Putting it into the context of: where's my strength, and more importantly where is his weakness, probably has some value even if it's just a thought exercise.

I agree that there's too many other variables to really draw solid conclusions about every matchup with just 4 axis. While modifying the graph to be able to handle that level of complexity would probably make it more confusing than the rulebook.

this reminds me a little bit about what me and my friends were talking about earlier... but has gotten off the path.

i think for a while the goal of this thread was to find a way to tip the scales of winning in our favor. and that means to eliminate the "chance" or "Luck" part of the game and make it skill dependent. like many of you here, i enjoy stats, numbers, ratios, that's why i'm doing accounting and finance. but to get back on the path...

i think some of this analysis is superflous, i agree that the graphs are cool and colorful and a breath of fresh air in this math hammer game we play...

but it seems too much like the four elements that was already proposed, useless. a water army (think gk's)sounds perfect, you get to exploit your opponents weakness because you have an absolute advantage against everyone. however it is usually the one with the comparative advantage that specializes and wins. water sounds good, "my gk's will dominate your banshee's in the shooting phase." but what happens when water doesn't fight on it's own terms, what if they HAD to fight the howling banshee's in cc. (not uncommon i might add, who gives you the chance to shoot at banshee's?)

the problem is that these graphs are too cut and dry, many things have value that don't show up on it. no one mentioned scoring units. what about a farseer, he isn't resilent, assaulty, shooty or fast, but he is arguably one of the best HQ's in the game. another problem is that the things that do show up are often times too hard to quantify bc of other factors. while it's true we could find a way to quantify a farseer's abilities or any other unit it, the graph wouldn't tell us anything we didn't already know. i know what units are durable, fast, shooty and assault oriented, infact the graph hinders my analysis, i don't know by exactly how much. i see you have a 5 for mobility and i have a 7, how many inches is that on the table? you have a shooting rating of 7, is that against tanks, hordes, or meq's? it better not be overall bc dark reapers rape marines but can't touch av 12, and unless i'm given specific numbers on str. ap. range and bs i cant tell you what that shooting rating means.

what i'm getting too is... the graph has the same problems as the 4 elements theory, it doesn't fit many situations and even when it does it's not all that useful. it's too generalized to give any unknown information, it seems like this thread is for the intelligent 40k players and we all know the general strength's and weakness of every unit. we don't the exact numbers by which we have that advantage.

an analysis would be easier, faster and more accurate if i just look at the unit and see what it has, rather then try to make a graph for every turn, every situation. the idea of overlapping the graphs as every one know's is about comparative advantages. and we can just do that the easy and effective way by simple math hammer. i think that we already have all the ratio's needed to tip the scales of battle in our favor. that is GEQ'S, MEQ'S, ROI'S and other ratios that are already in use.

for those of you into econ we could do a game theory analysis and i don't mean the simple prisoner's dilemma kind, i mean the intense kind with a bajillion variables. but the truth is we don't have to do that, we already know what to do when an opponent does something. the majority of math hammer is only useful in army composition, by the time we are done with the lists, we should know exactly what to do and when to do it. if we don't by the time we are playing we've already lost the advantage we are trying to seek. math hammer is simply controlling as many of the variables we can to give us a favorable outcome. if we don't do that with unit selection we've lost it. the rest is letting the dice fall where they will.

what many people don't use is standard deviation and that might be one of the most revealing stats. so maybe instead of making graphs we should add another dimension to warhammer stats. SD. since we are using dice we will have a normal distribution curve meaning we can use the z-scores in the back of our texts.

Moz wrote:The average player is probably capable of making the assessment, but doesn't necessarily think about it that way. Putting it into the context of: where's my strength, and more importantly where is his weakness, probably has some value even if it's just a thought exercise.

I agree that there's too many other variables to really draw solid conclusions about every matchup with just 4 axis. While modifying the graph to be able to handle that level of complexity would probably make it more confusing than the rulebook.

That’s the thing, though. Assessing unit strengths and weaknesses in army selection, deployment and turn by turn is really important, and a big part of being a good player.

It’s restricting a unit’s strengths and weakness to four elements and then attempting to quantify those attributes into a 0-10 scale that I doubt the usefulness of.

Think of it this way… if I have a gaunt unit in the second turn of the game, I can look at the unit and say shooting ‘poor’, assault ‘poor’, mobility ‘good’ and durability ‘good’, then decide… Even on the most basic level that's just not useful. Or I can look at that gaunt unit and describe it in real terms; ‘cheap unit, fairly mobile and fearless, unlikely to inflict much damage… so I can try and tarpit something or use them to sit on an objective’.

Moz...just another great idea those lovely graphs of yours.

ptlangley wrote:Has anyone come up with a fitness function to quantify these four traits?

Shootiness = BS * Avg Weapon Strength * Avg weapon Range
Assault = WS * I * Strength
Mobility = Move+Fleet+Assault
Durability = Armor * Invul Sv * T

It's not a bad idea, but you miss a lot of things, for example special attacks and in what way mobility, shootiness and assaultiness interact.
That should be added at some point - you might come up thinking a predator is very mobile and shooty at the same time. (If only judged by your math.)

gdurant wrote:
Statistics aren't theory.

Statistics are theory. Experiments only project reality...or try to do so, they are very influenceable by intend. At least this is a fact until you redo it for exactly infinite times.
I'm studying psychology, I gotta know this.

gdurant wrote:
A statistic is a data collection experiment, not a theory. For example, say I collect a sample of people and ask them there favorite ice cream flavor.
50% chocolate
40% vanilla
10% strawberry
Now I could make a hypothesis that I were to go and check local icecream sales that I'de see about 50% of people bought chocolate. But your right you don't experiment to get statistics.

How many people do you ask? Does it reach a mark where you can already consider it representive?
This is very important...maybe not with your example...but just switch it with something else...maybe a desease? And then you hit the point where you'd better be damn sure that you did enough research.

Any simple multiplication of traits is missing the very fundamental point of talking about any game philosophically. Simply put, the numbers on the paper don't matter, what is much more important is that we are looking at a paper with numbers and using that to play a game. We all know the numbers, but honestly, when I look around a 40k tournament, I don't think anyone knows the game. I don't think I do either. I don't think anyone in the world has a very good knowledge of 40K. We have been given a map by admittedly bungling cartographers, but we are just taking the map at face value rather than exploring for ourselves. I seek to explore ourselves (and not in vaguely masturbatory sense) and to try to see what the depth that the game does offer, if it offers depth at all, because I am sick of splashing in the puddles, and I know others here feel the same way.

And in response to deeply existential talk about foundational game theory, a trite list.

If your list loses to these things, you have failed... period.

Dark Reapers in 4+ cover save... if you lose to this, you deserved it, because you knew someone was going to bring a squad of reapers at some point, and plop them in 4+ cover. It's like walking around a crowded mall with a flaming stick while coated in gas, and then being surprised when someone bumps. You shouldn't have been wondering covered in gas in the first place (and the flaming stick is questionable outside some large social gatherings).

Looters in cover save... See above.
Legitimate unit in cover save.... see above, again.

Death Company.... see above. This is repetitive but hopefully become illustrative of the problem.

Plague Marines..... The horse is now dead. It has ceased to be. Needless to say, any successful army has a strategy that allows it to deal with singular problem units, otherwise it should not make the pretense of competitive and should be willing to be casual. Being casual is a good thing, it means you don't have to compete. Competitors will let you be casual if you stop making them be it too.

Do not lose to psychic powers. The emperor watches over you, the warp has no power over your army. Or at least Gork and Mork will kick the crap outta whoever tries to magic your army to death.

Psychic powers, despite their strengthening, are not the be all end all to 40K, and as such, there is little excusing tournament quality armies that lose to them. To trivialize it further, if you are playing Eldar, you should not lose to psychic powers, because if you are just bring Eldrad, and make the psychic phase yours, or at least even. If you lose to teleporting Epistolarian with FoD, it should be because of your opponents brilliant tactics, not because your army f-ing packs to Fear-bombs. Even if you are a snivelling commie tau, you didn't get to the year 40 jillion with face eating demons around you to get beat by that S--t did you?

Oh noes! Rear Charging. My girlfriend got angry about this, but she's a big girl and can deal with my simple assaults upon her backside. Your army should be more secure than my girlfriends jeans. You have burly men and women in armour with guns that core modern LAVs, we are disappointed in modern life when a bunch of sneaky gits comes in and wrecks our stuff, and these gits ain't that sneaky. You know they are coming. The opponent should work so that these win. You shouldn't lose to them because they are them, but because your opponent understands the importance of units like Snikkrits boyz and wolf scouts.

You have no excuse if you lose to a person who understands why cheating the rules (in game, following the books) is better than big stats. Necron's shouldn't be winning high level games because they get to get back up. We know, the cheaty undead bastards are getting back up... we all know it was happening, so where is your cowboy to their indian. If they are gonna cheat in the rules, why aren't you trying to find out how. I mean, these units are noticably good for a reason, Eldrad, Wolf Scouts, Necron's, Fear-bomb, old daemonbomb. They looked at the rules of the game, and went "we are ludicrously manly space vikings, we don't need no stinking badges" and have done there own thing. Doing that thing makes them good in the game, because they don't have to follow the rules of life that poor joe Guardsman does.

Speaking of Joe. If Joe and 300 of his friends show up, you better be ready to host them. They throw a hell of a kegger, but you aren't gonna drop the ball on joe are you? Falcons come with taps (SL/SC) for a reason. If you can't find something that kills hideous numbers of dumb dudes in a universe that considers continent nuking to be large scale tactical warfare, you are failing at 40k.

If you have founds this trite, funny and uninformative, you are ready to go were I want to go, because there is so much to explore.

Well, you got the trite and uninformative parts right. And the bit about your girlfriend's backside was pretty funny.

DarkHellion wrote:And in response to deeply existential talk about foundational game theory, a trite list.

Game Theory is a standing term for somithing slightly different than WH40k.
Of course both have something in common, but I don't think wargaming is part of the game theory.

If you'd like to look it up:
http://en.wikipedia.org/wiki/Game_theory8/
&
http://en.wikipedia.org/wiki/Combinatorial_game_theory (40k doesn't fit here either. Too random. Too inaccurate. Too unpredictable. Not a 'fair' game at all.)

Very interessting indeed. Maybe a little bit off topic, but the spirit behind game theory might be usefull in discussing WH40k tactics.

Can you agree? Or am I wrong and missed some facts?

sebster wrote:
But if you're sufficiently skilled in the game to make a correct assessment of the relative mobility, assault, durability and shooting scores of the two armies, then you're sufficiently skilled to make a more detailed, more meaningful assessment of the best way to approach the game.

I'm not sure that you're right here. Some people are more than capable of making distinctions between units, and still fail to make the correct choices. It sounds like an easy thing to do, but if it's so easy, why do so many players get it wrong?

My guess is that they fall into the mental trap of assuming that their own army will always hold the same role, and don't make the adjustments when they face armies that force them out of that role. I've seen this happen time and again, usually with armies that are somewhat focused towards one of the four extremes. The guy with the static Tau gunline who always assumes he'll outshoot his opponent, confronted with a better gunline. Or the marine player with two large assault marine units and chaplains who figures he has an assault army, and so pushes into assaults he shouldn't.

The goal here is to remove the element of luck from the game, not though raw application of statistics, but through intangible qualities. Two assault armies that simply charge each other are reducing the game to a series of dice rolls. As a game with points, if you're good somewhere, you've got weaknesses in other areas. And, even if your army is designed to win via frontal assaults, if you finally hit someone else who handles frontal assaults better than you, you need to either hope for a lot of luck, or change your battle plan.

squall8187 wrote:what many people don't use is standard deviation and that might be one of the most revealing stats. so maybe instead of making graphs we should add another dimension to warhammer stats. SD. since we are using dice we will have a normal distribution curve meaning we can use the z-scores in the back of our texts.

The vast majority of times when you roll dice in 40k you are not dealing with normal distrubution but binomial distribution.

Far more out of interest than any expectation of gaining an advantage (not that I play any where near as much as I would like anyway) I go for looking at unit matchups and the expected return in VPs gained or lost, probability of getting wiped in X number of turns etc. No way could I do it in my head (millions of calculations over 6 turns), but computers can crunch those numbers no problem, so If I want to know precisely what the VP difference between spiengaunts vs las/plas is compared to devgaunts I can, accounting for different start ranges, morale, rallying being routed of the board etc. Run the same units against a variety of expected matchups and apply what ever weighting you want. I suppose its a variation on the ROI mentioned earlier, except I'm using expected VP gain/loss thats been fairly accurately calculated.

It doesn't cover the things like benefit of sacrificial units, or terain hopping ability very well, and single unit vs single unit is somewhat out of context of how a game would go, but it beats relying on a simple mean average of I kill 1.3 marines a turn, cos we know that we will never ever kill 1.3 marines in a turn. Further more, calculating the full probability tree allows you to get a better idea of just how close some matchups actually are, e.g seeing that adding a single extra model can make a significant difference in some mathups, or how much difference arises if you only kill 2 models instead of 3 on turn 1 etc.

Redbeard wrote:

sebster wrote:
But if you're sufficiently skilled in the game to make a correct assessment of the relative mobility, assault, durability and shooting scores of the two armies, then you're sufficiently skilled to make a more detailed, more meaningful assessment of the best way to approach the game.

I'm not sure that you're right here. Some people are more than capable of making distinctions between units, and still fail to make the correct choices. It sounds like an easy thing to do, but if it's so easy, why do so many players get it wrong?

My guess is that they fall into the mental trap of assuming that their own army will always hold the same role, and don't make the adjustments when they face armies that force them out of that role. I've seen this happen time and again, usually with armies that are somewhat focused towards one of the four extremes. The guy with the static Tau gunline who always assumes he'll outshoot his opponent, confronted with a better gunline. Or the marine player with two large assault marine units and chaplains who figures he has an assault army, and so pushes into assaults he shouldn't.

The goal here is to remove the element of luck from the game, not though raw application of statistics, but through intangible qualities. Two assault armies that simply charge each other are reducing the game to a series of dice rolls. As a game with points, if you're good somewhere, you've got weaknesses in other areas. And, even if your army is designed to win via frontal assaults, if you finally hit someone else who handles frontal assaults better than you, you need to either hope for a lot of luck, or change your battle plan.

We all make mistakes, that's true, and decision models can help players make the best decisions in game. I'm not arguing against any of that... I came into this thread looking for some interesting insights into such models.

I'm saying that this particular model, breaking units down into four factors and quantifying their ability in each... is not a good model. I've made a fair few points against the model now, and they haven't been rebutted, people just keep returning to the idea that a decision making model is good.

Is this the right thread for discussion of important game effects like lines of sight, ranges, and unit formations? Or should I start a "Tactical Language" thread?

This is a very interesting thread.

I would like to make three points in my first contribution.

1. It's not worth arguing about dice and stats.
We are trying to develop a descriptive language for units (platforms) in a game that will be played by hundreds of players in thousands of match-ups throwing millions of dice. It can reasonably be assumed that over 1 million rolls of a D6, you will get 166,667 results of 6. That is close enough to calculate a percentage killing potential of a unit.

2. It should be relatively simple (though tedious) to make an ROI matrix featuring the shooty killiness of every unit or troop type in the game vs every other. For example, SM vs SM/Fire Warrior/Guardian/Boy/IG Squaddie/Etc..., Fire Warrior vs SM/Fire Warrior/Guardian/Boy/IG Squaddie/Etc... and so on.

This is only one tiny element of the entire problem but it would be a start and is probably the easiest thing to calculate as there is no arguing about the percentage chance for a Fire Warrior to kill an SM, for example.

3. Quantifying Mobility
PTLangley made a good post about this above. Shootiness, Assaultiness and Durability seem to be easy to quantify but mobility is more difficult partly because it relates to the other qualities and to the meta-game. For instance, an assault unit that can move 6+6 is obviously worth less than an assault unit that can move 12+6, but neither are so useful against an opponent that can move 24 unless you are on a small table.

ptlangley wrote:Has anyone come up with a fitness function to quantify these four traits?

Shootiness = BS * Avg Weapon Strength * Avg weapon Range
Assault = WS * I * Strength
Mobility = Move+Fleet+Assault
Durability = Armor * Invul Sv * T

I am not recommending those as I put almost no thought into them other than to pull the relevant stats. Coming up with Avg strength/range is tricky also. Anyway it is something I have thought about before but never pursued. I would try to find the max in each category and then standardize everything to the max. If you wanted higher resolution you could try to throw in corrections for all the special rules. In the end it would be quite the monstrosity. Anyone looking to do a Math PhD?

I have. I call it the DSM, or Dead Space Marine. I use it as a comparative unit of measurement between the various army lists I create to gauge the raw killing power and resiliency of units and my armies. So every unit has a measure of how many DSMs it can kill, and how many DSMs it can take before being rendered ineffective.

It is far from perfect, and is subject to all the variables of 40k, and doesn’t take into account mobility very well. In this respect, the Graph system is better. But I find my system to be a helpful tool. At the very least, it allows me to more quickly quantify and ‘chunk’ unit abilities and usefulness when playing the game and designing armies.

Oh, and I wanted to throw in a quick comment about auto-cannons and lascannons vs. Falcons. You actually want to include both, because an autocannon may have better ROI on glancing and immobilizing a Falcon, but a lascannon has a better ROI on destroying an already immobilized falcon (because of its higher likelihood to penetrate). That’s the key to dropping falcons. Use multi-shot units to immobilize (because 3 out of the 4 bad damage results with vectored engines will only immobilize, which is why VE is mandatory), then use high strength weapons to penetrate and destroy.