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Leveraging Quantitative Analysis in AoS


Veillotron
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“Quantitative analysis” is over-selling it… I have build myself a tool - a very simple Excel spreadsheet - to make sense of all the special abilities and better understand the average damage each unit can deliver and take in the course of a battle.

I am building a Stormcast army. In the context of matched play, I wanted to get a sense for return on points invested offered by each unit.

Recent threads made me think that some in the Community might enjoy / benefit from this tool, and so I decided to share it.

To make it easier to navigate, I’ll limit the original post to an intro, and through replies go into further details on specific topics – initially 1) mechanics / rationale of the analysis, 2) review of the results for the Stormcast army.

 

But before jumping into it, a small disclaimer:

·         The intent is not to reignite a debate on maths within AoS; I am just hoping that this will be useful to some.

·         My goal in building the spreadsheet was to clarify the damage output potential and survivability of each unit, not to create the most powerful army. I am in no way, shape or form a “power gamer” – I sometimes play games at my local store, but my main adversary is my 9-year old son J.

·         For clarity’s sake, I strongly believe that strategy (especially in regards to deployment and movement) is key to the game, that the game cannot be summarized to a few simple numbers.

·         The ‘tool’ does not take into account bravery, movement, the impact of abilities on other units, defensive spells, etc.

·         This is very much a back-of-the-envelope analysis, with a few underlying assumptions impacting the output (I will go over these later).

·         I would be surprised if I was the first one to do this. Thank you in advance for letting me know if there is a more complete model available.

·         I would think that most will want to skim / skip the “Mechanics” section, as it is relatively obvious stuff…

·         There are bound to be some mistakes in the file (misunderstanding of rules, typos, etc.) Thank you for letting me know if you see any (hopefully the Excel file loads up properly)

AOS_DO_AW_analysis.xlsx

 

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Concept of Damage Output and Adjusted Wounds

Despite not being a power gamer, I have been having fun recently going through the intellectual exercise of building “efficient” armies and trying to maximize the return on points invested. I work in finance so I do like to play with numbers…

Stating the obvious, stats and special abilities (most of them) can be translated into probability of inflicting damage upon an enemy. To make sense of all the varying number of attacks, probability of hitting, wounding, etc, I decided to try to calculate the Damage Output (“DO”) each unit should do per turn on average, as well as their Adjusted Wounds (“AW”) – their ability to absorb damage.

 

Calculating Damage Output  - Approach and Underlying Assumptions

 The following will be obvious to the majority, but worth going through to avoid any confusion…

The DO of each attack is calculated in the straightforward fashion (using the Lord-Relictor as an example):

DO_Calculation.png.1af8c0c277e5c9e12af17aab724fafa3.png

The Save Ratio corresponds to the chance of the wound generating damage, and therefore depends on the Save characteristic of the target. For this analysis, I have assumed that targets always have a Save of +4, therefore 50% of the Wound going through.

The % shown under Save Ratio corresponds to the Rend impact on the Save Ratio.  In the example, Rend of -1 increases the chance of the wound going through by 17% (1/6) to 67%. 

Mortal Wounds attacks have a Wound Ratio of 100% and a Save Ratio of 50% (50%+50% = 100% of the Damage going through).

A Weighting factor has been applied to attacks. 3 Main reasons:

1.        To reflect the probability of such an attack occurring. In the example below, on a Hit roll of 6+ a Dractoh’s Calws & Fangs will generate D6 damage – on average 3.5 wounds. 5 out of 6 times (83%), this attack with generate 0.89 damage per attack; 1 out of 6 times (17%), it will generate 3.11. The weighted average DO for this attack is therefore 1.26.

DOweigthingexample.png.22c3303612b5f4bf9ab7652ed54afbfc.png

2.       To reflect a different composition in a unit. The average DO is calculated on a per model basis. Therefore, in calculating the Weighted DO for a unit of 5 liberators with the Prime yielding a Grandhammer, I have taken 80% of the standard DO, and 20% of the Prime’s DO.

3.    Missile Weapons / Spells.   This is a tough one. A unit can do twice as many melee attacks as Missile attacks. However, a) that is not always the case and b) there should be a premium attached to being able to hit first and from afar. So I’ve decided to weight those attacks at 75%. Folks with a different viewpoint can of course change the value in the spreadsheet themselves… 

 

The Total DO is achieved through adding the weighted DOs of all spell, missile and melee attacks per model X minimum number of models ion the unit.

The Total DO is an important value, illustrating how many wounds on average a model will dish out during a full turn. In the context of Matched Play, more important is the DO Per Point (“DOPP”) Ratio. The DOPP formula as is follows:

Total DO per Unit / Points Per Unit X 100.

DOPP for me is the most interesting stat, as it really shows the value for point (purely from a fighting perspective, excluding of course any other ability such unit might have). Depending on the different types of armies I have been thinking of building, I have found this quite useful.

 

Key Assumptions / Methodology worth noting:

  • -       The Damage Output is always calculated at full strength for both Monsters and Units.

  • -       For Save Roll, all target assumed to have Save characteristic of 4+ and no save for MW.

  • -       I have tried to use the formation yielding the greatest damage output (for example, the Prime Liberator with the additional attack is wielding a Grandhammer).

  • -       I have calculated separately DO when units have different characteristics (for example, for Fulminators when charging, and Liberators when attacking enemy with 5+ wounds) – those are recorded as Max DO in the file.

  • -       For certain characters, I had to make specific assumptions which might not represent the reality (ex: how many units will a Knight-Heraldor hit with his trumpet blast on average every turn? For a lot of those, it was pure guessing work, I must be wrong in many cases.)

  • -       D3 and D6 have been replaced by the averages (2 and 3.5, respectively); therefore the analysis does not give more value for attacks yielding a fixed as opposed to a variable output.

  • -       Total DO for a Unit is assuming that every model can fight within a turn – this is not always the case

For those downloading the file, the first tab shows the summary output; the second one contains the formula / detailed calculations.

 

Calculating Adjusted Wounds  - Approach and Underlying Assumptions

 Adjusted Wounds is a better reflection of a unit’s ability to survive than just its Wounds characteristic. It takes inot account its Save characteristic, as well as special ability to gain wounds back and/or re-roll failed saves.

The formula used is more straightforward than calculating DO:

AWformula.png.524fde4aeef411142a28ebaa1d7fa2ad.png

For example, a Knight-Heraldor 5 Wounds and a Save of 4+ on average will require 10 AW before being killed: 5 / (1-50%) = 10.

A Knight-Questor is much tankier. He also has 5 wounds, but he benefits from his 3+ Save and ability to re-roll failed saves. On average, he will save 89% (4/6 + 2/6 *4/6) of the wounds directed at him. That results in 45 AWs. So in battle, on average the Knight-Questor can sustain 4.5x more successful hits than the Knight-Heraldor before going down.

Purely from a survivability standpoint, the difference is even starker when looking at the AWPP ratio (AW Per Point ratio – same principle as described for the DOPP ratio above). With the Knihgt-Heraldor costing 120 points and the Knight-Questor costing 100, the Knight-Questor offers a AWPP ratio of 45.0 against 8.3 for the Knight-Heraldor, 5.4x higher. Of course, the trumpet of the KH comes at a premium, but it is still an interesting comparison.

I have also calculated the Adjusted Mortal Wounds (“AMW”) and the AMWPP ratio. This is not an area of strength for the Stormcasts. With no protection from MWs, both KQ and KH have an AMW of 5, making them equally vulnerable to MW attacks.

I had to make assumptions in certain cases. For example, most Mortarchs have the feaster of souls ability, allowing them to heal 2 wounds at the end of each combat phase if they slay any model. That means that per turn, a Mortach could heal up to 4 wounds. Over 5 turns, that would represent a maximum of 20 wounds. This is not a scientific approach – I cut the figure in half. So the Mortarchs will show a higher AW and AMW, but this is based on them killing a model every turn for 5 turns. In reality, they are more fragile than the figure would imply, since they could be wiped out at a much earlie stage of the battle should they suffer enough MWs. Folks downloading the file could always change some of these assumptions to what they feel appropriate.

 Some models (such as the Mourngul) have an impact on their enemies’ hit roll – those modifiers have been taking into account in the Save Ratio calculation. For example, a model reducing an enemy’****** Roll by -1 would see its AW increase by 17% (1/6).

 

 

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Stormcast Results / Observations

Summarized in the table below are the DOPP/ Max DOPP and AWPP / AMWPP for every Stormcast unit. The Var (%) colomn corresponds to the variation in % to the total Stormcast average. I have split the units by type (I have separated cavalry units from the rest of the elites, as they are in my opinion a different type of unit) (apologies for the small print - easier to download the excel file...).

StormcastOverview.png.9bde9f73afa8929db22c083c3e7a5c07.png

I recently finished the analysis and need to spend further time reviewing the output, but here are some early & random thoughts:

 

Stardrake lovers rejoice (maybe?)

·         I remember reading some folks lamenting that it was hard to justify including a Stardrake in their team. The analysis would seem to suggest otherwise…

·         You are getting your money’s worth from a damage perspective. The DOPP and Max DOPP ratio are in line with the army’s average.

·         Moreover, the bonus which is not reflected in those numbers however is that a) the Stardrake can do all of its damage per turn (vs. all unit who will not have all their models engaged in battle every round, reducing the real potential DO) and b) the benefit of having one unit being able to dish out on average 14 wounds per turn.

·         It is a very mobile unit (move 12”, can fly) with great reach (Rain of Stars covering the whole board)

·         Where the Stardrake is weaker is on the AW side. Without any artefacts the Stardrake’s AWPP ratio is 24% lower than the average; his AMWPP ratio is even worse, 2.7 being 52% below the average.

·         However, when one invests so much points into one unit, it would be warranted to give him the tools to succeed… Make him your general and give him Armour of Destiny as an artefact (saving Wounds and MWs on a 6) and Shielded by Faith Command trait (Saving MWs on 5 and 6) and his survivability level goes back to almost normal, c.10% below the average.

·         I will get unto this later, but if you keep a Lord Castellant and/or a Lord Relictor nearby, he can become even tankier.

 

The Celestant-Prime is more compelling than I had though originally

·         Similar to the Stardrake, I have read comments on the CP from people wishing the play him but not being able to justify it. We constantly hear the term ‘glass canon’

·         The CP is indeed a glass canon – before any modifier, his AWPP and AMWPP are 60% below average – the CP offers the smallest return in the whole Stormcast army!

·    Going against him is the fact that one has to wait until the 3rd round to have him start doing some serious damage.

·    On the flip side, once he’s on the board on the 3rd, he’s one of the highest-hitting models/units within the SE. Combined with the fact that he can be placed anywhere on the Board, one can almost guarantee the destruction of the targeted unit.

o   Getting 3 turns out of the CP is not that bad – the large monsters / behemoths often get picked on early and do not last the 5 full turns…Having him on the Board for the last 3 might be better than the first 3…

·         One way to improve the CP’s longevity is to commit to only use his Orrery ability to change Save rolls , hopefully saving 2 wounds per turn. Doing so improve the CP/s AWPP ratio from 6.7 to 9.4

·         I have not come up with a satisfactory solution re his survivability, but 2 things that would go a long way is to have a Lord Castellant and Lord Relictor nearby.

o   The Lord Castellant’s light can have a huge impact on the the CP’s AWPP – basically doubling the amount of hits he can take before going down (and that is excluding the potential wounds healed on 7+ rolls). With the CP using his orrery ability on defence and benefiting from a Lord Castellant’s light, his Total AW and AWPP jump to 58 and 16.1, respectively. 16.1 would be above average…

o   The key problem remains his vulnerability to MWs…

 

 

Lord Celestant on Dracoth vs. Lord Aquilor

·         I put those 2 heroes aside because they are the mounted heroes (excluding the behemoths) and command a much higher price than the rest…

·         I really like the Lord Aquilor model. I bought it, am looking forward to painting it and putting it on the board.

·         However, looking at things rationally, if am somewhat disappointed by his value / ratios.

o   Someone fielding a larger vanguard team will be able to make good use of his command ability; the flexibility it provides is definitely worth the premium.

o   However, it does not make sense to take the model on its own. For an additional 20 points, the LCOD offers 50% more AW (31.5 vs. 21) and 20%+ higher damage output

o   The Lord Acquilor’s below average fighting stats mean that even if he moves quickly into enemy territory, it will be at a risk and he could get wiped out faster than the LCOD.

 

o   The LCOD seems the logical choice for me.

 

 

 

 

 

Choose your Heroes on abilities

·         Not surprising, but the Heroes command a premium, and offer lower value for point on all 4 tracked ratios (the average for AWPP is higher by 16%, but that is mainly driven the stats on the Lord Castellant and Lord-Relictor’s 40+ ratio, both based on the two heroes using their defensive abilities on themselves)

o   Having said that, the ratios are around 10% lower than the average, which is not massive.

·         The Knight-Vexilor with Pennant has seen his value drop significantly with the recent rules tweak. His pennant is still useful and can guarantee the move of one unit (vs. the Scions of the Storm which is riskier). But if you get him, you have to be comfortable that you are spending 140 points for that ability. In terms of damage output, his DOPP and Max DOPP are the lowest of the whole army, 80% below average; his AWPP and AMWPP are 33% lower than the average.

·         A lot of folks have been talking about taking the Knigth-Venator with the Luckstone… I’m not onboard.

o   I love the Venator, but his Star-Fated Arrow is soooo overrated IMHO.

o   The 4-9 damage is very attractive, but on average it will generate only 2.4 wounds per attemp – not the monster-killer I initially thought I had.

o   Even with Luckstone, the Star-Fated Arrow will generate on average 4.5 damage. This is good, it has range, but it is a one-off.

o   Putting things in perspective: 2 Knight-Venators + one Luckstone = one-off 6.9 wound. 1 unit of 2 Fulminators (for the same point price) can deliver that every round, and you still have a magical item to give to another hero…

·         The Knight-Questor:

o   I was surprised to see that, even against heroes, his attacking output is 34% lower than the average. In my head, this was some sort of kamikaze hero who didn’t have a multiplier effect for troops, but that you could send against a big monster to do some damage.

o   One can do that, but his real value comes from his tankiness. His 45 AWPP ratio is the highest out of the whole army; his 45 total AW is only 3 less than a Drakesworn Templar!! For this, I would see him more as a defender / somebody to hold a position.

·     The Lord Celestant remains one of my favourites -  great value for money, his AWPP and AMWPP are almost in line with the army’s average, he hits 25% harder than average – AND he has such a great multiplier ability (I would have my general use the Command trait enabling the LC to use his...). His only weakness is his lack of mobility…

·         The two I love the most however are the Lord Castellant and the Lord Relictor.

 

 

Using Lord-Castellant and Lord Relictor to support the "Heavy" units

·         I could easily see an army list with 3 lord Relictors and 3 Lord Castellants.

·         I have shown the stats for the Lord-Relictor using either the Lighting Storm or the Healing Storm on himself – the difference in AWPP is impressive at over 40, jumping by 20+ points over the course of a game.

·         Same thing for the Lord Castellant: his AW and AWPP are above 40, all because of his light. And what is great with the light, unlike the Lord Relictor, is that the benefits are guaranteed.

·         Those 2 heroes are great, but their abilities could have an even greater impact on the hard hitters – Stardrake, the Celestant-Prime, LCOD, and all the Fulminators / Concussors/etc.

·         Having a pair of those two following around say 2 units of Fulminators and a Stardrake would make those so much stronger/tankier.

o   Taking a Stardrake already powered up by the Armour of Destiny artefact and Shielded by Faith Command trait; should a Lord Castellant shine his light on him every turn, his save rate would be 97% ((5/6)+((1/6)*(5/6)) for normal wounds, giving him an AW total of 691… Basically the only way to kill him would be through MWs…

·         And even if your opponent decides to take them out, they will redirect firepower from your big units… Anyway, that is what I am thinking at the moment…

 

 

 Cavalry units offer some of the best value in town

·         Almost on all ratios these units perform much better than the average:

o   their damage output is c.25% higher than the average

o   their AWPP is 10% above.

o   their only flaw value-wise is being less resistant to MWs than the average by 18%

·         Similar to the Stradrake, these stats are really impressive especially given the fact that a) they are extremely mobile and can cover a lot of ground, b) they have good shooting capability and c) their low unit count means that it is more likely that 100% of the unit will be able to strike.

·         They do not hit as hard as the Paladins – but their mobility is a huge plus.

·         Given the rise of shooty armies, I would favour at the moment the Fulminators.

 

 The Vanguard come at a significant premium…

·         What I said for the Lord Aquilor is valid for the rest of the Vanguards – they are uber cool models and their ability to deploy is really interesting (especially with the ability of the Lord Aquilor to do it during play), but that ability comes at a significant premium.

·         The only unit that offers great value (on top of the ability to move) are the Vanguard Palladors. They are very comparable to the Dracothian guard units…

 

 

Retributors and Liberators remain awesome

·         Both the retributors/paladins and liberators continue to offer amazing value for money.

·         remains riskier. Because of this I prefer to them the cavalry units… The 2 starsoul maces per 5 paladins make them such a dangerous force. Their main problem remain mobility. With Scions of Storm they is somewhat resolved, but their deployment

·         The Liberators continue to offer one of the best value ratio in the army: delivering damage 16-27% higher than the average is good, but they are uber-tanky, with an AWPP and AMWPP 50 and 80% above average. That is some serious value for money…

 

 

If I had to build a 2,500k army right now, I might go for…

·  1 Lord Celestant on Stardrake                            - 600pts                    

o   General

o   Shielded by Faith Command Trait

o   Armour of Destiny artefact

·  2x Units of 4 Fulminators                               - 960pts                              

·  3x Lord Castellants                                         -300pts                                          

· 3x Lord Relictors                                             -240pts                                              

·4x Units of 5 Liberators                                   -400pts                                 

· Total:                                                       2,500/2,500                                                                   

 

 

 I look forward to your feedback / having my ideas get crushed ;-)

 

Edited by Veillotron
typos
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I think math can only take you so far in a game like this, at least while you're only doing single factions. You'd probably need to do full comparative analysis in order to get a perfect picture, for example a lord castellant becomes essentially worthless against clan skryre lists, liberators become significantly worse against sylvaneth and any hero with less than 7 wounds and no MW save will get much less value against beastclaw raiders. I also think you're undervaluing movement a bit.

That said these are great tools to begin to unravel what makes a unit good/bad in the game and to give people something to think about when building lists.

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14 hours ago, Veillotron said:

“Quantitative analysis” is over-selling it… I have build myself a tool - a very simple Excel spreadsheet - to make sense of all the special abilities and better understand the average damage each unit can deliver and take in the course of a battle.

 

I am building a Stormcast army. In the context of matched play, I wanted to get a sense for return on points invested offered by each unit.

 

Recent threads made me think that some in the Community might enjoy / benefit from this tool, and so I decided to share it.

 

To make it easier to navigate, I’ll limit the original post to an intro, and through replies go into further details on specific topics – initially 1) mechanics / rationale of the analysis, 2) review of the results for the Stormcast army.

 

 

But before jumping into it, a small disclaimer:

 

·         The intent is not to reignite a debate on maths within AoS; I am just hoping that this will be useful to some.

 

·         My goal in building the spreadsheet was to clarify the damage output potential and survivability of each unit, not to create the most powerful army. I am in no way, shape or form a “power gamer” – I sometimes play games at my local store, but my main adversary is my 9-year old son J.

 

·         For clarity’s sake, I strongly believe that strategy (especially in regards to deployment and movement) is key to the game, that the game cannot be summarized to a few simple numbers.

 

·         The ‘tool’ does not take into account bravery, movement, the impact of abilities on other units, defensive spells, etc.

 

·         This is very much a back-of-the-envelope analysis, with a few underlying assumptions impacting the output (I will go over these later).

 

·         I would be surprised if I was the first one to do this. Thank you in advance for letting me know if there is a more complete model available.

 

·         I would think that most will want to skim / skip the “Mechanics” section, as it is relatively obvious stuff…

 

·         There are bound to be some mistakes in the file (misunderstanding of rules, typos, etc.) Thank you for letting me know if you see any (hopefully the Excel file loads up properly)

AOS_DO_AW_analysis.xlsx

 

 

You are a math wizard!  Thank you for having too much time on you hands.  I'd love to see something like this for each major army played and how they stack up.  

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I understand that it's hard to deal with some of the aspects like bravery and movement, but without those I think that any mathmatical model is going to be undermined to the point of uselessness, and all you can do is model a one on one standing fight, which frankly most people can eyeball.

It's great that people want to push the envelope and develop useful tools.

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16 hours ago, Veillotron said:

If I had to build a 2,500k army right now, I might go for…

·  1 Lord Celestant on Stardrake                            - 600pts                    

o   General

o   Shielded by Faith Command Trait

o   Armour of Destiny artefact

·  2x Units of 4 Fulminators                               - 960pts                              

·  3x Lord Castellants                                         -300pts                                          

· 3x Lord Relictors                                             -240pts                                              

·4x Units of 5 Liberators                                   -200pts                                 

· Total:                                                       2,500/2,500                                                                   

 I look forward to your feedback / having my ideas get crushed ;-)

 

Because Stormcast were already powerful enough before a netlist.

Still good info.

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2 hours ago, Auticus said:

http://www.louisvillewargaming.com/AOSStats.aspx

These raw values are what I used to come up with Azyr Comp's formula for pointing, before GHB came out and rendered fan comps irrelevant.

Thank you for the link - whoa, you have gone through every model in every Alliances... Out of curiosity, how did you establish the efficiency ratings?

 

2 hours ago, BURF1 said:

I think math can only take you so far in a game like this, at least while you're only doing single factions. You'd probably need to do full comparative analysis in order to get a perfect picture, for example a lord castellant becomes essentially worthless against clan skryre lists, liberators become significantly worse against sylvaneth and any hero with less than 7 wounds and no MW save will get much less value against beastclaw raiders. I also think you're undervaluing movement a bit.

That said these are great tools to begin to unravel what makes a unit good/bad in the game and to give people something to think about when building lists.

I think that we are on the same page... Yes, math can only take us so far. And re movement -  I am not undervaluing it a bit, I simply am not taking it into account at all in this analysis. But as you said, I am seeing this as a tool to simplify the damage output and tankiness of each model, taking into account all of their stats and 1 re-rolls... To make an informed decision there are many other factors to take into account - abilities (especially the ones with "multiplier effect"), movement, etc.

If I see that 2 units have similar tankiness and damage output but one moves 12" vs. 4" for the other one, than of course the former will look more attractive (which is why I am more attracted at the moment by the Stormcast cavalry units)

2 hours ago, Taketheskull said:

The title of this article makes me want to smash it!

Thanks for the feedback. I was expecting your response - the fact that it came from someone with a Khorne avatar made is soooo much sweeter!! ;)

 

2 hours ago, Lord Aquillor said:

You are a math wizard!  Thank you for having too much time on you hands.  I'd love to see something like this for each major army played and how they stack up.  

Thank you for the kind words. I am far from being a math wizard, this has been much more of a simple data computing exercise than building complex algorithm...  I am happy you appreciate it. Over time I'd like to run the exercise for other units (as I am building also a Tzeentch army, they will be next on the list...)

1 hour ago, Lucio said:

I understand that it's hard to deal with some of the aspects like bravery and movement, but without those I think that any mathmatical model is going to be undermined to the point of uselessness, and all you can do is model a one on one standing fight, which frankly most people can eyeball.

It's great that people want to push the envelope and develop useful tools.

Yup. Same as my response above to BURF1, I agree that this is only part of the equation. Maybe worth repeating that I am rather new to the game, and lack the experience that many on these boards have. I guess for an experienced gamer it must be a lot easier to eyeball / get a sense of the worthiness of each model. For me it was a useful exercise as I got to know better each warscroll, and get a better sense of what is the real damage potential for each using simple probabilities...

 

 

 

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4 minutes ago, SuperHappyTime said:

Because Stormcast were already powerful enough before a netlist.

Still good info.

Cheers!

I'm assuming that a netlist is some sort of power/tanky list?  I wouldn't put too much value in that list to be honest - it was completely done in a vacuum and would probably get blown to pieces in a real game scenario...

I promise that I'll share the results once I've bought a Stardrake + 3 other boxes of Dracothian guards and tested the formation against my formidable 9-year old nemesis;):$

I did have fun through trying to find a way to fit a Stardrake into a list which could be competitive...

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17 hours ago, Veillotron said:

If I had to build a 2,500k army right now, I might go for…

·  1 Lord Celestant on Stardrake                            - 600pts                    

o   General

o   Shielded by Faith Command Trait

o   Armour of Destiny artefact

·  2x Units of 4 Fulminators                               - 960pts                              

·  3x Lord Castellants                                         -300pts                                          

· 3x Lord Relictors                                             -240pts                                              

·4x Units of 5 Liberators                                   -200pts                                 

· Total:                                                       2,500/2,500                                        

 

Where are you finding Liberators at 50 points for 5?

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2 hours ago, Auticus said:

Efficiency is basically points of damage put out per GHB point or points of damage one can take before taking a wound per GHB point.

The premise being that if I have a 200 point unit that does on average 5.5 wounds a turn against any given thing (find the average vs every type of save) and I have a 100 point unit that also does on average 5.5 wounds a turn, the 100 point unit is doubly efficient because it costs half less for the same output.

Got it, thanks

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