Raise the Banners! Are they worth it?

[Jedra]

Inspired by Serathail's post on the Banner of Resilience I thought I'd do a deeper look at some of our banner options (original post here: viewtopic.php?t=103120). Serathail looked specifically at how the BoR increased survivability of your unit, and when it was better to just spend the points on more troops. The answer is "it depends", largely on the strength of attacks you receive, but it's probably not worth it on a unit that costs less than 300pts, except Tiranoc chariots where the higher starting T means it's a bit better (still need 3+ Tiranocs to be worth it).

But... survivability isn't everything and WHEN you lose wounds matters (e.g shooting matters less than combat), and as you can get at most two banners in a unit there's also a question of if it is BETTER than alternative options. I've plunged into the deep end trying to puzzle through this and need to get it out of my head so here's a bit of a brain dump so that hopefully I can start thinking about something else .

I looked at 3 things:

1. Survivability: How much damage can you soak
2. Combat Result: How likely are you to win a combat
3. Damage: How much damage will you do (Ranged/Close Combat

Then I assessed the following banners with different units (brackets indicate which of the above it affects):

• Banner of Resilience (1,2)
• War Banner (2)
• Battle Banner (2)
• Razor Standard (2,3)

With Survivability only affected by the Banner of Resilience, and damage only affected by the Razor standard, most of my comparison focused on Combat Result. I did not directly look at the more intangible benefits of things like the rampaging banner which are impossible to assess like this.

Assessing Combat Result boost
The fundamental question I tried to ask here is: how likely is it to win a combat against a hypothetical enemy?

The basic method I use is to create a "Combat Matrix" (see below). I use a binomial distribution to calculate the chance of the unit delivering X wounds to their target, in both directions. Then combine them into the matrix to calculate the combined probability of e.g. elves killing 3, dwarves killing 1, and combine with the differences in static resolution to work out the chance of a Win/Draw/Loss for one round of combat. I had to simplify a couple things: first, I assumed the Battle Banner gave a flat combat res boost of 2. Not realistic, but the maths to accommodate variable static res hurt my brain and this is already complicated enough. Second, I reduced the number of attacks the 2nd attacker gets by the minimum number of wounds they would receive 50% of the the time (e.g. if in 50% of combats they'd have received 2 or more wounds, reduced by 2). This slightly undervalues going first and doing lots of damage. Again: the alternative broke my brain. The image below shows several win matrices as an example (not all of them - and note that I realised after taking this image that I got some of the Static Res figures wrong. This is corrected in the following table but not on the matrix image)



My hypothetical enemy is Dwarf Warriors with Hand Weapon, Heavy Armour and Shield (WS4, T4, S3). Why? The low int made it easier for me... I then made comparison units of Spearmen, Lothern Seaguard, Swordmasters, Phoenix Guard and White Lions. I probably should have done Sisters, but I didn't. Each unit is matched to as close over to 300 points as possible (e.g. 302 vs 307 allowed, 299 would get another model added), not including any command except a standard bearer. When the unit gets a standard, models are dropped to keep matched to ~300 points. Some scenarios also have a BSB added to both units: the elven BSB is using either the Battle Banner or the Banner of Resilience. The Dwarven BSB is using a rune than gives the unit a 5+ ward save, and the Dwarven unit has a +1 combat res rune (equivalent to the war banner), except in the "no unit banners" comparison that I used as a baseline.

I arranged the unit to have the "maximum frontage that didn't risk losing rank bonus", e.g. that would still have the same rank bonus if they lost 4 wounds. Unfortunately for the first pass with SM and WL I arranged them to have only 1 rank bonus, maximising attacks - this was a mistake, I think they suffered for it - the extra attacks were never worth the extra static res. I haven't included this in the results below, and re-ran them with the war banner and frontage set to maximise combat res (they do worse if you don't do this). I wish I'd run the Spearmen and Phoenix Guard with Razor Standard, but did not... and probably won't go back to this question, I don't think it would matter based on what I'm seeing with the Seaguard results. I also calculated the net wounds difference and total kills, as this is important to consider for subsequent rounds of combat. I ignored the damage from the BSBs themselves as it wasn't interesting for the calculation: let's assume they are locked in a challenge and both whiffed. If either BSB died it would totally change the results of the below, and low-wounds low-volume high-damage attacks are much more volatile.

The results are as follows:



(I just realise that I missed the scenarios where I ran with unit banners but no BSB... it's not super interesting. For most of them because I'm adding War Banner to both units it is the same as None-None. Phoenix Guard unsurprisingly win more when they have the battle banner vs war banner)

Looking at it the conclusion is perhaps... not that surprising: the thing that has the biggest effect on chance to win the combat is having lots of Static Combat resolution. None of our troops attack enough that boosted killing was better, and the banner of resilience absolutely helped win combats by reducing deaths, but not as much as the battle banner. The 5+ Ward Banner the Dwarves have is just better (at similar cost). The Resilience banner will help in subsequent rounds by slowing how much you die but it's only really saving about 1 wound per round *in this case* (heavier hitters it will save more).

What's not factored in is the shooting that leads up to to this... banner of resilience will have reduced deaths by shooting before combat, so depending on opponent you may have arrived with more troops. This becomes very hard to model! Additionally this is only one, middling quality not very heavy hitting opponent - I suspect the Resilience banner will be better against opponents with more attacks, but I've run out of steam to do that analysis right now (I might pick one for comparison, we'll see...)


Assessing Damage
The only thing that affects damage is the Razor banner so we can look at this alone. As shown above, it absolutely boosts damage, but on average by less than 1/wound per round in the above case, so not enough to be better than the War Banner for combat resolution. Unlike the War Banner though, it also affects shooting attacks - making it great on the sea guard, in theory.

So in the hypothetical scenario above of facing off against the dwarves running at you as fast as their little legs can carry them, let's assume you get 3 rounds of shooting off - 1 moving and shooting (long range), 1 stationary (long range), 1 stationary (short range). Comparing the Razor Banner to War Banner or no banner (the difference being you spent the banner points on more troops), the Razor Banner boosts yours kills enough to mean that you'll be reliably getting 1-2 more kills on the way in. Nothing terrible, but also not exactly the most amazing thing in the world... although this does mean that 50% of the time you will have killed 5 or more dwarves, likely knocking off a whole or most of a rank which is nothing to cry about. In the above scenarios, the dwarves would either have to change front (likely leading to more shooting) or lose attacks, so actually that could really matter.

However the Razor Banner is better the higher your opponent's toughness is (assuming they have armour 5+ or better), because at T5 or more, ALL of your attacks will get AB (at T4 50%, at T3 33%). The same three rounds of shooting against a T6 2+ save large target (e.g. dragon and rider) has you nearly tripling the wounds inflicted (ward save not included here - a 5++ save would reduce both by 1/3 so the relative advantage is the same). 3 rounds of shooting without moving is perhaps a little unrealistic against a target like this, but I wanted to be able to compare directly to the dwarves situation.



So the big problem with assessing the razor banner is... it depends on what you're shooting at. Low toughness low armour save it's minimal or nothing, high toughness high armour save it's a big boost. The good thing about this is that it's best against the things that are hardest to deal with.

Assessing Survivability
I don't have much to add here to the previous thread: as mentioned, there's no point in using this for survivability in a unit under 300pts of foot troops. One thing to consider though is that the effect is increased on Tiranoc chariots - which includes the BSB if they are on said chariot. An option would be to have the BSB on Tiranoc, either in a unit of Tiranocs (giving them both survivability and combat res), or attached to a unit of infantry or cavalry. For the infantry your only options are really Spears or Phoenix guard, and Phoenix guard seem to the most logical to me (a 300+pt unit of spears is still pretty weak even with the banner as shown above), and this allows the Battle + Resilience combination for a very solid anvil unit. Also the boost to damage from the Tiranoc BSB and good survivability of the BSB unit are quite important for a unit in that role! I ignored the BSBs in my Combat Res analysis, but the extra T and 4 wounds on the Tiranoc suggests that in a challenge against non-monster units they'd have a good shot at coming out on top. Silverhelms would be another good candidate, but our unit/character rules prevent other options.

Conclusions

To wrap up this rather long post.... so what. Here's my handy summary table:



The biggest surprise to me from this is that the Banner of Resilience is not as good as I thought it was - at least relatively speaking. If you have to choose between it and the Battle Banner, any combat unit will likely be better off with the Battle Banner. If you can take both though it's not bad to have at all and is definitely worth the points. The War Banner did surprisingly well for the price, and unless you have good reason to fill up your banner slots with something else it should probably just be an auto-include in the list.

I don't think the Razor Banner has any value over alternative options for anything except Seaguard - other low-AP units don't have the volume of attacks to make it worth it. The main benefit of it on the Seaguard is for allowing ranged shots to bypass armour of high T targets, which are pretty dominant in the meta. If you're facing only low-armour targets it's next to useless and you may do better from the war banner if it's not already in use.

[Ramesesis]

I really love the Battle banner with my Phoenix guards. I was thinking that Resilience would be better but maybe not. Still, I could bring both.

[Csjarrat]

I really love the Battle banner with my Phoenix guards. I was thinking that Resilience would be better but maybe not. Still, I could bring both.

That makes for one hell of a points sink though!

[Turion Rilyaloce]

I run battle banner on a Sun Dragon BSB. Helps him operate independently against small to mid units, and getting flank charges on a duel charge against a block goes a long ways towards getting a flee.

I run Razor Standard on a block of Seaguard from 22-35 strong. So looks like my instinct was there and it’s pretty obvious I guess that they can utilize it in more than one phase.

[Axiem]

I'm glad to see more data analysis on the forum -- love it!

Some feedback:

- The second table you shared is hard to read: the second and third column/sections appear to both indicate wounds inflicted, but is one of these suppose to be wounds suffered (in return)? I'm not understanding clearly what I'm looking at;

- In your summary table, what qualifies "Good" "Average" "Excellent" -- in your mind does this correlate to something like 10-25-35% improvement, or something else? Do you read Excellent as the same thing as "Auto-Include";

- In the choice between Battle and Resilience for the BSB on Tiranoc Chariot, how do you qualify the decision between picking either of the Excellent choices;

- Have you thought of modeling the comparisons similarly on Woodsmen (via BSB);

Nice work -- keep it up!

Kind regards,

Axiem

[Jedra]

Thanks folks. I need to try and redo the spreadsheets that underpin this: as I was finding the method as I went it's not currently in a state that I can go back and easily run alternatives, which is why there are some gaps that I didn't realise I needed to plug until too late... I also intend to make it easier to run both "defence" and "attack" scenarios at the same time. That will likely not be soon though. if you do have specific questions though now's a good time to answer them as I can consider how to weave that in...

I'm glad to see more data analysis on the forum -- love it!

Some feedback:

To answer your questions:

"The second table you shared is hard to read: the second and third column/sections appear to both indicate wounds inflicted, but is one of these suppose to be wounds suffered (in return)? I'm not understanding clearly what I'm looking at"

The middle part is showing "Net Wounds Inflicted" - this is the non-static combat res part (as no flank attacks etc happen), and is essentially "Elven Kills - Elven Losses". The second part is "Kills Inflicted" only, regardless of losses. In both cases, the easiest way to read them is with the colour scale: green areas are what you will expect to see on most turns, yellow probably will come up once or twice a game and red are technically possible but might happen once for all players across a whole tournament, at most.

The reason I included them (but I realise I didn't discuss this) is that winning 1 round of combat is only OK, you need to break the enemy and if they don't lose troops they will just keep FBIGO. What it shows is that Phoenix Guard and Spearmen in particular are absolutely just tarpitting this: they are winning combats but not inflicting (or receiving much damage). Again not a huge surprise to confirm that these are anvil units. Likewise it shows that while the razor standard isn't better than the War standard for *winning* a round combat, it is increasing both net and absolute kills .The Seaguard with Razor Standard may be less likely to win that round 1 combat than the Spears with War, but (factor in shooting) they've probably killed 10 dwarves to the Spearmen's 1 by that point, for similar losses. And of course in news that will totally shock everyone: the swordmasters and white lions kill more, despite not necessarily *winning* more in the process. Even when they lose, they have probably killed more dwarves than they have lost.

While none of that is *surprising* it is important to note when making choices (and explaining it has made me realise something about White Lions banner choices - will put that in the next section)


In your summary table, what qualifies "Good" "Average" "Excellent" -- in your mind does this correlate to something like 10-25-35% improvement, or something else? Do you read Excellent as the same thing as "Auto-Include"

Because the banners aren't all directly comparable as they benefit different things, it's not easy to put a general "X% improvement on it". Because banner choice is 1:1 match with a unit (i.e. 1 and only 1 unit can have a given banner) everything needs to be relative, and the top chart is useful for understanding *what* the benefit is so you can match the banner to the role of the unit, whereas the bottom chart shows a general assessment of it it makes sense to consider for that unit at all.

Everything "Good" or "Excellent" in either chart is unambiguously better than just buying more bodies, once you hit a good sized unit that will be maximising it's rank bonus and have a good frontage. Something is "Excellent" if it is unambiguously better than the Good choice. Choosing between two equal choices is going to come down to questions about your army comp, the role of this unit, whether you want the same banner elsewhere and of course how many points you have to spent (e.g. you may think the war banner is better value for the PG than the Battle Banner but you might have already put it in a unit of Lions and the Battle Banner on your BSB).

In the choice between Battle and Resilience for the BSB on Tiranoc Chariot, how do you qualify the decision between picking either of the Excellent choices

The real two choices in the below are for Seaguard (War Banner or Razor Banner) and BSB Tiranoc (Battle or Resilience). For the seaguard, it's likely you will have given the War Banner to another unit - if not, the question comes down to whether you want to maximise damage or its ability to anvil. FWIW I will be sticking with the Razor standard: it makes the Seaguard a valuable part of a combined threat against ridden monsters, with enough range to threaten them whenever they get within charge distance of your front lines. Also of course very useful against anything high T and high armour, which our lists traditionally struggle with: they are still a decent anvil and will likely at worst FBIGO from a first round of combat, and even with the war banner they will need support for later rounds.

For the BSB-Tiranoc combination... it is honestly tough and I do not think there is an obvious answer, which is why I put the both at excellent. . I *think* I'll be opting for Resilience myself in most situations but I am not sure. The BSB is much more likely to be receiving high-strength attacks than your regular troops, and by the time you factor in the unit + a BSB on Tiranoc you're talking about 600pts+ getting covered by the banner. With the BSB directly contributing to Static Res already, as well as the boost to combat res, I think keeping them alive is more important and with the boosted wounds from being mounted it makes resilience a strong personal buff that also boosts the unit.

That being said, if you expect to be receiving a lot of S6 attacks to the unit, the resilience banner is next to useless as a unit buff unless the BSB is also in a unit of Tiranocs. In general, the main things that would make you want to opt for the Battle over the Resilience come down to army comp - yours and theirs. Resilience boosts better against lower S attacks (down to S2 for normal units and S3 for Tiranocs), and gives no protection against higher S attacks (S6 for normal, S7 for Tiranocs). So what unit is it going in and what S attacks do you expect to receive? This isn't an easy answer. If it's in with infantry you might have less control over this as well (i.e. end up receiving charges) compared to Tiranocs (more likely to get the charge in). I'd not as well that it was less beneficial to winning combats for some units over others - the White Lions (and presumably Lion Guard) are a good example.

So yeah... I don't have a neat answer for that one. Both are great choices and which will be better depends on the details of the battlefield.

Have you thought of modeling the comparisons similarly on Woodsmen (via BSB)

Yes - and sisters, and other enemies, and modelling both attack and defence... as above I need to

That being said I had a quick look at the woodsmen with the Razor standard just now as it was easy. No tables but the summary is as follows.

In shooting:
Their performance against a T6 dragon will look exactly the same as the Seaguard. Against the dwarves, much like the seaguard it boosts their kills by about 15%, meaning with the 3 rounds of shooting they will usually have killed 7 or more dwarves with the Razor Standard before combat (6 without). It's a little harder to assess how many shots you will key with Skirmish though so that's one major caveat with this - the 15% boost in general is accurate. The big benefit is against T5 2+ monsters where it basically doubles their damage: with Razor they're going to be reliably knocking off 1-2 wounds in most rounds of shooting, 25% of doing 2+ wounds on (35% odds of nothing) on the Stand & Shoot. Without it, they're at 45% odds of doing 0 wounds even at short range (vs 25%) and will plink off most rounds of shooting.

In Combat:
The benefit will be very marginal, depending on what you're fighting. Unless they have a 4+ save it will do nothing, and unless they have a high toughness it will not kick in for most of their wounding hits. With their lack of ANY static res, it is likely the Battle Banner would be better for them as they get no rank bonus and no close order bonus, so start at -3 (assuming you took a unit standard and they have a BSB), which is a hard point to come back from.



Changed Assessment
I've thought about the banner assessment, and would like to up my assessment for White Lions and the War Banner from "good" to "excellent". This is the MOST important unit to boost Static Res for for two reasons: first, as Open Order it's coming in with a disadvantage. The extra kills it gives compared to Swordmasters are not enough to make up for this. But more importantly, it *needs* to be charging constantly and so winning a combat is more important for the Lions than the Swordmasters (or any other unit). Therefore I think it is critical to improve static res. This has also made me realise that I hadn't fully appreciated that the change for Lion Guard to Close Order (from the Open Order white lions) is bigger than I thought: I had thought that the removal of Open Order would make it harder to setup the charge (which it is), but it also increases the chance that they'll get to charge in later rounds of combat which is probably more important - most combats don't end on the first round after all. Adding the War Banner to them would be similarly beneficial.

So... if you are taking Lion Guard or White Lions, they are the best unit to give the War Banner to. If not... put it on some other unit that will be in combat a lot.

[Prince of Spires]

interesting write-up. I'm suprised at how good the war banner is and how bad the razor banner is. For the battle banner I'm not sure if / how you factored in the cost for the BSB, but that might change the results one way or another. I guess the resilience banner is more situational, though maybe that's not surprising. I think everyone just wanted it to be better because T4 elves!

I'm actually surprised at how well WL are holding their own. Though I guess they're facing their ideal opponents more or less. Did you factor in the killing blow for the SM?

[Serathail]

Very nicely put together!

Here's the real question though: How does the banner whose name shall not be spoken perform? Surely a 55pt standard would at least keep up with a 25pt one .-.

[Ielthan]

Very interesting analysis. I've found the battle banner to be excellent. I run mine on a mounted BSB, with a unit of 7 silverhelms with the war banner in 4x2. It puts out a massive amount of combat res, reliably, over a small frontage that lets you tag in e.g. a chariot prince or a dragon or something. The idea is even if the unit doesn't hit very hard (though now with the addition of 2 rings of fury to the unit it actually does), it reliably wins combats (first charge too) and forces the enemy to take breaks tests, even if it hasn't caused much damage. In this edition I've found people really underuse their BSB's compared to before (high elves are a bit unusual in that we still use ours a lot), and static combat res is underrated with only +2 rank bonus.

I'd be curious to see analysis of battle banner combined with a war banner on different units. I suspect on dragon princes and phoenix guard in particular it will be really strong, but I like it with silverhelms as it makes our mediocre core really very good.

The other thing I've been trying out is spearmen with shieldwall and the Banner of Iron Resolve. It basically makes them unbreakable the first time they're charged, which is actually really good and opens up some interesting ways to use them. E.g. deploying 21 wide (21 + 7 tooled up silver helms is exactly 500pts) gives you this massive "net" with which you can "shrink" the enemy's battlefield by basically a 1/3. It's very handy against evasion or fast armies, as none of them want to get bogged down for even a turn and get flanked. Usually I just deploy them in 5x4 or even in marching column and move them up the field towards enemy cavalry very aggressively. Directly they won't kill anything, but they are an excellent anvil for their points; guaranteeing you give ground rather than fbigo is fantastic at stopping cavalry and chariots.

Would it be possible to do analysis of this banner?

[Jedra]

One flaw I've realised with the above is my choice of opponent being relatively low damage. Thinking it through, i would expect the banner of resilience to perform better if the % wound reduction means it reduces wounds by 2 or more. With only 8 attacks, this ain't it. But say 21 attacks from Frenzied chaos warriors? It might. I'll need to improve how i model initiative for that to work.

Regarding BSB cost...i didn't factor it in, because i added an equal cost bsb to the dwarves at the same time (and then ignored them both). Bringing in multiple unit profiles really complicates the analysis, which is why i didnt run the combat result stuff for Cavalry or Chariots

Assessing the more unique banners like iron resolve, Ellyrion, Rampaging is harder... I'll think about it. Rampaging at least should be pretty easy to assess

[Jedra]

Very nicely put together!

Here's the real question though: How does the banner whose name shall not be spoken perform? Surely a 55pt standard would at least keep up with a 25pt one .-.

I'll have to run this when i redo the method it's so bad i forgot it existed! I might try to answer the question "how wide does your unit need to be to beat the war banner (spoiler alert: i think it's going to be ~20)

[Prince of Spires]

One flaw I've realised with the above is my choice of opponent being relatively low damage. Thinking it through, i would expect the banner of resilience to perform better if the % wound reduction means it reduces wounds by 2 or more. With only 8 attacks, this ain't it. But say 21 attacks from Frenzied chaos warriors? It might. I'll need to improve how i model initiative for that to work.

Maybe just run 2 scenario's. One where they go first and one where they go second.

Though of course, against anything S6 and over, the banner of resilience does nothing.

[Ielthan]

One flaw I've realised with the above is my choice of opponent being relatively low damage. Thinking it through, i would expect the banner of resilience to perform better if the % wound reduction means it reduces wounds by 2 or more. With only 8 attacks, this ain't it. But say 21 attacks from Frenzied chaos warriors? It might. I'll need to improve how i model initiative for that to work.

Regarding BSB cost...i didn't factor it in, because i added an equal cost bsb to the dwarves at the same time (and then ignored them both). Bringing in multiple unit profiles really complicates the analysis, which is why i didnt run the combat result stuff for Cavalry or Chariots

Assessing the more unique banners like iron resolve, Ellyrion, Rampaging is harder... I'll think about it. Rampaging at least should be pretty easy to assess

I think Rampaging is a really underrated banner, I used to run it on dragon prince in 8th ed and it was great, less important now tbh with countercharge though, but still nice when combo charging from distance. Otherwise it's BSB in silverhelms or maybe on a chariot.

[Jedra]

Not meaning to pick on Axiem but I saw this comment in a couple of army threads:

Only thing I would think about is taking more Sea Guard before adding on Razor Standard. I think the breakeven is something like 24 Sea Guard. Personal preference.

So of course it got me wondering: is this true? Wellllllll..... it's complicated but probably not.

The issue with assessing Armour Bane is it is highly depending on the opponent, so it's almost impossible to assess in the abstract. The short version is: the tougher your opponent (both higher toughness and higher armour save), the bigger % damage increase you'll get from AB. Here's a quick table for different opponents: each table shows for a set armour save (6+, 5+, 2+) and then each column is a different toughness with that save (2-5). 6+ behaves the same as 5, and 1 behaves the same as 2 (not that it comes up). Bottom line is the % increase in chance to wound.



So as you can see, tough opponents get a major boost from the Razor Standard - weaker opponents it doesn't give too big a boost. But even against relatively weak T3 5+ AS opponents (which is a pretty common low-level), the RS becomes worth it at around 15 troops, not 24.

Here's the damage profile for each. Left is with razor standard, right is without. The % shown is the odds of doing that many wounds with a single round of attacks. What I have done is look for how many models you need on the right to get a similar damage profile to the left. The issue of course is that you don't get 1 more attack for every person you add, so I've shown a range of situations:
LTS = Large Target Shooting (Everyone shoots)
VF = Volley Fire (I have changed frontage as the unit gets bigger)
M&S = Move & Shoot (this is also the assumed frontage in shooting mode)
CC = Close Combat (assumes shooting frontage - 5, and of course is assuming you attack before losing anything...)
MCC = Minimum Close Combat (assumes the whole front rank died and you only get your supporting attacks)




So in short: for a T3 5+ target, at about 15 troops with razor standard is basically the same as just spending on more bodies. As soon as you start shooting at tougher targets the razor standard becomes much, much better. And importantly: LSG don't really need a boost against low toughness/armour troops where they do pretty well already. It works perfectly for them precisely because it makes them better against the things they are worse at dealing with naturally.

If you know your enemy, that's probably the more important factor to consider than size of the unit: facing wood elves? Yeah probably don't get the razor standard. Brets? Seems like a good idea. Warriors of Chaos? Auto-include, take it every time.

[Axiem]

So in short: for a T3 5+ target, at about 15 troops with razor standard is basically the same as just spending on more bodies. As soon as you start shooting at tougher targets the razor standard becomes much, much better. And importantly: LSG don't really need a boost against low toughness/armour troops where they do pretty well already. It works perfectly for them precisely because it makes them better against the things they are worse at dealing with naturally.

Thanks for this -- always good to see more data.

I think the key here that (unless I'm misreading) might be missing here is that equivalent percentages between the scenarios really only matters when you result in an additional wound. For instance, assuming hitting on 4s, and wounding on 6s, I need 12 more shots to get another 6 to trigger from the AB. Small, single digit percentage likelihoods with small numbers of attacks adds variance into the process.

There's something about the VF scenario of 13 models with Razor Standard against 22 Models without that seems off -- maybe it's the 2+ Armour that's skewing things (probably is -- would be curious to see the 3+ Armour instead). There's also probably something to be said about considering the total number of attacks of BOTH a Stand and Shoot, along with the Spear Attacks.

What are your thoughts?

Love the detail -- keep it up!

Kind regards,

Axiem

[Jedra]

I should have said that the figures include an assumption of a 4+ to hit for both ranged and close combat - realistically on the table that's what you'll be seeing most of the time and it doesn't really change the conclusion if sometimes it's 3+. CTW (chance to wound) is the total ToHit * ToWound * ToNotSave.

Each stage as we all know from picking up and tossing dice reduces the chances to actually do some damage.
Now.. the reason AB is producing such a large increase in tougher targets is two fold:
1) the higher the toughness, the higher % of wounds are 6s (if you need 6+ to wound, ALL wounds are AB)
2) the higher the Armour value, the bigger percentage increase in rolls that bypass it (2+ save goes from 1/6 to 3/6 for a 300% increase, vs 150% from a 5+)

This is why the T4 2+ gets such a dramatic boost - 50% of wounds get AB, and each AB wound is 3x as likely to bypass armour.

So don't think of it as "how many attacks do i need to get a 6". You will be getting 6s some of the time during normal rolling, and AB makes those rolls more useful.

The simple calculation people generally do is multiply ctw with # attacks for "average wounds". I don't like this oversimplification as it doesn't reflect the chaos on the battlefield: 1 guaranteed wound and 10 with 10% ctw are each average wounds 1, but the 2nd one will do more than 1 wounf 25% of the time (and 0w 35% of the time)

What the 2nd coloured charts use is the binomial distribution of probability. The short version is it shows the chance of scoring that many woulds on any given toss of the dice. This factors in to hit, rolling random 6s and 1s etc.

What it says is that 15 seaguard with razor banner shooting at a large, t6, 2+ save target will do 1 or more wounds 50% of the time, 2+ 13% of the time. 20 seaguard without banner on the same target will do 1 wound 12% of the time and can basically forget about 2+ wounds.

You make a good point on the combined s&s and first round of combat. When i have time I'll sit down and run those numbers, as well as some plausible shooting scenarios, against a few hypothetical enemies to see how it stacks up. I suspect it will be dramatically in favour of RB though.

[Axiem]

I should have said that the figures include an assumption of a 4+ to hit for both ranged and close combat - realistically on the table that's what you'll be seeing most of the time and it doesn't really change the conclusion if sometimes it's 3+. CTW (chance to wound) is the total ToHit * ToWound * ToNotSave.

That makes sense -- it also makes sense if you're taking the toughest, highest armor comparisons. It's going to come down to what the "average" comparison is then. I'll look and see if I can find the other post where someone got to 24 as the breakeven to compare methodologies, but my guess is they were comparing to a much softer target.

Keep up the good work! Will be curious to see your next addition!

Kind regards,

Axiem

[Jedra]

Ok... another banner comparison for LSG. I didn't look at "what point is it worth it", but rather whether if you have unit of LSG of equal points around ~20 troops, what banner is best. The units are matched in points within 5pts, so more expensive banner = fewer troops. All units had a frontage of 10 for shooting and 5 for combat, except the No Banner scenario which was 11 and 6. I also decided to pretend that the Banner of Lothern was only 50pts and could be taken on an LSG unit just for funsies as I wanted to see how bad it really was (spoiler alert: bad).

I made 3 hypothetical enemies which I think cover it well. These are 3 core units all around the same point cost:
1) 9 Chaos Knights (T4, 3+ Save)
2) 18 Chaos warriors (T4, 5+ Save)
3) 20 Chaos Marauders (T3, 5+ Save)

Each "scenario" gives a plausible level of shooting, followed by calculating the maximum (no losses) and minimum (only supporting attacks) damage profile for the first round of combat.

For cavalry (1 & 3), the LSG get the following shooting rounds:
Long range, Move & Shoot (Front rank only, -2)
Long range, no move (Volley Fire, -1)
Stand & Shoot (Front rank only, -1)

For infantry (2) they have an additional Short Range, No Move (Volley Fire, no modifiers)

(side note: I'm not sure this is the best tactical plan but that's not in this analysis)

This produced a lot of hard to read data, so I've summarised it here. "Shooting" is the total damage before combat starts, "1CC: Min" is the combined damage from the Stand & Shoot and first combat round assuming the whole front rank dies, and "1CC: Max" assumes no one dies. The actual calculation to factor in what they're likely to lose is very complicated and I didn't try here. Each columns shows the total probability of doing that or more damage (Shooting) or Combat Resolution (1CC Min/Max). Note that the shooting damage shows different wound values for Knights as they are much tougher. The left shows the rank from best (1) to worst (5) for the banners in the Shooting or Close Combat round).



Let's put some narrative behind that as the numbers aren't the most obvious. The three banners that seem like decent options are the Razor Standard, War Banner and Banner of Confidence

Razor Standard
In what I think is not a surprise to anyone, the Razor Standard is the best performer here. In terms of shooting, the Razor standard is the best performer against all enemies, without contest. It's also the 2nd best performer in combat against tough enemies, although against the Marauders there was a 3 way tie between the Razor and Lothern (note: the table shows None as well, but this is actually slightly worse). It's a tie because they are different and no way to decide: if you lose the front rank, Lothern is better. If not, Razor is better (but the difference is so small you won't notice it on the tabletop).

The Chaos Marauders are about the worst case unit possible for the Razor Standard's shooting (low T, low AS and fast moving) and it's still the best performing. Basically, as long as the enemy has armour, the Razor Standard is going to be worth its points for a unit this size. For the knights, in 18% of games this is enough shooting to have killed more than half of them - 29% of games they'll have killed half the warriors before combat. For all other options you can basically forget about that possibility. For all 3 enemies, the RS unit will have knocked off a rank of the enemy in most games before combat starts - the odds of doing the same against the Marauders are still pretty good for all banners, but it's basically off the table for the two tougher opponents. The extra AB is better than extra bodies, which doesn't equate to many more attacks at these numbers.

War Banner
The War Banner obviously has no benefits for shooting, but is the clear winner *in terms of combat resolution* against all enemies, although it is killing less than the others. Basically the extra attacks/damage struggles to top the flat +1 reliable boost. On the table though the WB will be better at holding for the first round, but the lower damage does mean they're more likely to be fighting a larger unit - hard to predict how this will end up being overall.

Confidence
This banner is a little complicated. Basically, it only adds a boost when it really counts: the Stand & Shoot, which then boost the first round of combat. This means it does better against lighter armoured and/or faster moving units as it means the S&S is a bigger portion of the shooting attacks, and the extra wounds are likely to translate to kills if armour/toughness isn't high. Obviously if the unit doesn't get attacked, this doesn't have any benefit at all...


What Not To Take
Let's talk about the low performers: Banner of Lothern and no banner

Lothern (even at 50 points) was truly terrible value. In short, you gained fewer supporting attacks than you lost from having fewer troops or weaker blows. The only thing good about it is that the supporting attacks are guaranteed - it actually did better in the 1CC:Min scenario, because the minimum number of returning attacks higher. Unfortunately because of the bizarre decision to have no benefits for shooting in the Banner of Lothern, any slight combat benefits are offset by the worse shooting from the lower troop count.

With the frontage assumptions I had, the extra troops meant that in the "max" scenario Lothern and No Banner actually ended up with the same number of attacks in close combat + S&S, so they perform the same in that group. No banner might have done slightly better if I upped the assumptions on frontage - e.g. 12 and 7. I think at that wider frontage, it would be better than the banner of Lothern (although greater risk of losing static CR).

Conclusion
Take the Razor Standard on your LSG. If you have 2 units and you expect the 2nd unit to see CC, take the War banner on the 2nd one if you aren't using it, or Confidence if you are.

Don't take the Banner of Lothern under any circumstances: you'd be better off just spending the points in core instead of in character.

[Prince of Spires]

Thanks for the write up and the analysis. It's clear and consise, and it also gives a good direction.

Lothern (even at 50 points) was truly terrible value. In short, you gained fewer supporting attacks than you lost from having fewer troops or weaker blows. The only thing good about it is that the supporting attacks are guaranteed - it actually did better in the 1CC:Min scenario, because the minimum number of returning attacks higher. Unfortunately because of the bizarre decision to have no benefits for shooting in the Banner of Lothern, any slight combat benefits are offset by the worse shooting from the lower troop count.

With the frontage assumptions I had, the extra troops meant that in the "max" scenario Lothern and No Banner actually ended up with the same number of attacks in close combat + S&S, so they perform the same in that group. No banner might have done slightly better if I upped the assumptions on frontage - e.g. 12 and 7. I think at that wider frontage, it would be better than the banner of Lothern (although greater risk of losing static CR).

This definitely confirms that the whole thing is simply unplayable. The fact that you actually get the same number of total attacks with CC + S&S as having no banner at all just shows how ridiculous the thing is. I'm willing to forgive the army book writers a lot. But this thing is just so bad it just shouldn't have existed.

[Jedra]

This definitely confirms that the whole thing is simply unplayable. The fact that you actually get the same number of total attacks with CC + S&S as having no banner at all just shows how ridiculous the thing is. I'm willing to forgive the army book writers a lot. But this thing is just so bad it just shouldn't have existed.

Don't forget: this is EVEN WITH me assuming it was 50pts and could be taken as a unit banner! I was also probably slightly conservative on the extra file for no banner, you could probably risk an extra person against opponents that aren't so heavy hitting, in which case no banner trumps Lothern.

If it also applied to shooting (and was 50pts) it might be worth a second look. If it applied to other supporting attacks, maybe you'd have some value on a unit of PG. As it is there is literally no reason to consider taking it, ever. It is so bad it hurts.

[Serathail]

Well they did errata the berserker blade (for whatever reason) so maybe we get lucky and they change the thing's effect to a full rank and reduce its price to 50pts one day.
Though seeing as how every FAQ question for HE has been answered thus far I'm half expecting them to specify that you actually cannot use the banner of lothern during a turn you moved .-.

[Prince of Spires]

This definitely confirms that the whole thing is simply unplayable. The fact that you actually get the same number of total attacks with CC + S&S as having no banner at all just shows how ridiculous the thing is. I'm willing to forgive the army book writers a lot. But this thing is just so bad it just shouldn't have existed.

Don't forget: this is EVEN WITH me assuming it was 50pts and could be taken as a unit banner! I was also probably slightly conservative on the extra file for no banner, you could probably risk an extra person against opponents that aren't so heavy hitting, in which case no banner trumps Lothern.

If it also applied to shooting (and was 50pts) it might be worth a second look. If it applied to other supporting attacks, maybe you'd have some value on a unit of PG. As it is there is literally no reason to consider taking it, ever. It is so bad it hurts.

If it was 50pts, allowed the whole unit to volley fire instead of half, and it gave a full extra ranks of attacks, then maybe I could see a point. Even then that's expensive for S3 attacks. If PG could take it, then also maybe.

[Anduil of Elithis]

This definitely confirms that the whole thing is simply unplayable. The fact that you actually get the same number of total attacks with CC + S&S as having no banner at all just shows how ridiculous the thing is. I'm willing to forgive the army book writers a lot. But this thing is just so bad it just shouldn't have existed.

Don't forget: this is EVEN WITH me assuming it was 50pts and could be taken as a unit banner! I was also probably slightly conservative on the extra file for no banner, you could probably risk an extra person against opponents that aren't so heavy hitting, in which case no banner trumps Lothern.

If it also applied to shooting (and was 50pts) it might be worth a second look. If it applied to other supporting attacks, maybe you'd have some value on a unit of PG. As it is there is literally no reason to consider taking it, ever. It is so bad it hurts.

If it was 50pts, allowed the whole unit to volley fire instead of half, and it gave a full extra ranks of attacks, then maybe I could see a point. Even then that's expensive for S3 attacks. If PG could take it, then also maybe.

Or allow volley fire even if the unit moved. There were a lot of avenues to develop this banner, which makes one understand even less how this could make it into print.