Tag Archives: statistics

ETC2013 getting to 5th place

So, as I may have mentioned (every 5 minutes or so), team Ireland got its highest result to date at the ETC this year.  More than a few people were surprised (delighted?) that we reached 5th place so I thought I’d spend today’s post talking about the team and what worked for us.

irl serious

So firstly there’s the guys who have to take the punishment. Everyone has a term for them: bid lists, shields, prey lists, put forward lists etc. Basically if you lose the bidding roll off, who do you nominate? This year my shield guys were Necrons, and Eldar with Tau allies. They did their jobs magnificently with scores of 61 and 57 across 6 games, showing that even with a full set of choices of counterattack our opponents were only able to draw on average with them. Good job fellas!

The next three were our counters/finesse lists. Tyranids, Daemons, and Imperial Guard with Chaos Marine allies. These lists were generally used as counters to armies that the opposing team had bid, and there’s quite a bit of effort needed to find the right matchup for them. With the right pairing they can do serious damage, in the wrong one they can end up in bad place! I found it impossible to get a good matchup for everyone in every round, but as long as two of the three were good then I knew we could still do well in the round aggregate.

The final three were our all rounders, nasty lists that can take on almost anything. Here we had Chaos Marines with Necron allies, Tau, and Grey Knights. The strategy with these guys was just to avoid the small number of potential bad matchups and use them against whatever our counter lists weren’t able to handle. Here we were relying more on player skill and army strength rather than good bidding to get ahead. These guys really delivered. Our Chaos Marine and Tau players both finished both in the top 5 of all players in the ETC (also both were top player in their respective armies), and our Grey Knight player also finished ahead of the curve.

Practicalities aside, the ‘secret’ ingredient for us is team spirit. As anyone on the team will attest, everyone did a fantastic job of supporting each other and everyone worked well as a unit. I never heard a single complaint when anyone had to face a bad matchup so that others could get good ones. Simply put, everyone completely understood the joint effort required to win a round.

irl silly

The final point I’ll add is that we really do strive to play fair with our opponents and ensure that both sides have a good set of games whether we win, lose or draw. I think it’s the right thing to do, but also it has a psychological benefit for the team as we don’t end up totally stressed out by needless arguments throughout the day. I really hope that it’s something we can keep as a core value of our team now and in the future.

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ETC2013 the view from the top

So my last two posts have been about the overall meta at ETC2013, and today I want to take a quick look at the top 3 countries and how they compare to the overall meta.

As a quick refresher the top performing armies were:

  1. Tau
  2. Eldar
  3. Necrons
  4. Chaos Space Marines
  5. Chaos Daemons
  6. Tyranides
  7. Space Marines
  8. Dark Angels

Whereas the most popular armies were:

  1. Necrons
  2. Chaos Space Marines
  3. Tau
  4. Grey Knights
  5. Imperial Guard
  6. Tyranids
  7. Chaos Daemons
  8. Dark Angels

Germany got the top spot (familiar territory for these guys!).

Germany

They ran with:

  • Tau
  • Grey Knights
  • Necrons
  • Chaos Space Marines
  • Chaos Daemons
  • Tyranides
  • Orks
  • Dark Angels

So this includes 6 of the 8 top armies (they left out Eldar and Space Marines), and 7 of the 8 most popular armies (they avoided IG, which was the biggest underperformer of the popular armies).

Spain came in second,

spain

and their team comprised:

  • Tau
  • Grey Knights
  • Necrons
  • Chaos Space Marines
  • Chaos Daemons
  • Eldar
  • Imperial Guard
  • Dark Angels

Again they had 6 of the top 8 armies, leaving out Tyranids and Space marines. They also brought 7 of the 8 most popular armies, just leaving out the Tyranids.

Poland were third

poland

and they brought:

  • Necrons
  • Chaos Space Marines
  • Tau
  • Grey Knights
  • Imperial Guard
  • Tyranids
  • Chaos Daemons
  • Dark Angels

This also has 6 out of the 8 top armies (similarly to Germany they left out Eldar and Space Marines), and interestingly all of the most popular armies.

So the top three countries all brought 6 of the 8 top armies (though not the same ones) and all brought 7 or more of the 8 most popular armies.  There is a big overlap in that all three countries brought Chaos Marines, Dark Angels, Daemons, Grey Knights, Necrons, and Tau.

So, what does that mean for the army rankings I described previously? Well firstly it shows that picking the top 8 armies is not necessary to win, and places more weight on my caveat that just going on army rank is a simplification that needs to be tempered by the roles needed or the team – and the skillsets of your players!


ETC2013 Popularity vs Performance

So last time I put up a table of how the various armies performed (on average) at the ETC in Serbia. There were some interesting results, and today’s post follows up that line of thinking by comparing the popularity of army choices with their score rank. Popularity in this case just means how many teams included that army, and the table below puts the armies in order of popularity.
RankVsPop
So the numbers in the ‘Difference’ column highlights any disconnect between how popular an army is versus how well it performed at the ETC. A positive number means that the army performed better than its popularity, a negative number means that its popularity was higher than its performance warranted.

Tau weren’t the most popular army, but really the first three are so close that it makes little difference. The captains made those choices fairly rationally: Necrons, Tau, and Heldrakes are solid performers.

There is an interesting hiccup in places 4 and 5 where Grey Knights and Imperial Guard were both quite popular but didn’t do as well as their popularity suggests. Both armies were in the bottom half performance-wise but were both present in more than 75% of teams (my own included!)

Tyranids were fairly popular, and by the results that seems to be justified – similarly with Chaos Daemons (slightly under-represented), and Dark Angels.

Eldar were quite under-represented and were the ‘sleeper hit’ of the ETC, doing quite well for the 11 teams that brought them. Of the remainder, only Space Marines have a big positive difference showing that they did a better job than their low popularity would have predicted.

There is of course a big caveat here: armies fill particular roles on a team so simply picking the highest average scorers may very well lead you astray with too much of one role and too little of another. So we don’t have a magic formula for army selection just yet.

It also creates an interesting mind game for next year: do you bring a team that works well against the popular armies of 2013, or do you focus on bringing what did well in 2013, or do you bring counters to what did well in 2013? How much will the new codices between now and Aug 2014 change the meta?

Lots to think about for the new captains!


ETC 2013 Armies and Stats

So the madness of ETC2013 is over, and the post mortem analysis can begin in earnest.  I won’t start with my own team (Ireland), but rather I’d like to take a look at the overall meta.  Thankfully my job has been made easier by the organisers who have already published lots of data on who took what armies and how they fared in the tournament.

So, what armies generally did well?

ArmyRanks

So the number 1 slot is probably no surprise to anyone, Tau are new and awesome, they wrecked face at the ESC and are probably doing well at a tournament near you right now.

Number 2, Eldar is probably a bit more of a surprise – particularly considering that it was the OLD codex that was legal for the tournament, not the shiny new one.  My prediction beforehand was that they would be a solid army to ‘not lose’ I wasn’t expecting them to win big.  The fact that they were often backed up by Tau allies probably helped a little too

Necrons, Heldrakes, and Chaos Daemons round out the ‘winners list’ (i.e. the armies that are averaging >10 which is a win).  Again this isn’t very surprising Necrons are still crazy powerful, everyone hates Heldrakes for a reason, and Chaos Daemons can certainly be deadly in the right matchup.

It worth taking a moment to think about the remaining armies.  Everything else on that list was losing on average (i.e. <10).

Admittedly, that’s a bit of a sweeping statement as the performance of an individual can vary greatly from the group average, and not just down to player skill but also down to the team pairing strategy.  The table also doesn’t factor in the use of allies – which is perhaps a project for me for another time…

But, that said, this table does give us a line in the sand as regards what the 2013 meta was like and I’m sure it will influence team and army selection for next year!


More penetration: Ass versus Las

This weeks sandwich request comes from the inimitable Paul ‘Mandragoran’ Quigley (just back from Switzerland as part of the Irish team in the 40k world championships!). We’re taking another look at penetration today, this time factoring in the impact of rending. A useful reference point would be here where I’ve covered the efficacy of a variety of anti tank weapons, but the material in this post does stand on its own too. Right, question time:

A Black Legion tank commander is navigating his Land Raider through enemy territory. He’s caught in crossfire between two Razorbacks, one left, and one right. Both are at the limit of their weapon range, so the commander decides to rush towards one so that he can’t be hit by both. Should he drive toward the Assault Cannon armed Razorback, or the Lascannon armed Razorback?

So, rending against vehicles. You get your usual 1d6 plus weapon strength roll, with the added twist that if you get a 6 on the roll, then you get to roll a d3 and add it to your result. This means that an assault cannon at Str 6 could get a 15 and penetrate a Land Raider (Str6+roll a 6 on d6+ roll a 3 on d3 =15). The question is, can it do a better job than a Lascannon (which is a plain Str 9 + 1d6 with no rending)?

It’s a little tricky to do a straight like-for-like comparison here as a key feature of the assault cannon is that it gets four shots, whereas the Lascannon only gets one. So here’s my starting point. I’m assuming that there are no misses, and for the Lascannon I’m looking at the odds of a penetrating hit, and for the assault cannon I’m looking at the odds of at least one penetrating hit. Some of you may object to that approach, but bear with me for now.

(Just to note: the gap in the line isn’t a mistake, it’s simply that you can’t get a 12 on the assault cannon as rolling the 6 gets you an extra d3 making you jump from 11 to 13+).

So what have we got: one hit with a lascannon has a (just under) 17% chance of getting a pen on AV14, but 4 hits from an assault cannon gets you (just over) 17% chance of getting one or more penetrating hits on AV14. Okay the odds are only a tiny bit higher but you can get from one to four pens so the net effect can be a lot stronger. So the word on the street is correct, assault cannons are straight up better than lascannons at penetrating AV14?

Well, not so fast.

Let’s go back to those assumptions from earlier. None of the shots miss. “So what?” you say, “the assumption was the same for both!“. Actually it’s different. The odds of getting all hits on a one shot weapon are better than the odds of getting all hits on a four shot weapon (assuming equal BS). The analysis above assumes that the Razorbacks never miss, so the more unreliable the firer, the less accurate that graph becomes.

To illustrate the point I’ve run the same analysis showing the results for 4, 3, 2 and 1 hits on the assault cannon versus the lascannon.

The comparison is no longer quite so clear cut. We need to account for the end to end process from hitting through to penetrating. So lets’ do that. Lets assume BS4 for the assault cannon and the lascannon.

For the assault cannon we need:

  • 3+ to hit
  • 6+ to rend
  • 5+ to penetrate

This gives us a 4% probability of success. But we get 4 shots, if you’re thinking that 4 shots at 4% gets you a 16% probability of success then you probably need to read my blog more often; if you’re thinking the answer is 14% then you probably don’t need me at all. (Success here means one or more penetrate results)

For the Lascannon we need:

  • 3+ to hit
  • 6+ to penetrate

This gives us an 11% probability of success, and since we only get one shot, that’s the total odds.

So what’s the final verdict? The analysis clearly shows that neither the assault cannn or lascannon are particularly good at killing Land Raiders, but if they both have the same BS, the assault cannon is definitively better. It is worth noting that the lascannon can sneak ahead if fired by a superior marksman, so a BS5 lascannon is equal to a BS4 assault cannon, and a twin linked BS4 lascannon is better than a BS4 assault cannon (vs AV14).

I say final verdict, but there’s still a little more gas in the tank. I’ve plotted a couple of different weapons so you can check out the relative merits of weapons that I haven’t covered previously. Note that I’ve not done the full end to end calculation here, I’ve simply assumed all shots hit for this chart.

One final weirdness I wasn’t quite expecting, against the humble rhino (AV11) the lascannon is more reliable. It’s basically an artifact of the rend: if you get a 6 then your result ‘jumps up’ out of line with the non rending results. So while we initially were concerned only with AV14, we can in fact make a more general statement: AV12 and above, assault cannon more lethal, AV11 and below Lascannon more deadly!


Ka-blammo!

I first touched on scatter dice in my earlier post on deep striking. Blast weapons don’t use Ballistic Skill in the same way as ‘regular’ weapons, but it is still an important factor in hitting your foes. Question time:

A renegade Ordo Hereticus Inquisitor carrying a psyocculum is hunting the battlefield for Mephiston. The inquisitor is joined by his trusty squad of psyker henchmen with the Psychic Barrage (large blast) power. Assuming they pass their psychic test, what are the odds that they will hit Mephiston?

Right, blast weapons use the scatter dice described here. At its most basic, a 33% chance of a hit, and 67% chance of a miss; if you miss then it scatters 2d6 inches but unlike deep striking you can subtract the firing models Ballistic Skill (BS) from the 2d6 result. So if you roll a ‘miss’ but get a distance less than or equal to your BS then that miss becomes a hit (i.e. you don’t scatter). Naturally this means that the higher your BS, the more ‘misses’ get converted into hits, and if it does scatter then it won’t scatter as far.

To show the effect of increasing BS values I’ve pulled together a 3d plot. So each colour represents a BS value, from BS0 at the front to BS10 at the back. The odds of a particular result go from left to right, so taking BS0 as an example, the odds of a HIT is the leftmost blue column (at 33.33%) and the odds of a particular scatter are to the right, e.g. a 2 inch scatter has a probability of 1.85% (for BS0) and a 7 inch scatter would be 11.11% likely (for BS0).

So quick summary on how to read this:

  • the height of a given column is the probability,
  • each colour is a BS value, and the BS values get higher as you go back,
  • the foreground numbers are a HIT (leftmost) or a particular scatter distance (from 1 to 12 inches).

Since the the BS value is subtracted from the scatter distance, you can clearly see the maximum scatter get smaller with each step increase in BS. So looking at the BS10 scatter (all the way at the back in pink) it’s a 94% chance of a hit, 4% chance of a 1 inch scatter, and a 2% chance of a 2 inch scatter.

Given that the the psyocculum gives our Psykers BS10, is that the answer to the question, a 94% chance of hitting Mephiston?

Not quite, theres one more factor to take into consideration. Blast size. The regular blast has a 1.5 inch radius, and the large blast has a 2.5 inch radius. Against a vehicle, only the centrepoint of the blast gets you a full strength hit, but against infantry just clipping the base with the blast template is enough for the full whack.

So in terms of hitting Mephiston, it’s 2d6 scatter minus 10 for BS, and (effectively) minus another 2.5 inches for the radius of the large blast. So we’re subtracting 12.5 from a number that is at most 12, simply put they can’t miss! There aren’t many mechanics in the game that can say that.

The only caveat is that the extra bit of reach from size of the radius doesn’t get you a ‘full’ hit as it doesn’t land exactly where you placed it. You’ll definitely hit the guy you were centred on, but you’ll cover different models around him if it does scatter those one or two inches.

So, back to more general principles. You may recall my uber list of BS rankings, well I’ve now we can add two new charts to that list.

First up, regular BS accuracies with blast accuracies added (in pink). The blast accuracies are the probability of hit but disregarding the radius of the blast (i.e. the odds of the centrepoint hitting your desired target point). Blue columns are ‘regular’ shots, green are twin linked, and pink are blast. Hmmm I guess I left out twin linked blast, guess that’ll have to wait.

Secondly looking specifically at the effect of the radius (no ‘normal’ i.e. non-blast shots on this one) . So these are the odds of hitting with just the centre (in pink), versus blast (in blue), versus large blast (in green).

The pattern is actually pretty simple: BS10 centre is as accurate as BS9 blast, is as accurate as BS8 large blast (and so on down). Essentially each step up in blast size is equivalent to a one point increase in BS.

So there you have it – I thought I had all the BS covered, but there was still more to do; …always more to do.


Going Deep

Deep striking is a high risk/reward technique that can get your units anywhere on the table, in one fell swoop.  But when things go wrong, they can go very wrong, and on more than one occasion I’ve lost a 225 point unit of Obliterators to a bad scatter.  For that reason I often take some 3 man chaos terminator squads so I only risk 105 points for a chance at a cheeky melta shot.  But how should I be placing them when I deepstrike?  Consider the following:

Chaos Lord Harleck Wynne faces a wall of Imperial Guard tanks.  He has to deepstrike his terminators, as any walking squad or vehicle will be wiped out as it approaches.  Where should his combi-melta armed Chaos Terminators be placed to minimise the risk of mishap? Where should they be  placed to maximise the chances of getting into melta range? Where should they be placed to get a balanced risk of mishap versus melta range?


Ok, so deep striking is governed by scatter dice.  It’s a 6 sided die with two ‘HIT’ faces, and four faces with an arrow.  Place your model where you want him, and roll.  If you get a HIT then you land on target, if you get an arrow, then you scatter 2d6 inches away in the direction indicated by the arrow.  Because the distance is governed by 2d6, the distance follows a pattern already described here such that results of 7″ are the most likely and 2″ and 12″ are the least likely.

The arrows complicate matters as they don’t comply with the discrete probability that I normally use for these calculations, but we’ll touch on that later.

So, with two HIT faces out of 6, we have a 33% chance of landing on target, and a 67% chance of scattering.  If we ignore direction for a moment, then we can take a look at the odds of how far you’ll deviate from your intended location:

That was pretty much as far as my analysis went until quite recently.  This approach clouded my thinking, as I saw it as a straight up question of distance, so I may as well get super close to the enemy as the ‘most likely’ scatter distance was 7″.  Case closed, right?

Wrong!

If you don’t get a HIT, then it’s all about the arrows.  Let’s imagine a model with a 25mm base put on the table in his desired deepstrike position.  He can scatter up to 12″ in any direction, so lets consider a 25″ wide circle as the total space we could end up in (e.g. up to 12″ to left + 1″base + 12″ to the right gives us the 25″, see below).

Time for a fancy graph.  So I plot an area of 25″ by 25″, and represent the probability of landing at a particular point as a height, so we we get a sort of mountainous terrain where the highpoints are where you are likely to land, and the lowpoints are where you are unlikely to land.  In the first instance lets look at the widest case.  So you have a 33.3% chance of landing on target (i.e. a HIT), and a 66.6% chance of scattering.  See below:

As you can see in terms of a single point, the target at the centre is far and away the single most likely final destination.  In fact the difference is so extreme that all you can see of the scatter is some light ‘fuzz’ in a ring around the centre.  So the first point to note is that if you do scatter it would appear that you could end up pretty much anywhere in that 25″ circle we described earlier.  But that’s not particularly enlightening, so lets take a closer look at the ‘fuzz’.

I now remove the HIT from the chart, and the scale can then be changed to show the variation in odds for the scatter results.  It’s worth noting that I didn’t solve this analytically so we don’t get a smooth and pretty set of results, we get a somewhat noisy set of peaks and valleys.  But it’s still good enough to gain some insights and is still essentially representative of how it works in reality.

So as you can see from the dark blue peaks, the most likely area to scatter into is a ring around the target point, (specifically a ring with its edges about 5″ to 9″ away from the target point).  This is an expected result from our knowledge that the scatter follows the same triangular shape of the old 2d6 chart.  Do note how low the odds of landing at any particular point is: about 0.2% to 0.4%, tiny!  Working through the numbers, here’s a simplified version:

So this is a lot of exposition and I haven’t addressed the opening question at all!  What about those terminators?

Based on the calculations above, I carved out the probability of landing in a ‘safe’ area depending on how far away you place the terminators.  But that in isolation is not enough.  We want the terminators to land within 6″ of the tanks to get some hot melta goodness going.  So here I’ve plotted the odds of landing safely for a given distance, and also the odds of ending up safe AND within melta range for a given drop point (i.e. the point you selected to drop at, not where you end up after scattering).  So on this graph the x-axis is the distance from the tank wall you place the model initially, (i.e. before rolling for scatter).

The results weren’t quite what I was expecting going in, though do bear in mind that these findings are only true for the specific set up of the question – this graph isn’t a general rule for all deep strike situations!

So, what does this show?  Well, assuming the parking lot of tanks is the only other unit in the area then unsurprisingly the further away you place them the less likely they are to scatter on to the enemy and mishap.  But playing it safe won’t necessarily get you within the all important 6″ melta range.  Here’s the interesting bit, I had originally thought that putting the terminators 1″ away from the tanks would get you the highest probability of being in melta range with a trade off of slightly higher odds of mishap.  But I was quite wrong.  The odds of getting safely in melta range stay pretty flat if you originally place the model between 1″ and 6″ away, but the odds of a mishap are about 45% at 1″ but fall to about 25% at 6″.  So the tradeoff I mentioned in my opening question, doesn’t really exist – you can play it (relatively) safe and still go for the close range shot.

Lesson learned, drop those terminators about 5 or 6 inches away and you’re playing the right odds.

So how about a more general rule of thumb then?  This specific case aside, how do we make better deepstriking decisions on the fly?  In my opinion, the best general approach is to think in terms of area.  Visualise the 25″ circle around any particular drop point (some assistance here and here), and then look at the friendly and enemy units in that circle.  Now imagine a 1″ buffer around enemy units, and try to estimate what fraction of the circle’s area is covered by all the units and that buffer.  This is key to estimating the risk.

I’ve illustrated a few simple examples below; in each case the centre of the circle is where you initially place the model (i.e. before rolling for scatter), and the red areas have units or other features (such as impassable terrain) that would cause a mishap (don’t forget the 1″ buffer around enemy units!).  Do note I’m assuming that the centre point is a legal placement.  Also note the maths below isn’t quite exact, but is good enough for tabletop guesstimation.

So there you have it – even deep striking right up into someone’s face is not quite as risky as it looks.

Tune in next time when I apply all of this to blast weapons…


Stacking the Odds Part II

The previous post on the probabilities for making lots of saves generated a bit of interest, and (as usual) some clever readers pointed out scenarios that should bear further analysis.  Altmann from the Penny Arcade forums asked:

“Can you work in the probability of making 4+ feel no pains as well? I know we’re getting into NASA shit but I’m curious”

Followed by Joe “Maynard” Cullen (of WarHeads fame) who pointed out that some wargear items also add complexities:

“The Wolf Tail Talisman gives a 5+ invulnerable save that happens before the armour save”

So in a similar fashion to my ultimate Ballistic Skill chart, I took it upon myself to rank the performance of a variety of armour types with rerolls, with Feel No Pain (FNP), and just plain regular saves.  This will give some insight into the relative merit of the saving throws we normally encounter in 40k.

As with Stacking the Odds Part I, the chart shows how likely each type of save is to take no casualties from an increasing number of saves.

So chart number one:

This charts the various types of save (and combinations) showing the odds of taking no casualties for up to 6 saves (I cut it off at 6 as about half of them approach zero at this point).  The legend on the right shows the ranking from best to worst with a 2+ rerollable save being the best, and a regular 6+ save being the worst.  The sharper eyed in the audience may notice that some of the save types listed in the legend don’t show up in the graph – namely “5+ FNP” and “3+ FNP”.  Rest assured this isn’t an error, it is simply that they are coincidentally covered by other save types that perform identically.  So a 5+ with Feel No Pain save works out the same as a regular 3+ save, and a 3+ with Feel No Pain save works out the same as a regular 2+ save.

Or do they?

The calculations are correct, but you need to interpret the data in the context if the game itself.  So saving on a 5+ followed by a 4+ for FNP is statistically the same as a 3+, until you get hit by an AP5 or AP4 weapon, at which point all you get is the FNP, which is just a 4+ save (as you can see from the chart is a lot worse than a 3+).  The FNP could also be blocked by a high strength AP- weapon, leaving you with just a 5+.

In a similar vein, the 3+ with FNP is the same as a 2+, but what if they got hit by a battle cannon? the 3+ is negated by AP3, and (assuming we’re talking about T4 units) the FNP is negated by the instant death rule.  So no saves of any kind!  But a squad of terminators would still get their 2+ and (assuming that 5 are wounded by the blast) they have a 40% chance of taking no casualties at all!

So what about those opening questions?  Well Altmann was interested in the effect of FNP on terminators, and to show the difference I’ve scaled the number of saves taken up to 30, and dropped the weaker save types.

The effect is actually pretty strong, if we take say 20 saves, a regular terminator squad has only a 3% chance of being unharmed while the FNP terminators have an 18% chance (again assuming that they aren’t hit by something that negates FNP!)

Joe’s suggestion of the Wolf Tail Talisman (WTT) is charted below. Assuming the squad has power armour, then it works out quite close to (but slightly better than) a 4+ reroll, and worse than a 2+ save.

This should let you compare the various save types available to you, but don’t forget the context of how saves and FNP get negated! If there are any other save types you want to see included, then please do leave a comment.


Stacking the Odds Part I

This is a topic I touched on briefly before, but I think it’s time for a more comprehensive review.  As I’ve said previously, many players have bad instincts for how odds ‘stack up’, and I often hear comments like ‘if a terminator has to make 6 saves, you’d expect one to fail’.  Time to challenge some assumptions.

A squad of terminators come under bolter fire and have to take 6 saves, what is the probability that they take no casualties? A squad of marines come under a similar hail of bolter fire and also have to take 6 saves, what is the probability that they take no casualties?

At tournaments, and during club play, you may often hear cries of consternation as someone can’t believe that their opponent just made X number of saves in a row.  I think this ties in to certain types of (erroneous) expectations.  Nothing in this game of dice is certain; and you can never get a 100% guarantee of success.

That sounds pretty trite, and taken purely at face value, it is.  But I’m trying to get at something a little deeper.  If a terminator has to make ten saves, or a thousand saves, there is always a chancing of making it, but the odds don’t scale in the way that people expect.  Simply put: a thousand bolter shots is not one thousand times more likely to kill a terminator than one bolter shot; nor is ten bolter shots ten times more likely. As the number of saves to be taken increases, the odds of survival go down in an exponential way (for the non math types that means they start high, and gradually get lower but never quite reach zero).

Here’s one I prepared earlier:

This graph shows how terminator armour and power armour behave as the number of saves to be taken goes up.  Terminator saves are in red, and marine saves are in blue.  The x-axis represents the number of saves that have to be made, and the y-axis shows the odds of the squad taking no casualties for the corresponding number of saves.

So this gives us the answer to the opening question.  If the termies have to take 6 saves, then there’s a 33% chance of them taking no casualties (i.e. find 6 on the x-axis and then look at the corresponding point on the y-axis for the red line).  The other group aren’t so hot, if the marines have to take 6 saves, then there’s a 9% chance of them taking no casualties.

If we extend the analysis a bit, the marines have only a 1% chance of taking no casualties from 12 saves, whereas the terminators have a more respectable 11% chance.  Even at 18 saves the terminators still have a 4% chance of walking away without a scratch.  Now 4% may sound like very long odds, but in truth its not far off the odds of getting a ‘perils of the warp’ result for a psyker.  So not something you’d see a lot, but hardly beyond belief.

One (slightly esoteric) point to note is that this is a ‘memoryless’ system.  This gets a bit subtle, but what I mean is that the current odds aren’t affected by what happened before.  So if a squad of terminators all survived 6 saves last turn and are now facing 6 more saves in this turn, the odds don’t stack to 11% (i.e. for 12 saves), they stay at 33% (for 6 saves).  Whatever happened in the past doesn’t affect your current action.

Now that we’ve covered some specifics, I’ve taken the liberty to graph the behaviour of saves from 2+ to 6+ when having to make up to 6 saves in one block.  Each coloured line represents a corresponding type of save from red for a ‘terminator’ save, blue for power armour, and so on through to the grey line for a 6+ save.

This follows the same pattern as the previous, it just shows more armour types.  But as an interesting illustration, based on the graph check out the following:

A terminator squad taking 6 armour saves has a 33% probability of taking no casualties

A terminator squad taking 6 storm shield saves has a 9% probability of taking no casualties

A terminator squad taking 6 cover saves (4+) has a 2% probability of taking no casualties

A terminator squad taking 6  invulnerable saves (5+) has a 0.14% probability of taking no casualties

Do keep this in mind the next time you fire your hydras at my obliterators!


The Joy of Penetration

5th edition games often feature a lot of vehicles, and understanding how best to crack open that armour and feast on the goo inside can be a crucial skill for any player.  With that in mind, here’s a question:

After some poor manouevring by your normally brilliant tank commander, your shiny new Leman Russ gets hit by a Lascannon, and by a Battle Cannon.  Which is more likely to penetrate?

The ambush continues, and the Russ is hit by a Demolisher Siege Cannon, and a Multimelta at close range.  Which of these is more likely to penetrate?

For most weapons, armour penetration is relatively straightforward, i.e. weapon strength + D6.  So, for example, a Krak missile can get results from 9 to 14 (not bad against a Rhino, but smacks of desperation against a LandRaider).  However many of the best Anti-Vehicle weapons don’t follow such a simple pattern.

For example, ordnance weapons roll two dice and pick the highest to add to the weapon strength, and melta weapons at half range get to add 2d6 to the weapon strength. This produces results that aren’t as simple, and can have a couple of quirks.

How does this apply to our terrified tank commander?

The interesting thing about the opening questions, is that it depends on what side the tank is hit from.

Let’s take the lascannon versus battle cannon first.  For a rear shot (AV10) the lascannon is more likely to at least glance, but the battle cannon is more likely to penerate.  For a side shot (AV13) the battle cannon is more likely to at least glance, but the lascannon is more likely to penetrate.  From the front (AV14) the Lascannon is the clear winner and is more likely to glance, and more likely to penetrate.  Not that the lascannon is remarkable against AV14 (with <20% chance of penetrating) it’s more that the battlecannon can’t pen Av14 at all!

It wouldn’t be a WarHamSandwich without some charts so let’s take a look at the comparison.  The graph shows the odds of getting at least ‘X’ for an armour penetration roll with each weapon.  So to get the odds of penetrating AV13, we look at the 14 result as this gives us the odds of getting at least 14 (the 13 result would get the odds of at least glancing).

So we can see a crossover from 10 to 11, and from 13 to 14 where the relative efficacy of each weapon against that AV switches.

So what about that second volley of shooting?
Again it depends on the angle. The Demolisher is more likely to penetrate against side and rear, but once we get to the front this flips and the multimelta becomes more likely to penetrate.  The crossover is clearly shown in the chart, below.

So what’s the point Vanessa?  There certainly are some comparisons where you can unequivocally say weapon X is better at anti-vehicle than weapon Y, but often it’s not so black and white.  With a bit of analysis you can pick the best tool for the job at hand.  Here’s a comparison of some of the common anti-vehicle weapons so you can gauge the relative merits against various armour values.

That said, this analysis doesn’t look at the end-to-end process, from hitting to penning to what you get on the damage chart.  I guess that will have to wait for next time…


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