Math With Birdhunter - Dragonhide Banner (2011)

Introduction

Hello everyone!

I was doing a team battle with a friend of mine who plays beastmen, and I showed him the banners. He noted that the dragonhide was nice, but I quickly pointed at the 60 points and we agreed that was too much. Shortly after I thought: is that even the case? So I started calculating. Halfway through I found a thread on here that shows some of the numbers, but I decided to post mine since I included more variables as well as cost effectiveness.

Explanation of the calculations:

I decided to exclude the BSB itself since his performance is the same for IG’s and Bulls, although he will almost certainly reduce the cost effectiveness of the unit. I also did not continue after T6 since the IG’s numbers are just repetitions of the bull’s, and such strong units are very rarely seen in normal battles. I did not include impact his because of the uncertainty of it’s strength or actual hit. The stomp attacks are also left out, since it is uncertain how many for example the bulls would get. So bear that in mind, these are the attacks only! I used a to hit roll of 4+, since this is most common. Here I decided not to add in failed LD tests. Lastly I kept the number of bulls and Ig’s the same throughout comparing them. I used 16 models here for the optimal results, but in the conclusion I explain how large the units need to be.

Against T1 of T2:

No banner (16 Bulls)

48 attacks
48x(1/2)=24 hits
24x(5/6)=20 wounds
Cost effectiveness: 0.036 wounds/point

Banner (16 Bulls)

48 attacks
48x(7/12)=28 hits
28x(35/36)=27,2 wounds
Cost effectiveness: 0.044 wounds/point

No banner (16 Ironguts)

48 attacks
48x(1/2)=24 hits
24x(5/6)=20 wounds
Cost effectiveness: 0.020 wounds/point

Banner (16 Ironguts)

48 attacks
48x(7/12)=28 hits
28x(35/36)=27,2 wounds
Cost effectiveness: 0.035 wounds/point

Against T3:

No banner (16 Bulls)

48 attacks
48x(1/2)=24 hits
24x(2/3)=16 wounds
Cost effectiveness: 0.029 wounds/point

Banner (16 Bulls)

48 attacks
48x(7/12)=28 hits
28x(7/9)=21,8 wounds
Cost effectiveness: 0.035 wounds/point

No banner (16 Ironguts)

48 attacks
48x(1/2)=24 hits
24x(5/6)=20 wounds
Cost effectiveness: 0.026 wounds/point

Banner (16 Ironguts)

48 attacks
48x(7/12)=28 hits
28x(35/36)=27,2 wounds
Cost effectiveness: 0.033 wounds/point

Against T4:

No banner (16 Bulls)

48 attacks
48x(1/2)=24 hits
24x(1/2)=12 wounds
Cost effectiveness: 0.021 wounds/point

Banner (16 Bulls)

48 attacks
48x(7/12)=28 hits
28x(7/12)=16,33 wounds
Cost effectiveness: 0.026 wounds/point

No banner (16 Ironguts)

48 attacks
48x(1/2)=24 hits
24x(5/6)=20 wounds
Cost effectiveness: 0.026 wounds/point

Banner (16 Ironguts)

48 attacks
48x(7/12)=28 hits
28x(35/36)=27,2 wounds
Cost effectiveness: 0.033 wounds/point

Against T5:

No banner (16 Bulls)

48 attacks
48x(1/2)=24 hits
24x(1/3)=8 wounds
Cost effectiveness: 0.014 wounds/point

Banner (16 Bulls)

48 attacks
48x(7/12)=28 hits
28x(7/18)=10,9 wounds
Cost effectiveness: 0.018 wounds/point

No banner (16 Ironguts)

48 attacks
48x(1/2)=24 hits
24x(2/3)=16 wounds
Cost effectiveness: 0.021 wounds/point

Banner (16 Ironguts)

48 attacks
48x(7/12)=28 hits
28x(7/9)=21,8 wounds
Cost effectiveness: 0.033 wounds/point

Against T6:

No banner (16 Bulls)

48 attacks
48x(1/2)=24 hits
24x(1/6)=4 wounds
Cost effectiveness: 0.007 wounds/point

Banner (16 Bulls)

48 attacks
48x(7/12)=28 hits
28x(7/36)=5,4 wounds
Cost effectiveness: 0.009 wounds/point

No banner (16 Ironguts)

48 attacks
48x(1/2)=24 hits
24x(1/2)=12 wounds
Cost effectiveness: 0.016 wounds/point

Banner (16 Ironguts)

48 attacks
48x(7/12)=28 hits
28x(7/12)=16,3 wounds
Cost effectiveness: 0.020 wounds/point

Conclusion:

The Dragonhide banner is actually a very good banner if you are on the charge, while in bigger units the cost effectiveness does not really change if you don’t get the charge. If you do charge though, the banner is quick to win back it’s points. See below.

Banner is better or equal for bulls at 5 (4,7) models supporting the BSB.
Formulas compared (with ‘n’ being the models in the unit):       
-with banner:   (3n x (chance to hit) x (chance to wound)) / (35n + 60)
-no banner:   (3n x (chance to hit) x (chance to wound)) / (35n)

Banner is better or equal for IG’s at 4 (3,4!!) models supporting the BSB.
Formulas compared (with ‘n’ being the models in the unit):       
-with banner:   (3n x (chance to hit) x (chance to wound)) / (48n + 60)
-no banner:   (3n x (chance to hit) x (chance to wound)) / (48n)

It is important to note that while the Ironguts regain their cost effectiveness sooner than bulls, they are in fact less cost effective until T4 and higher. This could be sooner already when the enemy fails their fear test and we hit at 3+! (48 attacks would give us 36 wounds on average!  ) They can however take rune maw and have armour, which becomes an easy way to maintain a healthy advantage over bulls. They would be my preferred unit to use this banner with. Add in a tyrant with thundermace and you have all hell breaking loose when it works, and half of hell breaking loose when it doesn’t. Don’t forget you get re-rolls on charges, stomp AND armour saves as well!

Thanks,
-Birdhunter

I normally spit on Mathhammer but you added a convincing argument.

I intend to try this one out the next time I play.

None of that math matters to me, just this:

Magic Banner > 25 points = Must be carried by BSB

Magical Banner + BSB = BSB without other Magic Items.

BSB without other Magic Items = Easy to kill BSB

@Shadowlord That's great

I must say that to me maths is a part of the game. I hardly play competitive lists, so I use some math to get a decent army aswell as nice new ideas to keep my opponents guessing  Besides that, I do think that new players (and sometimes even old players stuck in old habits  ) could benefit alot from these sort of calculations.
Anyway, I'm glad you are going to try it, and I most definitely will try it too!

@Mercules your BSB can still take a bigname, so a T6 char will not be that easy to kill, besides, on your charge the changes of T7 or regen are relatively big, so that also adds up. Also you can simply put him on the side of the rank so fewer hits can be allocated there.

Thanks,
-Birdhunter

Well, I often use the Thundermace on my Tyrant which means I don't want him in challenges. The obvious solution is to give my BSB Mawseeker and a Ward Save and left him challenge. Since so many characters have ways to ignore armor or high Strength Attacks I don't find the toughness boost alone to be enough to allow him to survive.

In addition there are plenty of ways to wound someone without rolling to wound. Death Spells, Poison, and more.

Hmm, good point. Well of course it all depends on your style of playing. I will try this out though, maybe throw in another bruiser to challenge and a tyrant to cause havoc! 

I might have to try this out sometime(but not at Ard Boyz thank you )

With the rise of large units that chuck out bucketloads of attacks, the Dragonhide has most definitely risen from it's previous state of being so shockingly appalling and contemptuous. As other have hinted at, the main problem now is the options that it's competing with. There are three banners which are arguably better than it (Runemaw, Eternal Flame and Discipline) and you'll only be able to take two of 'em in any army. Furthermore, the only model that can take it also has better options in the form of conventional magic items.

Still, the Ice Magic immunity is nice......

Still, the Ice Magic immunity is nice......

Damn Kislevites!...

With the rise of large units that chuck out bucketloads of attacks, the Dragonhide has most definitely risen from it's previous state of being so shockingly appalling and contemptuous.

Actually, the unit is already more cost effective at those 5 bulls or 4 IG's, so you don't even need large units!

I played Dragonhide in a few tournaments in 7th with a big group of Maneaters... the results were mixed.

Basically if you don't get the charge it's a huge waste of points and a potential liability. Very risky.

Very nice post, thank you for posting it.  I have been using dragonhide for a couple years regularly to much success.  So its nice to see this math equate with what I have been advocating.   It is a vital part of my thundermace deathstar, as it increases the chances of the thundermace activation.  That alone is worth it to me.
 
Part of my playstyle is not getting into combat with my deathstar unless I charge.  I will sacrifice almost any of my other units besides the deathstar for the charge.  Vs other deathstars in 8th edition it has won vs a dwarf deathstar, a chaos warrior deathstar (both had ward saves).  I am not afraid to charge anything with it, and have yet to lose a combat with it, I have even "contemplated" removing crown of command from the unit as I get less and less worried about losing combats.  As far as bsb carrying it, mawseeker bsb with an extra hand weapon lives long enough to do the damage needed to win any game.  Most of the time the opponent focuses on killing the slaughtermaster, because of the gutmagic fear.  Which is why he is the one who gets decked out with the 4+ ward save and takes care of all the challenges.

Part of my playstyle is not getting into combat with my deathstar unless i charge. 

Isn't that the playstyle of almost every Ogre army? The problem with this banner is when that doesn't or can't happen. Then it's a very expensive waste of points.

p.s. I have edited your post to be more in line with the standards of the Stronghold. Please take the time to use proper punctuation and spelling. Thanks.

I use it on a regular basis. Overkill (love the band!) on anything but hordes IMO. Crack a 50+ unit of skaven in a hurry, to be sure.