Game Design 40k – Curving the relationship between Power and Effectiveness

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TinBane, our favorite Aussie number-gazer, is back to wax philosophical on game design and balance in 40K.

If you don’t want to read about maths, theory, game design, and why 40k isn’t balanced, then hit the back button. Game design isn’t worth talking about without mathematics, and balance isn’t worth talking about without an appreciation for game design.

In a number of places in this article, I’ll talk about some numbers. If you want to know more about conversion rates, and what the hell that means, check out my article on death-stars. It’s also important to couple figures with points values, as 40k is above all else a game that is currently based around efficiency measures in the competitive scene.

Good game design starts with an aim. The aim of 40k has changed a lot over time, and unfortunately with the departure of the “old guard”, the “new guard”, the “guys the new guard taught” and Alessio Calvatore there isn’t much written on how the design of 40k in terms of gaming principles works any more. Maybe Jervis does it, and makes the decisions based on rolling a d6 whenever he gets to a hard question.

I’ll give you my aim for 40k though. I’d love 40k to be a game where codexes can compete on a relatively level playing field, and there are multiple builds within each codex. Are we at that point now? Hell no. You can name many of the current codexes after their best lists. We have codex: Riptides, codex: Heldrakes, codex: White Scars Bikers, codex: Flying Daemons, codex: Flying Insects. I spent a while trying to think of something for DA, but the best I could come up with was codex: Librarian with divination and a power-field as allies with something good.

chaosmarinesvswaveserpent

Magic The Gathering is a popular card game, and while I have no interest in playing it, it does have a great take on pegging power levels to their ‘cost’. In MTG, you generate mana, and under normal circumstances your generation increases by 1 per turn. So turn 1 you have 1 mana, turn 2 you have 2 etc. Now a mana 2 creature therefore needs to always be more useful than a mana 1 creature. Because you can summon mana 1 creatures a turn earlier, and also you can summon 2 mana 1 creatures in the same turn your opponent can summon 1 mana 1.

In MTG, the stats for the creatures often ramp up proportionally to the mana cost. I think they used to work so a “base” creature without special rules might be 1/1 at mana 1, 2/2 at mana 2. Now because of the random nature of MTG, taking mana 2 creatures are riskier than taking mana 1 creatures. You might not be able to summon them, so performance needs to scale exponentially. The bigger the creature, the most risk in putting it in your list, so the more payoff if you survive long enough to play it.

The way MTG does this, for starters, is that the “health” of a creature resets each turn. Imagine how much better land raiders would be if they reset to 6 HPs every turn! Suddenly the difference between 3, 4, 5 and 6 hull points is no longer proportional! Well that’s how MTG works. A creature might have lower attack than expected, if it has more health. It might have lower health than expected if it has more attack. It might have lower of one or  both of these stats, it if has some cool game changing rule.

Now there’s some big differences in 40k. The first is that there is no mana curve. 40k is run though resource allocation, you start out knowing how many points you are going to have. In 40k it makes no sense for more expensive things to be exponentially “better” in one way or another, unless there’s an inherent risk in that large purchase. Spending 200pts isn’t inherently riskier than spending 100pts on a unit, it’s twice as much resource, but unlike mana where there is a time element, there’s no risk of the game ending before you can get the 200pts to bring in that unit.

So the fairest option, is to make the effectiveness of the unit linear with it’s cost. A space marine at 14pts, needs to be 40% better than a scout at 10pts. The lower the cost of a unit, the more risk of the effectiveness being manipulated to make that unit a capable flood unit. A good example is a blob of 50 guardsmen, with fearless and a 4+ invuln save. In that context, the benefit to the 50 guard of being fearless and having a 4+ invuln, is probably MUCH greater than the cost it took to purchase it in the first place. For this reason, cheap units are normally “less efficient” on the curve than the accepted baseline model. In 40k, this means that Cultists, Guardsmen, Gants etc are normally (on their own) over costed. The optimum is around the Eldar/Marine baseline. So Guardians, Dark Eldar Warriors, and Space Marines are probably around “optimal”.

Let’s imagine a 40k power curve. For the purposes of this thought experiment, we’ll assume that the Instant Death rule doesn’t exist. So we’ll add a new unit to the codex, it’s a Space Marine capable of firing two Bolters, with two wounds, and twice as many attacks. Otherwise identical to a stock Space Marine. Now how do you cost that unit? At 28pts, it’s efficiency is linear with a regular space marine. But as this takes damage, it will still be as effective until it’s removed. If you scale it up to being the equivalent of a Space Marine squad, the problem becomes more pronounced. So the game designer needs to design efficiency drop-off into the game. A unit that is twice as good for an intended role needs to cost more than double.

I was (rightly) taken to task in my article on death stars for saying that Terminators are balanced. Obviously I don’t know what I’m talking about, right? Terminators are a trash unit. Well, I disagree. Chaos Terminators are 31pts base, 2.4 times the cost of a chaos marine. Let’s characterize a comparison between these two units, and include guesstimates of efficiency:

General case – Poor AP hits – Chaos Terminators are twice as tough as Chaos Marines, which means that against Bolter fire Chaos Terminators last twice as long. Conversion of Bolter shots is 11.1% vs 5.5% for terminators.

Best case – Moderate AP (AP 3) hits – Chaos Terminators are six times tougher than Chaos Marines in this case. Conversion of missile shots is 55.8 vs 9.3 for terminators.

Worst case – Nasty AP hits – Chaos terminators have 1/3 chance of surviving. Conversion of plasma shots is 55.8% vs 37.1% for terminators.

Ultimately, Terminators are not as tough as their points suggest. But that’s not the only factor, they also have improved firepower, and more importantly massively better assault capability. A Chaos Marine converts at 8.4% (without extra CCW) which gives them a cost per wound inflicted against a MEQ opponent of 167pts (83pts for a Chaos Marine with CCW). A chaos terminator converts at 25% for a cost of 62pts per wound with a power sword, 13.8% for a mace at 113pts per wound and at 33.6% at 46pts per wound with an axe.

So overall, the Terminator is quite balanced against a Marine. The problem is that the prevalence of “Worst case” weapons in 40k undermines this value. Terminators have had one serious balance change in 40k since 3rd ed started, and that was the addition of a (free) 5+ “Crux Terminatus” save. Yep, it wasn’t always there, and it was brought in because plasma/Starcannons were so prevalent.

This is the example of another curve being broken. 6+ armour is useless because of the prevalence of AP6- weapons. In fact, I don’t bother to check whether weapons are AP 6 or AP – when I’m playing. If I don’t know their weapon off the top of my head I don’t bother taking my Cultist saves. 5+ is the ‘baseline’ save, it has some value, but it rarely saves anyone because AP 5 is the most prevalent value. 4+ saves are worth some points, but probably less than 1pt per model if IG players are anything to go by. While there are less AP 4 weapons, there are enough of them to make life miserable for anyone with Carapace Armour. 3+ saves are real value, they are valuable because AP 3- weapons are expensive to acquire. But the broken thing in this progression is the ease with which things are given AP2. Imagine 40k where Plasma Guns were AP 3 (in 2nd ed, they were only -1 armour save mod, so I have no idea where the 2+ comes from). Suddenly you are relying on weapons like Demolishers and Melta Guns to take down Terminators (in early 3rd ed). Had that design decision been made then, there would have been less of a follow-up arms race for all the races to have mass AP 2 guns with reasonable range.

You can see from the above example, the usefulness of having a curve. The cost to field a weapon, should be proportional to it’s use. The prevalence of AP2, and AP2 like effects, have undermined Terminators, and they haven’t been updated to deal with this (rending and similar effects did not exist in early 3rd ed, certainly not for ranged attacks, they were added for Genestealers in the Nid codex, and eventually ported to the Assault Cannon). Because of this skew in curve, Terminators have always been marginal, and their utility entirely based on whether they can be transported into battle. While 6th ed gave Terminators a buff, removing “ignore armour” in close combat, the overall nerfs to close combat have rendered terminators largely unusable.

If there’s a problem with Terminators, it’s that there are better choices. Space Marine Bikers for instance, can become troops, and they are nearly as good as terminators at bouncing bolter shells (7.4% conversion). Against Missile Launchers, they aren’t as good as Terminators, but are much better than space marines (36.8% conversion), and against plasma they are on par with Terminators. Bikes are half the cost of Terminators, and AP 3 weapons are relatively rare. You can see here, that bikes (which got huge buffs this edition) are just not priced appropriately against Space Marines OR Terminators.

Hopefully by this point you are starting to look at 40k again. Look at the popular units, and ask yourself if they are priced effectively. Is fortune priced rightly, and easy enough to get, given it can be combined with 2+/2+ armour and 4++/4++ within it’s own codex? Is a Farseer worth less than a Dark Apostle or a Chaplain? For the fun of it, we are going to do a comparison of the Wave Serpent, considered by many to be one of the most cost-effective sources of firepower in the game.

To kick off the comparisons, I’ve built a unit benchmarking system. This is but the first of many experiments, and I’m interested in feedback of match ups you’d be interested in. Let’s compare a squad of chaos marines with two plasmaguns to a wave serpent. The serpent is armed with twin-linked scatter lasers and the shuriken cannon upgrade, as well as a holofield. The chaos marines are a squad of 10 with two plasma guns.

This comparison will only be looking at damage output vs range. The comparison (at this stage) looks at three target types, standard MEQ in 6+ cover, warlocks in the open, and plague marines in the open. I’ve produced a handy graph to highlight the difference. The system ran through thousands of pseudo firings, and the average output was taken from both units. This output was normalized against 1000pts value, before we created a “best case” or “worst case” set of scores by applying one standard deviation to either benefit or hinder the wave serpent. Now if two units were equal, we’d expect the best and worst case scenarios to straddle the middle. The space in between the best and worst case scenarios accounts for about 65% of instances.

We can see from this graph, that this is far from correct. On damage output alone, the wave serpent FAR surpasses a full squad of chaos marines even within rapid fire range, and the estimate of how often the chaos marines would output more damage against tactical marines is less than 18%. It’s a pretty disappointing outcome, considering the difference in capabilities such as manoeuvrability etc these units have.

This is just the beginning! Hit up the comments, or join us on the forums to discuss the analysis you’d most find interesting.

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44 Responses to “Game Design 40k – Curving the relationship between Power and Effectiveness”

  1. TTT April 13, 2014 1:17 am #

    I have a VERY hard time understand your graph, what are on the axis (damage% and range?) and what are the different staples? Which represent the marine squad and which are the wave serpent shooting? Also I don’t really understand your normalization, did you normalize the targets or the attackers?

    Sorry if this was really obvious from your text, but I’m not a native English speaker and I found the whole paragraph… confusing.

    How does your benchmarking system work? You mentioned pseudofirings so I assume some kind of monte-carlo simulation, but wouldn’t it make alot more sense (and probably require less computation power) to look at the sum of the binomial distributions for the different weapons and normalize the damage against different targets to the cost of the unit firing.

    • TTT April 14, 2014 5:15 am #

      Sorry if I’m being a dick about this but your graph is horribly confusing. I’ve shown it (and the accompanying text) to a few friends who like me are interested both in Warhammer 40k and math, none of of them are native english speakers however. I am truly interested in this and would love to understand it so could you tell us if we’re on the right track here:

      Y-axis: difference in dead targets between 1k points of Wave Serpents with Scatter Lasers and 1k points of marines with 1 plasmagun per 10, positive values being WS favoured.

      X-axis: Range (in inches) at which they fired their weapons.

      Both these conclusions leave a few questionmarks, like how the marines are supposed to kill someone 38″ away or how the WS fired it weapons (i.e. did it stand still and fired all it’s weapons at full BS or did it move and snapfire 1 out of the 3 it has?). Clarification would be VERY appriciated.

      I think the article was very good and interesting however the graph is (in my opinion) a mess, this is how one of these SHOULD look like (I can’t guarantee the actual results as I threw this together quickly just for this):

      http://i57.servimg.com/u/f57/18/62/03/90/frtlng10.jpg

      this with text explaining the hell is shown and maybe expected values and variance etc. is so much easier to… well understand.

      I also noticed you tried to talk trash about the binomial distribution earlier and I don’t agree with you that one should look at the poisson distriubtion instead. In the limit p(sucess) -> 0 trials -> inf (which admittedly is very common in wh40k, lets call it the WH40k limit) the two distributions more or less coincide, the poisson should be easier to use here, however it wont work if you mix weapons as it requires a uniform successrate, then you need to look at the sum of binomial distriubtions with different success rates (there’s a paper by Butler and Stephens called ‘The Distribution of a sum of binomial random varibles’ from Stanford who gives a formula for doing this). If we leave the WH40k-limit (say two ignores cover S10 shot hitting a Raider) the binomial distributions should be undisputed king.

      • TinBane April 14, 2014 8:45 am #

        No problem!

        Firstly, it’s 2 plasma guns per 10 marines (CSM/SW).
        The “negative” result under worst case at 38inches, is because I didn’t limit the range on the WS to 0 (whoopsie!). So below zero kills is within one standard deviation of the mean at that point.

        No weapons were snap shot, however can’t the wave serpent move and fire all it’s weapons? Or am I confusing it with something else?

        Hmm, maybe I didn’t explain myself. I didn’t intend to trash talk binomial distributions, they are great (but do get complicated, when you have to propagate them out). If I was trashing anything, it’s the assumption that these kind of events would fit a normal distribution (which is an assumption implicit in using standard deviations, even if they are useful (if not SUPER accurate otherwise).

        And yes, the graph can use some clearing up! Mine is a little more complicated, but labelling does help a great deal! I shall endeavour to be clearer in the future, but this is very much an initial article introducing the idea of a power curve, and testing out the modelling I’ve been working on. I’m planning to try and demonstrate some of the properties of the “GW curve” soon!

        • TTT April 14, 2014 9:31 am #

          Ah, thanks this clears up a few questionmarks we had.

          But still shouldn’t you only look at <8(grenade + rapid fire), 8-12 (no grenade, still rapid fire), 12-24 (all bolters in range, no rapid fire), 24-36 (only scatter laser and serpent shield in range), 36-60 (only serpent shield can shoot and is thus not twinlinked). It seems very… arbitrarily chosen range intervals.

          The Wave Serpent has three weapons, TL-shuriken catapult (12", can be upgraded to shuriken Cannon 24"), TL-scatter laser (36", twinlinks the serpent shield/cannon if it hits) and serpent shield (60", 1d6+1 shots), a fast vehicle that moves 6" can shoot all 3 at full BS, however if it moves 6-12" it can only shoot 2 and has to snapfire the last one.

          Indeed, probability theory gets complicated very quickly and I agree completely that these events would not fit a normal (gaussian) distribution (we need large N and high P for that…). HOWEVER a standard deviation is not specifically tied to the normal distribution at all (which I think is what you're saying), any distribution has a standard deviation (it's the squareroot of the variance) and it gives the 'spread' of data points. The binomial distribution's standard deviation is given by sqrt(np(1-p)) (np being the mean).

          Labelling is so important, one should without much explenation at a glance be able to tell what the graph is about! I would like to see your distributions aswell if possible (for example 1k pts of WS and marines) , as you mentioned yourself the mean is only half the story although I suppose you did implicitly print the std aswell. It'd get very… cluttered forcing 8 (WS, marines for each of the 4 targets) distributions into the same graph though so I'd suggest doing 4 different ones, one for each target.

          • TinBane April 14, 2014 2:59 pm
            #

            Oh and it’s all batched, hence the range increments.
            It’s just a x + n * y where n is the cycle number type scenario.
            I didn’t think it really worth investing the time into making the system work out the “meaningful” ranges. However I can manually specify the ranges for each run.

    • TinBane April 14, 2014 8:51 am #

      And yes, monte-carlo. My previous modelling efforts entirely used binomial distributions and the simulation thereof. But I found I got some weird results “setting aside” differing classes of results. For instance, if you try and implement rending using binomial distributions, you have to work out the probability distribution for a “normal” result, and a probability distribution for rending results separately and recombine them. Whenever I did this, I found the numbers were off.

      The monte-carlo simulation method, while less accurate, should be “good enough” for these applications assuming enough runs, and at least it’s MUCH easier to troubleshoot and work out if you are getting the right results. Having done this, I might inter-calibrate it with the binomial version and try and get rending working properly.

      If you have any ideas on sorting that out, I’m interested in hearing 🙂

      • TTT April 14, 2014 9:43 am #

        The best way to implement rending into binomial distributions is to look at the total chance of causing a wound including rending and will be different for different targets;

        Example: Shuriken Catapults (rending…ish S4 AP5) against tactical marines with a 6+ coversave,
        the chance of causing a wound is: P(cause wound without rending) + P(cause wound WITH rendnig)

        P(cause wound without rending) = P(hit)P(wound WITHOUT rolling a six, i.e. roll 4 or 5)P(armour save) = (2/3)(1/3)(1/3)

        P(cause wound WITH rendning) = P(hit)P(wound with a six)P(cover/inv save) = (2/3)(1/6)(5/6)

        P(kill a marine) = (2/3)(1/3)(1/3)+(2/3)(1/6)(5/6) <- the one you want in your binomial distribution

        If this was say a wraithlord (T8) P(wound WITHOUT rolling a six) would be 0 and all your wounds would come from that rending 6.

        Generally monte-carlo simulations are just fine if you have an unchaotic system (which we do) and you run "enough" simulations (maybe 1000 for this case is enough, I have no idea really). If you prefer and feel more comfortable with monte-carlo stick with those. What program do you use for this? I generally run my mathhammer in matlab (as I get it for free).

        • TinBane April 14, 2014 2:57 pm #

          I’m working on objects for modelling 40k in python. It’s free for everyone, and once I have it working nicely I’m thinking of making it publicly available. Thanks for your valuable feedback, I’ll definitely work on the graphing and information display.

          Hmm, problem is, the number of rends you get, reduces the number of attacks going into the pool of normal attacks. I initially set it up the way you mentioned, and the result was that I was getting probabilities for getting more kills than it was possible to get! Because there was the odds of getting lots of rends + the odds of getting lots of non-rending kills.

          See what I mean :/

          Each range increment was run at 100,000 iterations.

          • TTT April 15, 2014 4:05 am
            #

            I don’t get the same problem, remeber the total number of attacks is resctricted, here’s a program I threw together: (written in matlab everything after any % are my comments)

            % Guardians firing Shuriken Catapults at Tactical Marines without cover or invul saves

            clf %clears old saved variables and vectors, just matlab syntax, nothing important

            ProbX = []; %In this vector I save the probabilities so that the first position corresponds to 1 dead marine and 2nd 2 etc.

            p = (2/3)*(1/3)*(1/3)+(2/3)*(1/6)*(5/6); %The chance of causing a wound, see my earlier post for derivation

            n = 20; %Total number of shuriken shots fired, this would correspond to a 10man squad without a heavyweapons platform

            for i = linspace(0,n, n+1) %i loops over all possible number of dead marines, i.e. 0 to 20

            P = nchoosek(n,i)*(p^i)*((1-p)^(n-i)); %the probability for i dead marines is calculated according to http://en.wikipedia.org/wiki/Binomial_distribution#Probability_mass_function

            ProbX = [ProbX P]; %the probability is saved

            end %loop ends

            sum(ProbX) %prints the sum of the vector elements in my matlab terminal, nothing is changed in the ProbX vector here

            %This is just plotting stuff, all actual math/implementation is finished here
            hold on
            plot(linspace(0,n, n+1), ProbX(1:n+1), ‘r*’)
            title(‘Probability of X dead marines out of cover. Unnormalized, using binomial distribution.’)
            xlabel(‘Number of dead Marines’)
            ylabel(‘”DeadMarine”-distribution’)
            legend(’20 shuriken catapult shots at BS4′)

            and here’s the plot it gives me:

            http://i57.servimg.com/u/f57/18/62/03/90/frtlng11.jpg

            the sum of all of the elements in ProbX is 1 (as it should be). It’s been awhile since I did anything in Python so afraid I can’t “translate” my program for you to test.

            I think you just tried to sum two distributions together for the nonrends and rends, it should however be the same distribution.

          • TTT April 15, 2014 4:08 am
            #

            WOOPS one of my comments is wrong:

            ProbX = []; %In this vector I save the probabilities so that the first position corresponds to 1 dead marine and 2nd 2 etc.

            should say:

            ProbX = []; %In this vector I save the probabilities so that the first position corresponds to 0 dead marines and 2nd 1 etc.

            so that when I plot this vector against [0 1 2 3…] (i.e. the linspace(0,n,n+1) line) I get the corresponding probabilites right.

          • TinBane April 15, 2014 1:10 pm
            #

            Oh, I see.
            You’ve added the probabilities together, to produce one p value for the entire process.

            What do you do if you have a reroll? Do you just set the “to hit” to the inverse of two misses?

            I’m really interested in if the binomial pattern works with this. You see, to me intuitively, it seems like you’d get a different outcome than actually rolling the dice, because you are crunching the probabilities down into one figure. But then maybe it’s just a bit of monty hall syndrome on my part, and I’m as retarded as the people who insist you roll the dice one at a time when you have a reroll on a one dice event.

          • TinBane April 15, 2014 1:11 pm
            #

            But that’s awesome, thanks for sharing.
            If it works, then I’ll be super-stoked, and binomial distribution will be back in (will save me heaps of calculation time anyway).

  2. DCannon4Life April 13, 2014 4:29 am #

    Could you comment on why you chose a 6+ cover save? 5+ cover is so easy to get. Would using 5+ cover have diminished the difference or accentuated it? I’m imagining it would accentuate it, making the targets more survivable vs. the plasma, and strengthening your argument that Wave Serpents are broken (vis a vis their point cost).

    • TinBane April 13, 2014 5:18 am #

      The point shouldn’t be to accentuate the argument 🙂 The warlocks are a better example of a unit that the wave serpent will do better against than the plasma gun squad.

      6+ cover save is what I consider “minimum” when making these comparisons, simply because you can get it by hitting the deck anywhere. To get a 5+ save, you need some level of benefit from the environment.

      The 6+ cover save has no benefit to the warlocks, and the plague marines are unable to hit the deck.

  3. David Key April 13, 2014 7:37 am #

    This is fabulous work, I really enjoy what you are doing. I have always tried to get DW Terms to work with single turn mass saturation. Essentially giving the opponent one turn of shooting before the being charged. My reasoning was that on a point by point basis, Terminators have an underpriced damage output given a max of one round for each player to fully shoot and charge.

    The problem I often have is that despite low efficiency on bolter-like fire(low ap/str), the opponent can kite and often get 2-3 rounds of shooting. Terminators are slow. How would you factor this in?

    I have one other quick question too. Is there any math to support that the loss of each member of a 5 man Term squad reduces its efficiency by MORE than 20%? Just wondering, this intuitively seems true, neutered units suck, but IDRK. Ha

    Keep up the good work!

    • TinBane April 13, 2014 9:04 am #

      You don’t necessarily need math to tell you that deep striking is a hard sell!
      Against forces like Eldar, you are possibly NEVER going to get them into a fight, unless the eldar want you to. In terms of how you factor it, it’s pretty simple. You are going to suffer two to three times the damage that a fast unit would take, if it was equally tough. And given bikes are pretty much tougher against most powerful weapons than terminators, and can close the distances very fast, you can see why they are popular.

      Poor terminators just have nearly everything stacked against them, and it’s probably because they were overly dominant in 2nd ed!

      Yes, there is evidence to support that the loss of each member of a 5 man squad reduces is efficiency by more than 20%. For those studying stats at the moment, look up binomial distributions. As you lose terminators your ability to do SIGNIFICANT damage drops massively. You need to be outputting 3+ kills a turn, minimum against 10 man squads to make it worth being in assault, otherwise you will be tar-pitted by cheaper units, or even ground down especially if they have hidden nasties you can’t challenge out. So say you set a target of 5 kills on the charge, that gets harder to achieve with each terminator that dies.

      Terminators especially, aren’t as tough as their points are “worth”, they are actually an offensive option. So each terminator that dies is worse than the equivalent amount of tacticals dying for instance, if you are looking at “most efficient” use of points to absorb fire-power.

  4. Vidar April 13, 2014 7:41 am #

    I am not doing well in stats. But that’s probably cause my teacher doesn’t speak to me in math hammer. Thanks!

    • TinBane April 13, 2014 9:07 am #

      Look at the binomial distribution, and start thinking about how it helps answer questions in 40k. Such as “What are the odds of doing 4 unsaved wounds when X unit charges”.

      Likewise, when you are looking at normal curves, remember that when people work out the “average” number, they are only telling you one part of the story. You need to look at the width of the distribution around that centre point too. And additionally, sometimes the mean is weighted “out of position” and isn’t even the most likely outcome.

      Look up the poisson distribution as well, it’s more generally useful in games like 40k, where outcomes normally have an asymmetrical curve too 🙂

      Hopefully you find these things as interesting as I do.

  5. Shane April 13, 2014 10:50 am #

    Not trying to take away from the point of the article because I completely agree on the ballance issue.
    However if 40k we’re to become a game of x=y I feel a lot of the magic might be lost. That’s why I believe in a concept you didn’t mention, internal alliance of one codex to another. Because of the force org chart requirements individual units don’t have to be balanced against each other across codex’s.
    However in 6th ed with addition of allies, that system of internal ballance has been broken because you can just plug any gap with an ally.

    • TinBane April 13, 2014 3:00 pm #

      I agree with you. It’s not about making units equivalent, or equivalently powerful.

      That said, if unit A has a SUPER efficiency advantage, then it’s very hard to counter that. Back in the day, that unit would be 0-1 (which they got rid of). Some of the most broken lists from back in the day, were the ones that removed that 0-1 limitation (like 3.5 ed Iron Warriors with oblits, for example).

      As you point out, allies has also undermined those differentiators. If you are imperial especially, or at least can ally with imperials, you get a pick and mix of so many different options, that it’s just a bit crazy.

      For instance, having super-cheap inquisitor add ons from the formation, with not real useful minimum “spend” to get the benefit, means you “may as well” include it if you are lucky enough to be in that sphere of allies.

  6. Leth April 13, 2014 10:51 am #

    Yea, If the riptide had been AP3 we might see more of them. Same with Shuriken rending. It is just there is so much ap2/ap3 that being a marine doesnt mean shit anymore.

    However I think it has less to do with the prevalence of Ap2 and more to do with GWs outdated pricing for weapons.

    Power fists are still 25, power weapons 15, plasma pistol 15, etc. They just charge to much for guys including these in their basic kitouts. Especially when assault is so difficult in this edition.

    • TinBane April 13, 2014 3:03 pm #

      Absolutely! I was shocked to read the AM codex this weekend, and find the guardsmen pay the same price as space marine heroes for their melee weapons. For some of these things, it seems GW just wants to maintain the status quo, rather than truly balance things. Imperial Guard characters gain a LOT less bonus from these items than other heroes.

      Terminators are partly undermined by their configuration. Each terminator “wound” in the squad has as you point out a powerfist. And even with the discount they get, it means they are more expensive. Imperial terminators would be a lot better if they had the option (ala chaos) to be lower cost with power weapons. And chaos terminators would be better if they had ATSKNF or other morale control.

  7. Shane April 13, 2014 10:54 am #

    Sorry, auto correct failure. Where it says “internal alliance” above it should read “internal ballance”

  8. Joe TwoCrows April 13, 2014 11:14 am #

    I do find your work interesting. Also, I want to give you props for using distributions. Please carry on.

    However, I’m immediately curious about your approach reconciling 40K, the Game, vs 40K, the game system. You provide your aim as having mutually competitive codicils. Is there a single environment for this? I may struggle explaining my question further, but please bear with me.

    In my view, the Game includes the game system, the background, and the social experience. I suspect this view is similar to that of GW, although I disagree with their implementation. The social experience of a tournament is radically different than basement beerhammer, which in turn is different than FLGS pick-up games, Rules that work in one place may not work in another. And, in the background of a future consisting of war, I find it difficult to say (or hear), oh, this or that over-powered. This, despite usually being on the short side of power, as I play DE.

    So, is your aim specifically for tournament play?

    • TinBane April 13, 2014 3:26 pm #

      Thanks for the question, Joe!
      Personally, I find that in everything from online games to tabletop games, if you balance for high level play, then you balance for low level play.

      I play quite a lot of “beerhammer”. I’m far from a competitive fiend. However balance has to come from the top down. If imbalance exists at the top level, then people in your group, your pickup games, etc will mimic the lists and tricks of the top level players.

      Balancing the game for tournaments, doesn’t “take out” the fun. If you look at games like war machine, or dropzone commander they are incredibly balanced, but when you play it casually you don’t need to factor in any changes. You just build equivalent lists.

      When I play chaos vs my friend’s eldar, I reckon I need a 20% more points handicap if I don’t take helldrakes. Even some of the lest effective options in the Eldar list, plain better than the middling Chaos Space Marine options by a significant margin. Frankly, it’s as dull for the player with the higher powered list as it is for the person who struggles to stay in the game.

      • Joe TwoCrows April 13, 2014 5:33 pm #

        TinBane,

        thanks for the reply. I must confess I don’t quite follow it. Your main points seem to be the game system has to be balanced and that top (competitive) players have to realize they affect the play of the non-competitive players. Am I correct?

        If I am, then I’m completely missing the idea of my question in your reply, which I might restate to be ‘Are you trying to find a way to make the 40K game system statistically suitable for competitive play, despite the non-competitive elements?’ Except that reads like I’m critical of that goal, and I am actually neutral on it.

        I think you agree tournaments, beerhammer and FLGS pickup games are all fun from a social point of view, just with different social rules. What’s fun in a tournament (and I will say I think the *best* games are the most unpredictable ones) may or may not be fun in the basement. Taking a tournament list to a pick-up game may be great, or it may be reviled.

        Making “one rule set to rule them all” may not be possible, but making one set for a specific environment may be. That’s where my question comes from.

        • TinBane April 13, 2014 5:41 pm #

          Yeah, I think I understand your point.

          My point is that having a balanced ruleset, really doesn’t “hurt” anyone.
          Rules that benefit competitive play, and harm casual play, normally do so because of complexity, not balance. Likewise, having internal balance in the codexes (so they don’t have only one “good” pick in each category) means that whatever units you pick, you’ll have a hope of doing okay against any opponent.

          In short, I don’t think it’s mutually exclusive. Good game balance benefits all levels of play, in my opinion.

          • Joe TwoCrows April 13, 2014 7:40 pm
            #

            OK, I see now. Thanks. What was throwing me was the thought about balancing helps everyone.

            From the background standpoint, a fair (balanced) fight would be 1 combat squad (5 models) of Astartes standing against a 30 model mob of orks, without a nob. That’s not game balanced because it’s 75 vs 150 points. IOW, in this case, the background would say some game points are more equal than others.

            And, I think that’s the root of the problem. In my view, GW wants some points to be more equal, because the are passionate about the background. If they could figure out how to have Hollywood Marines, and still make a profit, I think they would. They also appreciate that in a world of war, nothing is fair, some things are overpowered, and the weak wither.

            I think your statistical work is stellar. It shows just how unfair the game of 40 K is and where the power lies. That work could well lead to a really excellent game system where adding new or unusual elements is straightforward yet doesn’t unbalance the larger system.

            But, there’s another thing: complex systems take on a life of their own. Their internal logic becomes difficult to reconcile, and their external interactions follow the rule of unintended consequences. 40K is just such a complex system, and that’s part of its attraction for me. I don’t play WFB, or Infinity, or Warmahordes because the world(s) they present is finite. 40K is a different beast. In a sense, the unintended consequences of the game designers choices is part of its magnetism. The designers cover their collective butt by the ‘Most Important Rule”, but really, I think they want the game to have unexpected twists and turns with each new army, ruleset, even model. Change Lillith so she can realistically damage t7 or t8 opponents, and the entire DE army changes.

            Would it still be 40K if it were deterministic?

            anyway, thanks for the conversation. Allow me to repeat myself; I’m fascinated with your work.

          • TinBane April 13, 2014 8:32 pm
            #

            Thanks, mate 🙂

            My take on what you are talking about, is the difference between fluff and crunch. Now the points per unit, need not be set. You could maybe set orks to be worth 2pts each, or space marines 30pts each, and change how the game works. But the balance (how much “goodness” you get per point) could still be part of it. Does that make sense? Back in 2nd ed, space marines literally cost 30pts per model, and that’s why lists were smaller at a set price point.

            Now the “movie marines” you are talking about (referencing an ‘army list’ from chapter approved in 3rd, IIRC) don’t exist any more. In 2nd ed, marines were WAY better than other troops. They had bonuses to resist blinding, bonuses against virus grenades, all kinds of stuff. When 3rd came along, the ability of a marine vs an ork (and vs everything else just about) dropped. Daemons cost a lot less points than they did just one codex ago, and this changes how good they are.

            With your example, you can add features and abilities to a hero no problem. You can make heroes better, more nasty, etc, but at the end of the day you have to raise the points.

            In infinity, one of the races kind of has a “space marine” unit. Basically these bad arses in power armour. But they cost like 1/4 of a tournament list each!

            There’s an argument for inbalance, in terms of prowess. But it’s important to redress that with GAME balance. Because at the end of the day, if it’s harder for me to win, like seriously harder, and my focus i on winning, then I’m going to have less fun. In Dropzone Commander, there is a race that nearly always wins “straight up” fights, the PHR. They are the space marines of DzC, but they don’t win more games because they are better at fighting. They are slow, it’s hard for them to contest objectives, every battle for them is a struggle while outnumbered.

            In 40k, the OLD codex for grey knights did this. Your base troops were 26pts each, and winning was HARD. But you could do it, and when you did it felt great. And the reason it was hard, was because your units were great, but every casualty took more from your force, because of scarcity of numbers.

            Heroic rules like ATSKNF belong in a ruleset where space marines are actually rare. To make that happen, you need to emphasise (in the rules) that every space marine is both important and valuable. These guys take decades to “produce”, and yet tactical marines are neither expensive nor considered very capable.

            If you start designing a game from scratch, with the idea that you use maths to work out how things should be priced, it’s not too hard to set costs. It’s hard when you’ve gone and already written 12 codices without apparent rhyme or reason to the costs.

            A good example of a bad rule, is the Champions of Chaos rule. Why does it exist? What does it give you? Well, it takes away your tactical choices, because you get an “advantage” from a random table. And the problem with that is:
            1. The random table is often no value
            2. There’s no incentive to equip most of your champions so they can win fights
            3. The rule compounds the leadership issues chaos already has

            At the moment, 40k is balanced by throwing up your hands in the air, and saying “it’s just too difficult”. You could fix it with three decisive changes:
            1.Restrictions around buff stacking (ie you can’t fortune a unit that has it’s armour improved) or limiting the effect some buffing powers can have.
            2. All allies are allies of convenience
            3. Slightly buff assault units, by changes to the core rules.

            If you made those changes, you fix 90% of the issues 40k has with balance.

            And none of that needs to detract from the game.

            I’m not a proponent of needing everything to be 100% balanced, mathematically. But balance at the moment is a joke, it’s like they don’t even bother to try.

  9. IndigoJack April 13, 2014 4:28 pm #

    You’re math hammer foo is stronger than mine, nice article! My math hammer generally only extends to standard deviations, but explaining those principles to people at my FLGS generally results in a lot of blank stares and statements like, “Well I still think the icarus lascannon is a better option.”

    • TinBane April 13, 2014 5:45 pm #

      Thanks IndigoJack 🙂

      Some people believe mathhammer is “always wrong”. My opinion is that most people do mathhammer poorly, and just talk about the averages in isolation, which gives it a bad name. You can lead a horse to water, but you can’t make it drink.

  10. Reecius
    Reecius April 13, 2014 5:49 pm #

    Another nice article, Sir!

    • TinBane April 13, 2014 6:08 pm #

      You are too kind!

  11. Gordon April 13, 2014 10:41 pm #

    It’s worth noting that some other games, namely Warmahordes, have uber-buffed units similar to what exist in 40k. The key difference is that it’s actually difficult to pull off those buffs. While your caster might have a powerful feat that stacks with a unit’s mini-feat that leads to absurd damage output or threat range when you also toss on a special ability from X character, if your opponent is smart they can take out that character, position their units to block your uber unit’s charge, and then you’re forced to waste your one turn of godliness. If you pull off your buffs, you might be incredibly difficult to deal with, but it’s not necessarily easy to pull the buffs off. It’s not like the Seer Council where all you have to do is pass a leadership test or two and go crazy.

    Also, mobility and deployment options are a big factor that is worth mentioning that doesn’t necessarily show up in the math.

    • TinBane April 14, 2014 12:09 am #

      Absolutely.
      Warmahordes takes the approach of closely limiting those choices (normally you can only take one). They need to be in position to be used, and often losing them is game over.

      So there is an element of risk, an element of rarity, and it consumes a resource you use to manage your troops. So it’s often manifested as an awesome combo, that limits the versatility of the rest of your forces.

      Mobility is huge, and very hard to work out. But with something as manoeuvrable as a seer council on bikes, they pretty much get their pick of the assaults 🙂

      • Alex Y April 14, 2014 10:32 am #

        With the 6th ed victory condition, 40k is no longer a “killing” game. What you said is true but only part of the “40k game balance”. Without including all other elements,it is just a nice read with good info. it didn’t even come close to answering why 40k is not balance.

        • TinBane April 14, 2014 3:01 pm #

          Killing is one side of the coin, the other being survivability. While I agree, they are FAR from the be all and end all, there are units you buy for their ability to soak up firepower, and units you buy for their ability to dish out the hurt. This allows those comparisons.

          The user of the tool needs to recognise the limitations of the tool, and us it for what it’s good for.

          • Alex Yuen April 14, 2014 3:54 pm
            #

            Well start writing the rest of them. I agree, if you apply the limitation, it is very good.

          • TinBane April 14, 2014 4:00 pm
            #

            Are there particular comparisons you are interested in, Alex?

          • Alex Yuen April 14, 2014 9:24 pm
            #

            I love to see movement but I have no clue how or where to start on that. looking forward to a good write up

  12. Cameron April 15, 2014 4:25 pm #

    Great article! I too had some problems with the unlabeled axes on the graph.

  13. TinBane April 15, 2014 7:16 pm #

    I’m sorry for the confusing graph. If you are interested in how I’ve improved the graphing, among other things, I’ve started a thread at:
    http://www.frontlinegaming.org/forums/viewtopic.php?f=9&t=946

  14. Edwin April 21, 2014 12:54 am #

    As a Dark Angels player who foolishly plays Deathwing primarily I’m certainly not saying that terminators are a good investment of points, however I feel I should point out that the switch to melee weapons having AP values instead of all power weapons ignoring all armor was a great boon to terminators as the only things that AP through terminator armor, save for the odd exception, are weapons that strike last.

    40k is definitely a shooting game right now, but it was at least something.

  15. SandWyrm May 2, 2014 6:17 pm #

    Nice article. But I do think you’ve missed something (or at least glossed over it) in your analysis.

    Given a choice between 2 Marines, and a super Marine that’s exactly as tough as 2 normal Marines, I’ll take the 2 Marines. Why? Reliability.

    2 shots is inherently better than one double-good shot. Because the single shot is more vulnerable to bad luck. Rolling more dice increases the odds of getting at least one hit.

    More bodies can also occupy more of the board. Boosting the effectiveness of proper movement.

    The best example I can think of is playing a Tiger Tank in Flames of War versus 3 or more Shermans. The Tiger is costed linearly to the Shermans, and it’s a monster. But at the same time, it can only be in once place at a time. As soon as the allied player learns to move properly, and drop smoke on the Tiger, they will win every game. Because while the Tiger can kill anything it hits, and is hard to kill, it still only has 1-2 shots per turn. While the 3 Shermans have 6 shots on the move with which to get the one lucky side hit that will knock out the cat.

    Bring an army of Tigers and their bane will be Stuarts, one of the weakest tanks in the game. Because these can zoom past the cats and put pressure on their home objectives. Which keeps the Tigers from being able to move where they need to. Put a line of infantry in front of them, and they’ll stop cold. Because while they’re tough, they can only kill one model a combat round. Giving the infantry plenty of time to roll that lucky armor penetration. Or have the Tiger hang up on difficult terrain and be captured.

    So elite units need to scale non-linearly in terms of cost for their power. Because they’ll be fighting lesser units that can use their numbers as an inherent movement/reliability advantage.

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