How destructive are Tesla Destructors?

We know about Tesla Destructors, and we know that they can be spammed (by my count you can fit 9 into 1500 points, although you start to look a bit unbalanced...). But how destructive are they really? Can you rely on them to break a wall of Rhinos, Razorbacks or Chimeras?

Scarabs II - moving vehicles

In a previous installment we looked at how many scarabs it takes to destroy a stationary vehicle. Now, lets look at the effect of increasing the target speed and the hit roll required.



Two things are immediately clear: scarabs still do nasty things to vehicles while needing a 4+ to hit, but equally, requiring a 6 to hit starts to really slow them down.

Scatter in 40k

There was once a young gunner from Cadia,
Who fired a missile over the top of his barrier-
It was aimed at some Orks,
But scattered off course,
And hit the Sarge in a very delicate area!

We know, more or less, how scatter works in 40k. But I've been interested in teasing out some of the mathematical detail, beyond the simple probability of scatter distance, to calculate the probability of a model at any given distance being hit by a shot that is subject to scatter.

Why? Well, two reasons, really. First, I want to look at the types of squad formations, and how a squad might best balance blast marker defence without diluting its onfield presence to unacceptable, or unworkable levels. Secondly, I think it would be useful to develop some kind of metric to math-hammer Blast weapons; ie, just how many shots is that 'Blast' designation worth, and will it be worth the points we pay for it?

So, before I present some common formations, and the expected number of hits to various weapons, here is a graphical representation of some of the data I have derived, for four of the most common cases. Probability is coded by colour, according to the scale on the right hand side of each pic (scale is the same for all pics). Distance from the epicentre is also labelled.

For kicks, try printing an image at 1:1 scale, and put your miniatures on in your favourite formation, against a typical opponent, and see how many of your guys are in the danger zone! (Actually, the resolution probably isn't good enough for that. Sorry! )

Small blast, BS4

How many Scarabs does it take to destroy a vehicle?

Less than 42, for sure :)

So, in the chart above, 'destroyed' includes both the wrecked and explodes! results. The vehicle is assumed to be stationary, thus hit automatically; I'll be getting to do run the numbers on moving vehicles a bit later, same with stunned, immobilised etc.

AV 10 will be most vehicles, as most have rear AV 10; some Leman Russes and other Necrons will be showing off AV 11, Monoliths and Land Raiders naturally have AV 14 all around. I can't think of anything with rear AV 12 or 13 at the moment, and dreads using their front armour won't be hit automatically, voiding the results above... but I've included them for completeness. Never know what crazy stuff will be in the next codex hey ;)

You can see that a mere 3 charging scarabs is enough to wreck most stationary vehicles in the game (95.56% and 88.62% respectively)! Entropic Strike really is that good, at least while applying the AV reduction before the roll to penetrate! At least that's how I read it, we'll see if the FAQ tones things down a bit... even AV14 vehicles can be comfortably handled by 5 charging scarabs (95.54% chance of destroying it), although using only 3 is a bit more touch-and-go, but still within the realms of possibility (43.56%).

For comparison, a BS4 melta-gun has a 32.41% chance of destroying an AV 10 vehicle. A squad of four such guns has a 79.13% chance of destroying an AV 10 vehicle.

Pretty good, eh?

It's clear, armour is no defence against scarab swarms. How useful going faster (or hell, moving at all) will be in protecting yourself, we'll examine next installment.

Combat Calculator v1.0

I've been tinkering in Excel, and have come up with a prototype spreadsheet to calculate the result of any given Warhammer 40k melee combat.

Now, I don't mean the average or expected number of hits, wounds or kills, that i see a lot of people math-hammering on various forums (fora?). That stuff is pretty easy; attacks x chance to kill = average kills. But how informative is it? If your guys are going to average 3.4 kills and his are going to average 3.2, it's clear that the combat could go either way. What is the chance of actually winning the combat?

That question is what I have sought to address.


Download the file here. It is an Excel file, but no macros.

So, I present an Excel spreadsheet. Into this, you have a Squad One (under a blue heading) and Squad Two (under a yellow heading). Squad One is the squad that will get to throw its attacks first. There is also a section headed 'Strikes simultaneously?'. By writing 'TRUE' in this box, the calculator will assume that both squads hit simultaneously. No shit.

Next, fill in the probabilities for each squad to hit, wound, and beat armour (ie, for the opposing squad to fail its saves). For example, if squad one is a bunch of Incubi, and squad two is a mob of angry assault marines, I will write in for my incubi: to hit, =2/3 , to wound 0.5 (or =1/2, whatever floats your boat), failed save, 1 (because their power weapons will ignore the puny marine armour). For the assault marines (in squad 2): to hit, 0.5, to wound, =2/3, failed save, =1/3 (because the Incubi pass their 3+ save 2 times in three, they fail one time in three). Easy so far, right? The spreadsheet will proceed to calculate the odds of a 'kill'; note that this 'kill' field is the only one of these used for the actual result calculation. Thus, if you have a special case that doesn't quite fit into the hit/wound/save mould, such as Rending or Blinding Venom, you can skip to filling in appropriate 'kill' probability, and everything will be groovy.

Also fill in the numbers of, and attacks each, for each squad. You'll notice that there are two columns, number, and special weapons. The first is for all of the squaddies. The second allows you to specify a different chance to kill, for example a sergeant with a power weapon or fist in a squad of tacticals. Unfortunately at this stage of development I haven't allowed the capacity to split initative steps, so all of Squad One's attacks are resolved before Squad Two's. Bad luck if you have a power fist in Squad One :(. Maybe next version.

Then, you will see output in three different graphs, and some numbers for the curious. How is this output achieved? By calculating every possible contingency in the assault. Caveat: currently only 10 kills per squad are really supported, so it will not be entirely accurate when looking at large squads, or squads with large damage outputs. Next version I plan to upgrade to 120+, but for now think of it as a demo.

Anyway, in each of the three graphs, Squad One is blue, and Squad Two is yellow. The first graph is a small bar graph, showing the probability of scoring 0, 1, 2 ... 9, 10 kills. Next is a bar graph showing the probability of a range of combat results, from winning by 6+ to losing by the same margin, so that the math-hammering general can get a feel for the likely morale check. Finally, a pie chart shows the actual probability of winning the combat, expressed as a percentage.

Again, the colour coding should allow you to interpret the results very quickly and visually. The graphs showcase all of the relevant results; ignore all of the other number on the screen, they are really just part of the workings. I plan to move this to a less visible location next version, but that may be a while, so in the mean time I will unleash the beast!

All comments are welcome. I know that the user-interface is probably not so great at the moment, suggestions are welcome! Finally, let me know if it works for you, and helps plan your game. One day, when we are bionic, we will be able to use tools like this on the fly; when weighing up whether or not to assault, or telling your friend exactly how unlikely his gretchin trashing your reavers in hand-to-hand was (yep, true story)...

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...