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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.

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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