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6th (and 3rd, 4th and 5th) Edition Mathhammer: Vehicle Kill Probability.

Started by Wargamer, July 25, 2012, 04:04:24 PM

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Wargamer

Since it came up in another thread, I thought I'd do some number crunching to discuss the statistical shifts in our engine kill capabilities through the ages.

For this, I am mainly going to focus on Imperial vehicles, but the maths apply across the board.

I'm going to number crunch on damage outcomes based on damage inflicted, ignoring the odds of causing that damage. The reason I'm doing that is that, for shooting at least, it really hasn't changed much; Str 5 has had a 1/6 chance of glancing a Rhino since 3rd, and so we'll skip straight to what counts; the Glancing and Penetrating Hits!

Disclaimer - a note on damage:
In every Edition, the chance of causing damage to a vehicle (ie: Weapon Destroyed or Immobilised) is the same: 1/6 for each of them (so 1/3 combined of doing some form of damage).

3rd/4th Edition:
3rd is where the damage table we all know and love (to varying degrees) originated from. It's also the one with the fewest modifiers; only Open Topped applied. 4th Edition didn't change this much, but it did add the rule that meant you could 'ping' a vehicle to death by causing weapon destroyed and/or immobilised results until it couldn't move and had no guns left. For now, however, this is not important. So, let's do some math!
Glancing Hits: 1/6 chance of a kill.
Penetrating Hits: 1/2 chance of a kill.

So, here's our benchmark; a single Glancing should have 16.67% chance of killing a tank (assuming it has landed), whilst a Penetrating Hit is a much higher 50%.

5th Edition:
Oh boy, we've had some changes here! 5th Edition uses a single damage table, albeit with several modifiers. For now, since we're focusing on a normal hit against a normal vehicle, we can ignore that. So, let's have at it!
Glancing Hits: Unable to inflict a 'kill' result.
Penetrating Hits: 1/3 chance of a kill.

As you can see, vehicle durability has gone up quite noticably. Of course, this ignores fundamental changes in how vehicles worked, but in terms of raw damage rolls, vehicles in 5th were less likely to die than before.

6th Edition:
Another radical change; this time, vehicles have been given Wounds, known as 'Hull Points'. 3 Hull Points is the norm, and when a vehicle loses all three Hull Points, it is wrecked. On to the dice!
Glancing Hit: 1 Hull Point lost, no damage roll.
Penetrating Hit: 1 Hull Point lost, 1/6 chance of a kill.

So, it would seem vehicles have gotten even tougher, yes? The odds have been halved since 5th of your Penetrating Hits actually doing anything, and Glancings never roll on the damage table so even ping kills are gone! Except that pinging is alive and well; it's just done differently. Remember that "1 Hull Point lost" bit? Remember how I said most vehicles only have 3 Hull Points? Pinging has now become not only viable, but actively encouraged.

Let me show you what I mean with an example...

FIREWARRIORS VERUS RHINOS!
12 Firewarriors are camping an objective when a Rhino rushes up to them, seeking to contest the point and stop the Tau winning. They have a Markerlight supporting, and they Rapid Fire; 24 shots, giving 18 hits.

These Firewarriors can only inflict a Glancing Hit on their target, and statistically they should get three. Let's assume they do... what are the odds of them actually killing this Rhino?

3rd Edition:
Easiest of the lot. The odds of inflicting one or more wrecked results with those three glancing hits is 42.1% (not 50%. I know why you might think it is, but it isn't.).

4th Edition:
More complex, as we have to allow for 'pinging', but we can do that... it just requires every dice to come up as immobilised or weapon destroyed, and then add that to the odds of blowing the Rhino up 'properly'. That gives us a total of 45.8%, an improvement on last edition.

5th Edition:
A paltry 3.7% chance of a kill here; the only way they can do it is to ping it. That's a nasty limitation, and the odds are not in the Tau's favour.

6th Edition:
100%. Those three hits each took a Hull Point off, and the Rhino is wrecked.

Now you might say this example is unfair. After all, if they only cause two Glancing Hits then the vehicle is fine! That is true, but by the same token it is entirely possible the unit could cause more than three, in which case the vehicle is still just as dead, yet in every other Edition there was a chance that it would survive.

Furthermore, 'pinging' kills are rarely done all at once. Vehicles tend to shed weapons, or be ground to a halt, over the course of a game. In practice, a vehicle that dies due to pinging, if it happens at all, is probably killed slowly over 2-3 turns.

Let's move on to another hypothetical then...

MARCH INTO KRAK MISSILES:
Here, we follow the adventures of Bob the Dreadnought as he marches into a storm of krak missiles. Due to a quirk of statistics, Bob suffers a Penetrating hit every turn. Just one, no more, no less.

What are the odds of Bob being alive at the end of any given turn?

3rd Edition:
Turn 1   50.00%
Turn 2   25.00%
Turn 3   12.50%
Turn 4   6.25%
Turn 5   3.13%
Turn 6   1.56%

Oh dear... really not looking good for old Bob, is it? Realistically, I would not expect him to be around at the end of turn 3, but it is possible he'll live...

4th Edition:
I really don't want to do the math on this one. It's bloody complex, fiddly as hell, and ultimately it'll give me a headache.

So, the simple version is that in 4th, his odds of survival are the same up to turn 4. At turn 4 and beyond, the odds of survival decrease because now he could potentially die to 'pinging'.

5th Edition:
Again, 'pining' has not been factored in here due to the complexity of the math, but here's the odds from the straight up damage rolling:

Turn 1   66.67%
Turn 2   44.44%
Turn 3   29.63%
Turn 4   19.75%
Turn 5   13.17%
Turn 6   8.78%
Turn 7   5.85%

So, it's still long odds he'll see the end of the game, but if you end on Turn 5 the odds are a little under 1 in 7, and lower with the ping, but it's an improvement on before.

6th Edition:
Here we go! Bob's on his fourth walk into Krak Missile alley! Let's see how far he gets!

Turn 1   83.33%
Turn 2   69.44%
Turn 3   0.00%

Ouch! Right off the cliff!
Hull Points have crippled our poor Bob. It means he has no chance at all of living through his third turn, making 6th the worst Edition for walking through suspiciously consistent anti-tank fire!

Now keep in mind we haven't even touched on AP modifiers or Open-Topped, or the benefits / penalties to close combat. Throwing AP1 at Bob in 3rd won't make a difference to his odds. In 4th, it'd make the Penetrating hits more likely. In 5th, his survival odds drop to 3rd Edition levels (remember to add ping). In 6th, he also goes down to 3rd Edition survival odds, but the Turn 3 wall remains as well - 50% odds of surviving turn 1, 25% of surviving turn 2, 0% of surviving turn 3.




So, is it all doom and gloom? Are vehicles now so hopelessly outclassed they have no place on the table? Well, perhaps not.

Let's try and get through that storm of Krak Missiles once more! This time, we're going to bring a Land Raider! We're going to assume for this one that the Land Raider itself doesn't matter - it's passengers do. Our goal is to get them as far down the table as possible! This time, we've been savvy and equipped Extra Armour, so Stunned won't do squat against us! Let's see if we can avenge poor Bob!

Odds of not being killed / immobilised on any given turn:

3rd / 4th Edition:
Turn 1   66.67%
Turn 2   44.44%
Turn 3   29.63%
Turn 4   19.75%
Turn 5   13.17%
Turn 6   8.78%

Pretty solid performance; those Krak Missiles are bouncing off the hull for the most part, but even so our Land Raider could well be brought to a screeching halt by a lucky shot.

5th Edition:
Turn 1   83.33%
Turn 2   69.44%
Turn 3   57.87%
Turn 4   48.23%
Turn 5   40.19%
Turn 6   33.49%
Turn 7   27.91%

Now you see why everyone liked Land Raiders in 5th; the odds of stopping that tank at all with our 1 Glance per turn volley is pretty poor. Given that in just 4 turns the Land Raider could cover 48", odds are it got to where it needed to be.

Can 6th beat it?
6th Edition:
Turn 1   100%
Turn 2   100%
Turn 3   100%
Turn 4   0%

Ah, the wall! Welcome back! But notice what happened before then; our Land Raider was not only shrugging off the hits, but it had zero chance of being damaged! That tank was not only free to move, but it was free to return fire as well! In every other Edition the tank would have at least been shaken, and potentially had guns blown off as well. In 6th, the glancing hits are being completely ignored right up until a critical mass is reached.

WHAT HAVE WE LEARNED?

The numbers speak for themselves; vehicles in 6th Edition are better equipped to handle individual hits, but cumulative hits are fatal. Moreover, I know I didn't touch on combat, but now vehicles are much easier to hit in melee, as enemies never need worse than 3+ to do so. That means you'll be taking more hits than before in combat, which means more chance for your opponent to get those glancing and/or penetrating hits, which means you'll be running out of Hull Points that much faster than you would have under 5th Edition rules, or any other Edition for that matter.

Specific vehicle types, and use of the battlefield itself, may be able to mitigate some of this damage. However, overall I am sorry to say the next four years are looking bleak for tread heads.
I wrote a novel - Dreamscape: The Wanderer.. Available in paperback and pdf.

Quote from: Liberate the Warhammers
People who have no sense of Sportsmanship have NO PLACE designing any Gaming system

Arguleon-veq

They really are. Vehicles are going to be seen less and less unless they fly. My Ork Lootas have glanced to death countless tanks this edition including a lot of Necron and Blood Angel AV13. Last edition thanks to extra armour, being a death company dread or having living metal those glances wouldnt have really been a big deal. Now its equals a lot of dead tanks.

Add those glancing kills to the fact that Meltas are just as good as they were all adds up to a very bad time for tanks.
X-Wing Tournaments;
1st - 38
11th - 33

Pottsey


Arguleon-veq

...cover saves actually got worse for vehicles. Sure you can get a great one with nightfight but with old nightfight you had a good chance of not getting shot at all.

Theres a reason why top players who were using their 14+ AV12 spam Guard, Psyback/Dread spam GK and Barge spam Necrons have dropped those builds.

Have you played or watched many games of 6th yet? you will quickly see how crippling the whole glance death thing is.

At the end of the day most arent open topped anyway so glances couldnt kill them, most tanks now get 5+ cover where as most of the time they got 4+ cover last ed. A lot of your weapons are AP1 or 2 that will be shooting at tanks anyway and those can kill tanks in 1 shot just as well as usual. Then on top of that you kill them in a few glances. Holo Fields, Venerable, who cares, just glance them and they die like everything else.

Add in the fact that transports suck now and you cant contest with tanks or score from in a transport just makes them worse and worse. They also took a hit in terms of not being able overwatch when infantry can.

Flyers are the new tanks. Every army will spam them like Razorbacks/Chimeras etc were in 5th.

I do think AV14 tanks that want to be shooting got a little better though. They are very hard to glance and even when they do you get to shoot back. That is nice, but as always, its nothing a meltagun doesnt fix.
X-Wing Tournaments;
1st - 38
11th - 33

Wargamer

I wrote a novel - Dreamscape: The Wanderer.. Available in paperback and pdf.

Quote from: Liberate the Warhammers
People who have no sense of Sportsmanship have NO PLACE designing any Gaming system

Matt1785

Hrm,

While I do see where you're going with the math, I don't see it having an overall affect on people and what they're going to bring for transports.  I'm sorry, but with the changes to cover saves (Both good and bad) transports are still STRONGLY recommended.  Foot-slogging lists will have a hard time surviving without superior numbers.  It is the main concern I have going into the tournament I am going to be a part of.  I have marine foot sloggers and in the past few games I have just been getting CRUSHED!  Of course, I've been playing against stacked Necrons.. but it's still tough.

Some things that I find interesting is that Fast Skimmers got a lot better in my mind... armies like Eldar and Dark Eldar got the boost of auto-receiving a 5+ save by simply nudging their vehicles to the side.. which helps them survive.  I don't think I'll be seeing guardsmen walking, I'll see them loaded into Valkyries... not to mention, with front armor 11 and 12 are most armies really that more afraid then in 5th?  I mean, my bolters still won't be putting any vehicles down if they're coming straight at me.

Another thing to make note of is that glancing hits can no longer slow vehicles down.  Glancing used to give you the chance to stop a vehicle from moving and shooting at the very least... at this point, you have to continue hitting that vehicle even if you glance it with another squad.  This ups the amount of squads you'll need to fire at a particular vehicle.  Things like Land Raiders are super excited IMHO.  Meltas are still really the only way to put them down and that means things have to be close, which is fine in their standards because usually there's something packed inside of it that is happy for things to get close.

I will 100% AGREE with you on walkers.  The Kan wall is a thing of the 5th past.  Most of my ork friends are horribly upset about the new glancing rules and have rolled over on the wall.  As for me, I can't get my Dread through turn 2 so I agree with everything you've said about walkers... they just can't cut it with HPs.

Do I agree that vehicles are in trouble in 6th?  Oh heck yes, but will it change the game entirely?  I doubt it.  We'll still see highly mechanized lists dominating IMHO... as sad as I am to say that...  I LOVE to see models, and not vehicle models, its why I refuse to bring vehicles, even if I still do get killed all the time.  I like to see models.  (Although I will admit that I will bring a Deathfish with my Tau allies... they're just too neat!((hypocrite warning!)))


Pottsey


Wargamer

Quote from: Pottsey on July 26, 2012, 08:22:06 AM
Quote from: Wargamer link=topic=573.msg11557#msg11557
I wrote a novel - Dreamscape: The Wanderer.. Available in paperback and pdf.

Quote from: Liberate the Warhammers
People who have no sense of Sportsmanship have NO PLACE designing any Gaming system

crisis_vyper

I guess it is warranted that I say this once again.

Quote

If you want to use mathematics and probabilities into the equation, you will have to realize one thing; there are two parallel systems in destroying vehicles which makes the traditional mathematical calculations for warhammer in a loop to begin with which is the hull point system while the other is the penetration chart. Those two systems have their own quirks and combining them can often be very difficult as we are not accustomed to the idea two parallel damage systems on one particular unit type.

Look into the programming currently being attempted for this at the link below.

40k Metrics: 6th Edition Vehicle Mathhammer by Nikephoros

There's two parts to the question; which system do you want to exploit to destroy vehicles, and what is your target vehicle?

For the light transports, glancing it to death is a much more viable method, and for the heavier stuff, the penetrating would be much better. Since there is no such thing as stun-locking anymore one will have to figure out how they want to neutralize that vehicle fast.

Pottsey


Wargamer

Pottsey, what you seem to have missed is I am talking about Glancing / Penetrating Hits that are inflicted on a vehicle. In other words, if you had a save, you failed it.

Now kindly drop the matter, because you are pissing me off now. Vehicles getting cover saves is not a new idea, nor is vehicles with an Invulnerable Save. Overall, based on real experience in real games, I have not seen a significant increase in saving throws. Yes, some armies are getting Cover Saves where they didn't before, but that's only for Skimmers, who are at their most vulnerable state to date when it comes to being attacked in close combat, which means they won't be getting that precious cover save anyway.

Oh, and because I know you're going to bring it up again... that pre-measure comment? It has no basis in reality. "Just stay 13" away" is not going to save any vehicle ever. Why? Well let's show you!

On 2D6, the average roll, statistically, is 7. This is also the most likely single result to come up. 6" move + 2D6" charge should give 13" total ground covered. I lost a Land Raider to a 9" charge in my last game.
So, to be entirely safe from being charged, our vehicles now need to end their turn 19" away from Infantry, or 25" away from Jump Infantry / Bikes / etc. There are plenty of vehicles who need to be within 24", and possibly a lot less, to fire at full effect. Transport vehicles, especially those carrying assault troops, probably want to be much closer to the enemy than that!

But none of that is the point of this thread. This thread is not about how vehicles are weaker because you can't pop smoke after moving flat out, or how Flyers are a must own, or anything else. It is about how much damage you have to inflict to kill a vehicle, or at least have an acceptable probability of doing so.

That's it. End of. Drop your irrelevant tangent.
I wrote a novel - Dreamscape: The Wanderer.. Available in paperback and pdf.

Quote from: Liberate the Warhammers
People who have no sense of Sportsmanship have NO PLACE designing any Gaming system

Matt1785

I see where Pottsy is coming from, but also know that to do a statistical study such as this with numbers it is difficult to factor in the idea of cover saves.  You'd need to factor a percentage of the time a vehicle will be in cover, and then figure from there how many of the hits will be saved by cover.

Your mathammer is done in a vacuum with no cover saves just saying X vehicle is facing Y shooter, how many hits / pens / glances does he get.  And in that simple regard I do agree that you have proven that 6th Edition has made vehicles a weaker prospect.  Also didn't mention the AP 2 - 1 Factor which has changed things...

I read the blogspot as well, interesting point of view, but I do believe that the short answer is that vehicles are easier to kill in the vacuum, but may not be easier to kill when taking into account all of the other game mechanics.  In a way both arguments are correct, although I would still argue that vehicles are slightly worse off in this edition for my simple reasoning that you can finally glance something to death with reliability.

Pottsey

Quote from: Wargamer on July 26, 2012, 12:23:47 PM
Pottsey, what you seem to have missed is I am talking about Glancing / Penetrating Hits that are inflicted on a vehicle. In other words, if you had a save, you failed it.

Now kindly drop the matter, because you are pissing me off now. Vehicles getting cover saves is not a new idea, nor is vehicles with an Invulnerable Save. Overall, based on real experience in real games, I have not seen a significant increase in saving throws. Yes, some armies are getting Cover Saves where they didn't before, but that's only for Skimmers, who are at their most vulnerable state to date when it comes to being attacked in close combat, which means they won't be getting that precious cover save anyway.

Oh, and because I know you're going to bring it up again... that pre-measure comment? It has no basis in reality. "Just stay 13" away" is not going to save any vehicle ever. Why? Well let's show you!

On 2D6, the average roll, statistically, is 7. This is also the most likely single result to come up. 6" move + 2D6" charge should give 13" total ground covered. I lost a Land Raider to a 9" charge in my last game.
So, to be entirely safe from being charged, our vehicles now need to end their turn 19" away from Infantry, or 25" away from Jump Infantry / Bikes / etc. There are plenty of vehicles who need to be within 24", and possibly a lot less, to fire at full effect. Transport vehicles, especially those carrying assault troops, probably want to be much closer to the enemy than that!

But none of that is the point of this thread. This thread is not about how vehicles are weaker because you can't pop smoke after moving flat out, or how Flyers are a must own, or anything else. It is about how much damage you have to inflict to kill a vehicle, or at least have an acceptable probability of doing so.

That's it. End of. Drop your irrelevant tangent.
Well you very clearly you do not care about the realistic acceptable probability of killing a vehicle between 5th and 6th. A lot of what I said is not a tangent and it perfectly valid for dissuasions on tank killing power between 5th and 6th. I noticed you skipped over all my valid none cover save points that disagree with your view, just like the other thread you ignored anything that disagreed with your view. What I said is very relevant as it applies to real games which is what matters. Your math hammer is misleading as it makes it look easier to kill vehicles when in real games it harder.


Arguleon-veq

Well the first few big 6th Ed UK 40K Tournaments are coming up in the next few weeks so I will get my mates that are going to see how tanks are doing overall and what the top table lists are looking like this edition.

Ive seen a lot of top players thinking about Foot Eldar right now which is pretty telling. Just have to see if it works out.

I seriously think we will see a serious reduction in vehicles when you consider that month in month out for the last few years of 5th 90% of competative tournaments were won by Psyback/Dread spam GK and Wraith/Barge spam Necrons.

Just as a quick run down of my personal experiences so far, these are games in which I either watched the whole thing or I was playing.

No Tank Orks vs 5th Ed Style Guard - Orks easy win, tanks were decimated.

No Tank Orks vs Flyers and Foot Guard - Orks easy win although no tanks so doesnt matter.

No Tank Orks vs Flyers and Foot Guard - Orks easy win although no tanks so doesnt matter.

No Tank Orks vs AV13 Spam BA - Orks easy win, tanks got decimated.

No Tank Orks vs Necrons with 3 AV13+1 AV14 - Fairly close but an Ork win, only the Monolith lasting the game [only the Monolith lasting past turn 2].

No Tank Orks vs 5th Ed Style GK with Necron Flyers and Barge - GK win but mainly due to the Flyers and Purifiers, 1 Dread and 1 Razor survived the game from the Vehicles [not including flyers] from 3 and 6 respectively.

Foot Wolves vs 5th Ed Style GK with Necron Flyers - Wolves easy win, no tanks survive the game.

Paladin GK vs 5th Ed Style Mixed Tau - Easy win for GK although the Tau Tanks survived they just werent shot at as there was nothing they could do to take the objectives from the Paladins.

My mates are playing Paladin GK vs 5th Ed GK with Necron Flyers on sat as a warm up for Ribble Rumble which is a big 50+ player tournament that a lot of the top players go to. I will let you know if 5th or 6th ed GK wins out and how those tanks do.
X-Wing Tournaments;
1st - 38
11th - 33