Threat Radius II

The previous post attempted to define a value-multiplier based on a unit's range based on the threat radius said range accorded the unit. This is all fine and dandy, except that some ranges are more important than others. In particular, the fact that standard infantry move 6".

The 6" move enforces a degree of granularity on what might otherwise be a continuum of range, because it governs exactly how many shots a shooter with a certain range will be able to plug into an approaching Ork before said Ork is forcibly putting his choppa into yonder hurty bits. Thus, while we can quantify the proportional increase of threat radius with range on the one hand, we can compare it to the practical application, the number of firing opportunities, on the other.

To consider firing opportunities, let's start with a hypothetical Guardsman in the exact center of a common 6' x 4' board, and give him a heavy weapon of range x. Not being able to move and fire will obviously simplify the situation here. For a target, we provide an Ork in one of the corners of the board, 43" away from the fellow with the gun. Roll for first turn, then rock on.

Going first will clearly only matter in the case of a 48" range. Assume that the Ork can judge distance well enough to stay out of range if he wants to, this means that he will move to 1/2 an inch beyond any maximum range of <48" the turn before he starts his run.

Then they're off and racing! The Ork enters max range at a full 6" move, then runs a further d6", until he is in assault range. Against a foot-bound foe who is determined to be in assault as quickly as possible, the guardsmen will get:

Range		Firing Opp
48		4
42		3.722222222
36		3.092592593
30		2.416666667
24		2
18		1
12		1
6		0

Note that the firing opportunities depicted as decimals represent the average of probabilities incurred by running. For example, when using a 36" range weapon, the Ork has a 90.75% chance of making it to choppa range before the guardsman gets a 4th shot, but a 9.25% chance of rolling poorly enough for run rolls that he is able to take it.

What does this tell us? Well, the utility of low ranged move-or-fire weapons is clearly extremely limited. Equally, the number of firing opportunities in this hypothetical example increases linearly, rather than by the square - since we are dealing with an Ork moving in a straight line towards a static target this is hardly surprising. Since an actual game gives a whole extra dimension to move in, I am inclined to somehow take an average of the number of firing opportunities presented in this linear system and the ratio of increased area provided by extending range in two dimensions. If I normalise firing opportunities to the number of opportunities at 24" range, just like I normalised the area ratio to 24" range, then this should be doable.

Range	Area Ratio	Firing Opp	Norm FO	Average
48	4	4	2	3
42	3.0625	3.72222	1.86111	2.46180
36	2.25	3.09259	1.54629	1.89814
30	1.5625	2.41666	1.20833	1.38541
24	1	2	1	1
18	0.5625	1	0.5	0.53125
12	0.25	1	0.5	0.375
6	0.0625	0	0	0.03125

And that is what we get!



By plotting the area ratio, normalised firing opportunities and the average of both, we end up with a delicate curve in betwixt the two. So in this hypothetical rating system, shots with a range of 12" are worth 0.375 as much as shots with a range of 24", and shots with a 48" range are worth 3 times as much as 24" ranged shots.

So does it work? Will it give a sensible result for comparison of weapons with different ranges? I don't know! I guess I'll have to give it a try...

Threat Radius in Warhammer 40,000

The concept of a threat radius (or threat range) is already well established in 40k. At its simplest, it is merely looking at the range characteristic of a weapon, and estimating how many targets it could choose to fire at that turn. To be more involved, a player might mentally add his unit's movement to their range, and visualise the area in which they could potentially destroy their foe in a turn or two.

Where the concept is less well established is in the evaluation of different weapon choices in list building. Often, a unit will have several different weapon loadouts to pick from. It is relatively easy to quantify the interaction of S, AP, and number of shots. Weapon type is a more qualitative query, but nonetheless often easily answered by army philosophy. Range can be a tricky factor, sometimes falling between the two. It is a number, after all - but how can we quantify something as intangible as a threat radius?

Firstly, it is worth pointing out that a range is a straight line, but that a unit's shooting is conducted in a two dimensional area. Thus, the area that a unit can choose to fire in increases as the square of the range. If the game was played in three dimensions, then it would increase as the cube of the range, but I digress. Anyway, the point is that a longer range increases a unit's options exponentially, not linearly.

So, on a gaming table devoid of scenery and stretching infinitely in every direction, a gun with a 48" range has double the range of a 24" range weapon, but can choose a target from an area four times as large as the shorter-ranged weapon. Its threat radius is four times as large.

Of course, our gaming tables are not devoid of scenery, and are finite. And frankly even if the above table existed my Dark Eldar wouldn't touch it with a barge pole. Scenery is difficult to model for, given the sheer variety of types and placements, but table width is easy - so let's start there.

One point is immediately obvious. Sure, that lascannon may be able to touch every corner of the table if you stick it in the dead-centre, but why would you? Instead, you'd put it firmly inside your deployment zone, where the extra range will limit an opponent's ability to retaliate. As a consequence, the majority of its threat radius will be removed from consideration, due to it being off the table, behind you.

For that matter, how often are your units called upon to shoot behind them? The majority of most units' effective threat radius is contained in a semi-circle to their front, at best. However, if we assume that the angle of that threat arc or semi-circle or whatever is constant, then the proportionality will hold: a threat area will still increase proportional to the square of the range. A lascannon will still have four times the threat area as the bolter will, despite having only double the range.

Perhaps this suggests a convenient model to rate a weapon's threat radius, for comparison with other weapon choices; by normalising it to the humble bolter. In doing so, at common ranges we get:

48"+: 4.0000
42": 3.0625
36": 2.2500
30": 1.5625
24": 1.0000
18": 0.5625
12": 0.2500
6": 0.0625

So these numbers tell us that an 18" range weapon has 56.25% of the threat range of a (stationary) bolter; likewise a 36" range weapon has 225% of the threat range. Note that there are some irregular ranges, such as 30" and 42"; these are included so that movement may be added to threat radius, if desired. Ranges larger than 48" suffer from diminishing returns, given the size of the average tabletop, and so are not included.

Of course these numbers mean nothing in a vacuum. But perhaps they will come in useful when comparing different weapon options, by factoring into the points per kill or hit equation.

For example, were I to forsake the standard blasters on my Trueborn for more poison - perhaps to combine with the Duke for a nifty amount of 3+ to wound shooting - I may be tempted to compare the shardcarbine option to the splinter cannon, or splinter rifle. Splinter rifles are 12 points (the cost of the dude carrying it), carbines are 17 points, and cannons 22 points. Because they all have the same chance to wound and penetrate armour as each other, I am only really interested in the number of hits I can generate per point.

So:

Rifle (<12"): 1.333 hits, 0.111 hits per point.
Rifle (12 - 24"): 0.667 hits, 0.056 hits per point.

Carbine (<18"): 2 hits, 0.118 hits per point.

Cannon (moving, <36"): 2.667 hits, 0.121 hits per point.
Cannon (stationary, <36"): 4 hits, 0.182 hits per point.

Although the Cannon is a clear winner so far, I am still curious about whether the rifle's longer range may help. So I multiply each category by the threat radius relative to 24", and get:

Rifle (<12"): 0.111 x 0.25 = 0.028
Rifle (12 - 24): 0.056 x 1 = 0.056

Carbine (<18"): 0.118 x 0.5625 = 0.066

Cannon (moving, <36"): 0.121 x 2.25 = 0.273
Cannon (stationary, <36"): 0.182 x 2.25 = 0.410

The carbine's ability to score more hits within 18" win out over the splinter rifle's ability to score some hits at 24" range using this metric. Of course, with its long range, the Cannon shows it is the pre-eminent choice of splinter lovers everywhere. ∫But, I still haven't considered the total threat range, including movement and weapon range. If I were to do so, we would see:

Rifle (<18"): 0.111 x 0.5625 = 0.063
Rifle (18 - 24"): 0.056 x 1 = 0.056

Carbine (<24"): 0.118 x 1 = 0.118

Cannon (moving, <42"): 0.121 x 3.0625 = 0.371
Cannon (stationary, <36"): 0.182 x 2.25 = 0.410

Now that we take into account the ability of a moving carbine to make up the same range as a stationary splinter rifle, we can see a clear benefit to taking the carbine at the points cost listed (again, subject to the validity of the metric being used). But, we can add one more echelon, by putting out Trueborn in a Raider and effectively giving them a movement of 12", provided that they are happy to disembark:

Rifle (<24"): 0.111 x 1 = 0.111

Carbine (<30"): 0.118 x 1.5625 = 0.184

Cannon (moving, <48"): 0.121 x 4 = 0.484
Cannon (stationary, <36"): 0.182 x 2.25 = 0.410

Here, we can see that although the carbine has only a moderately superior output of hits per point than the rapid-firing rifle, its ability to disembark and hit a target up to 30" away from the Raider's start point values it much higher than the rifle - but still nowhere near the Cannon. The path is clear: Cannons for those who can, carbines for the rest. Don't forget the Duke!

Definitely, this is still a work in progress. But if we can reach a greater understanding of the role range plays in weapon power, it will benefit everyone.

Stay tuned for the next installment of TL; DR - I mean, Creeping Darkness - where we will look at interaction between threat radii and opponent moves - or try to!

The gentle art of going first

The first turn is... mine

For those of us who can remember the bad old days before the new book, there was one thing on every Dark Eldar player's wishlist. If only i could affect that one crucial roll... if only I could enhance my chance of going first.

Now, the heathen curses of those spiky elf pirate pioneers have been partially answered. The Baron, and Asdrubael Vect are both on hand to make sure you really are too fast to go last.

We know the mechanics of the bonuses. But how good are the bonuses really?

First, lets look at the default. If there are no bonuses to either side, clearly each player has a 50% chance of winning the roll for first turn. Each player then has the option of seizing the initiative, and a 16.6% chance to do so - obviously this remains balanced at a 50% chance each, assuming no shenanigans.

Before we go any further, let me assume that the opponent wants the first turn as well. If they don't, and you do, then you have the start of a beautiful relationship!

But let's assume that they do want to go first, perhaps out of spite for your own best-laid plans, or perhaps because smashing spiky-ears is a lot easier before they can start revving their engines. How far ahead will the Baron get you, in the first turn arms-race?

+1 to the dice roll is a pretty handy advantage. At first glance, we can easily see that the Baron will win the first turn roll 21 times out of 36, the opponent will somehow prevail 10/36, leaving 5/36 rolls drawn. Then, we realise that the 5/36ths of rolls that are drawn must be re-rolled, with the Baron's advantage still in play. So another 21/36 of these 5/36 draws go to the Baron, and so on. Ultimately, this puts the Baron's first turn figure at a shapely 67.7%, with his hapless victi- opponent, taking up the slack with 32.3% first roll wins.

Woof! Turning a 50/50 into a better than 2/1 proposition is not bad, not bad at all! But there is a downside - winning that first turn more often leaves his nibs more exposed to having the initiative seized from him. Instead of the opponent seizing 16.6% of 50% (8.33%), he will seize 16.6% of 67.7%, or 11.2%. Similarly, there will be fewer opportunities for the Lord Hellion to seize the initiative from his opponent, only 16.6% of 32.3%, or 5.36%.

So, bringing those figures together, your net chance of winning the first turn with the Baron is 67.7% - 11.2% + 5.36% = 61.9%. Still quite a bit better than average, but perhaps not as good as it seemed first time around.

The codex provides what seems an obvious remedy for this problem, in the person of the self-styled Lord of Commoragh himself, Asdrubael Vect. Employing him (or is he employing you?) in addition to the Baron will help you regain the initiative from your foe even more often; in fact 50% of 32.3%, or 16.15%, almost what a normal army expects to seize from an even first roll! This also means that if the two Lords decide to act together for you in a game, your enemy has only a 16.15% chance of winning the roll to go first, and then proceeding to do so.

Unfortunately, as we have seen, this is not the only way for him to go first, and taking into account the chance to have the initiative seized from you, the Vect-Sathonyx tag team has a 72.7% chance of going first.

But, does Vect really need the help? Recall that the Baron increases your exposure to enemy seizes, which Vect cannot stop, and reduces the opportunity for Vect to seize himself. If we were to leave the Baron to his own devices, and just take good-old-Asdrubael, we have a much starker equation: 50% to win the first roll, less 8.33% enemy seizes, plus 25% (!) Vect assisted seizes, equals a 66.7% chance to go first. Not quite as good as the combo, but certainly lets us know who the major player is.

This is not to go into the different deployment strategies required - for example, balls-out with Vect, playing for the seize? Neither does it go into the chance that your opponent will adopt a more defensive strategy in light of his failure to win the first roll, and decline to attempt the seize. Nor does it utilise the most complete method of victory, of subtly convincing your opponent that they do not in fact want first turn at all!

But, if the spiky-eared space corsairs really need that first turn boost, unlike the old days, now there are no excuses. It can be... mine!

Hellions

The first Hellions to join the Kabal of Creeping Darkness have emerged unscathed from the painting table. How long the flimsy skulls attached to them will last is anyone's guess, but I have emerged with a new respect for Revell's Contacta plastic glue!

Vehicle Synthesis Rules

This was born from a whinge I stumbled across on a 40k forum, complaining that in the next edition, the rules for vehicles should be more closely integrated with the rules for infantry and other unit types. This is what I came up with.

In this experimental rules set, all vehicles have their AV replaced by a single Toughness value, and receive a profile the same as other models.

AV 10 becomes T6, AV 11 becomes T7, AV12 becomes T8, AV13 becomes T9 and AV14 becomes T10. Convert based on the vehicle’s front armour value.

Additionally, vehicles receive an armour save based on their type. Open topped vehicles receive a 4+ save, and all other vehicles gain a 3+ save. Perhaps some special, heavy tanks like the Monolith could receive a 2+ save.

Each vehicle then has a number of wounds, ranging from transports with, say, 2 or 3 Wounds, to heavy battle tanks with 4 – 5 Wounds. Naturally these values are arbitrary, and entirely subject to testing.

Walkers retain their WS, while other vehicles are assigned WS -. All vehicles gain a Ld stat equal to the basic Ld stat of their race.

Interacting with vehicles: shooting them

So, under the synthesis system, shooting at vehicles is exactly the same as shooting at everything else. However, it would be more fun if there were still some way of representing a damage-based metric of performance impairment. So I suggest the following extra rules for all multi-wound models:

Crippled!

A multi-wound model that is reduced to or below half of its starting Wounds must half its WS, BS I and A characteristics (rounding up) for the rest of the game, and may no longer run. Additionally, models with the ‘Vehicle’ unit type may only move at half their normal speed (so combat speed is 0 – 3”, cruising speed is 3 – 6” and flat out is 6 – 9”; remember that skimmers moving fast must displace 18” to gain a cover save, which most crippled vehicles will find impossible).

Critical Damage

When a multi-wound model survives an unsaved wound, the attacker may opt to try for critical damage. Roll a d6, and if the result is a 6, roll again on the chart below.

1 Shaken: the model must pass a Ld check to fire any weapons in its next turn.

2 Stunned: the model must pass a Ld check to move or fire any weapons in its next turn.

3 Disarmed: the model has lost a weapon, perhaps from having a turret or an arm blown off! The attacker chooses one weapon which may no longer be used. If the model already had no functioning weapons, then count this as result 4 below.

4 Immobilised: the model has had one of its motive systems, either legs or tracks, forcibly removed. It may not move or pivot in place for the remainder of the game.

5 Crippled!: If the model is not already crippled, either from sustaining this result previously or from being reduced to half wounds, then it becomes crippled. If the model was already crippled, then it is killed instead!

6 Annihilated!: The model is spectacularly annihilated! If a vehicle or a monstrous creature, then all models within d6” will suffer a S3 hit from the explosion/death throes, with normal armour saves allowed. The vehicle or monstrous creature is then removed from play, as are any other models suffering this critical damage result.

Squads of multi-wound models treat 4 Immobilised results as 5 Crippled!, and results of 2 Stunned as 1 Shaken.

Astute readers will notice that this is essentially the current vehicle damage chart. Under this proposed rule set, it becomes a characterful addition to all multi-wound models, and not the be-all and end-all of vehicles, which will more commonly be destroyed by running out of wounds.

Tyranids probably don’t like having their monstrous creatures subject to having arms or legs blown off, but they can perhaps take solace in eating the Reclusiarch’s thunder hammer!

Other rules that interact with vehicles

Of course there are a few more rules that interact specifically with vehicles at the moment, so here is a stab at covering them.

AP1

Weapons with AP1 add +1 to the roll to cause critical damage, and so will do so on a 5+.

AP-

Weapons with AP- never cause critical damage.

Lance

Lance weapons treat Toughness greater than 8, as 8.

Melta

Melta weapons within half range may re-roll all rolls to wound.

Grenades

Grenades may be used in an assault, by any model that is carrying them. However, trying to fix them in place can be difficult against a target that is retaliating! Models using grenades only ever make one attack per round, regardless of any other factors or attack bonuses. Furthermore, against targets with a Weapon Skill, the grenade will only hit on a ‘6’, again regardless of other bonuses or special rules. Against vehicles with WS -, grenades will hit as normal for the speed the vehicle has travelled; ie automatically if stationary, 4+ if it has moved up to 6”, and 6 only if it has moved over 6” in its last movement phase.

Haywire

Instead of causing a wound, will cause a critical damage roll on a 2+.

Monstrous creatures

In addition to their other rules, monstrous creatures may re-roll all to wound rolls.

Anything else? Monstrous creatures re-rolling wounds is an attempt to emulate their special effect against vehicles, but makes them even deadlier against infantry – perhaps this balances their new vulnerability to critical damage?

Some other odds and sods:

In the rear!

An attacker shooting at a multi-wound model from behind may add +1 to his roll to cause critical damage. This may stack with other bonuses, such as from AP1 weapons. ‘Behind’ is defined as to the rear of the center of mass of the model. For models that do not have a clear ‘front’, a point of reference should be established before the game.

All close combat attacks are considered to use this rule, as vulnerabilities are easier to exploit from face range!

Note that some vehicles that are symmetrical all around, such as the Monolith or Drop pod, or others that are just that badass like the Land Raider, may not be affected by this rule. This should be noted in their description.

(Simply defining vehicles to have a front and back makes up somewhat for the loss of side armour values, and may make perpendicular Rhinos giving cover to their brethren a thing of the past!)

Poisoned weapons

Models with the ‘Vehicle’ unit type are not affected by a poisoned weapon’s fixed wound roll. The weapon or unit’s base Strength must be used instead; if it doesn’t have one, then it can cause no damage.

(To stop Dark Eldar and snipers from raping every vehicle they see in a wholly unrealistic manner! This leaves some weapons out – witch blades and agonisers, notably – can be covered separately.)

Movement

I’ve got no issues with vehicle movement and shooting as it stands currently. I do like the idea of crippling vehicles to slow them down and reduce their general efficacy short of killing them though!

Comments? As I have noted, it no doubt needs extensive testing. Of particular note is how many wounds a vehicle should receive, and whether the T and Sv stats assigned are appropriate.

I will craft a follow up looking at some of the numbers involved, and compare the average number of shots to kill in this system compared to the 5th ed rules. Keep your browser tuned!

The Kabal of Creeping Darkness

HaHA! The kabal prepares to march forwards! With guns, and whips, and... more guns, and... backup?

I finished these guys a few weeks ago now, my first of the lovely new Dark Eldar plastics. Yes, I am a slow painter. Please forgive the dodgy photoshop, I am still learning the gentle art of miniature photography. For some reason I had serious focus issues trying to get the whole squad into a single shot.

Currently I'm working on some Hellions. Man, they have some serious detail going on. No doubt I will clutter the webz with some more photos when I am done :)

Wacky Dark Eldar Armies, 1 - Haywire!

Disclaimer: Creeping Darkness does not support or condone 80s hairstyles or pouty looks.

I hate tanks. I hate the smarmy grins of the untouchable missile launcher guys, safe in their oversized metal longjohns. And most of all, I hate watching my dark lances bounce off their protective layer of Darklight Protection Factor 30+ Zinc cream.

In fact, I found the disabling and disintegration of these glorified wheeliebins problematic even in 4th edition, before the 5th edition damage chart revised their survivability to levels that may see Land Raiders joining the other cockroaches after the nuclear holocaust. Even when I resorted to packing more dark lances than splinter rifles, the thrice-cursed boxes often took the distinctly rude option of placing themselves in cover, ensuring that not even a direct hit from Ron Jeremy's wang could remove them from the tabletop.

Hence, one of the curvier Dark Eldar lists that I've come up with, and now share with the anonymous internet at large. As you may have gathered from the title and preceding rant, it picks the haywire ball up from where a drunk Phil Kelly left it, and runs screaming toward the distant horizon of suicide-by-horde-army.

At 1,500 points:

Haemonculus with liquifier and venom blade [65]
8 Wyches, including a shardnet and a hekatrix (agoniser), all with haywire [136]
Raider with dark lance and enhanced aethersails [65]

Haemonculus with liquifier and venom blade [65]
8 Wyches, including a shardnet and a hekatrix (agoniser), all with haywire [136]
Raider with dark lance and enhanced aethersails [65]

10 Scourges, including a solarite and 4 haywire blasters [270]

5 Scourges, including 2 haywire blasters [130]

5 Scourges, including 2 haywire blasters [130]

Talos with chainflails and haywire blaster [115]

Talos with chainflails and haywire blaster [115]

Voidraven with 4 shatterfield missiles, night shield, flickerfield [205]

Total 1497 points, 10 haywire blasters, 12 KP, only two troops.

Obviously there are only two units that can actually take haywire blasters, so this somewhat limits the spammability of them. Luckily, a Talos is one such unit; putting some power weapon hand to hand grunt into an otherwise pretty oddball list.

In objective missions, the two wych squads start in reserve, and hope that the enemy have grown tired enough of static shocks that they are milling around on foot. In kill point missions they can get stuck in straight away, using their haywire grenades to fuck shit up, or at least give little tickles to any tanks that they can find. Hence the haemonculus, giving them Feel No Pain as a modicum of protection against both annoyed vehicles that have the temerity of exploding instead of being quietly wrecked, and also against the wrath of passengers who have now realised that they will have to walk home.

The Scourges fly around at approximately 24", stunning vehicles left, right, and centre. The large squad can pick preferentially on vehicle squadrons; any damage result prevents a squadroned vehicle from shooting (at least, with its best gun), as immobilised results lead to death. Four haywire blasters in a unit have a respectable 40% chance of inflicting 3 or 4 damage rolls on an unsuspecting adversary, and a 76.5% chance of inflicting at least two. Naturally these may be subject to cover saves, reducing the odds of rendering a whole squadron ineffective, but still, good times.

The Talos' provide some support to the Scourges, picking other vehicles to try and stun, and if possible assault. With the chainflails, a Talos can be quite deadly to vehicles, and unlike the rest of the Dark Eldar army, has a decent chance of monstering whatever was inside, massed power fists notwithstanding.

The voidraven could be swapped out for another Talos, or a foot squad to hold home base, but is really here to add a more conventional dimension of ranged anti-tank with its twin void lances. That, coupled with 4 rather dangerous shatterfield missiles to thin out the numbers of any advancing hordes before they get too cocky. The S7 missiles mean that in a pinch they could be used against a parking lot, especially if other passengers have been forced out nearby for a two-fer.

Of course, Tyranids will laugh at this list, and so will any foot castle based armies. At least the Scourges can still kick out some anti-infantry poison with shardcarbines, though personally I would reserve everything and hope for the best.

Worst case, at least opposing tank commanders should be mildly annoyed. And that's what really matters!