How to Kill Your Dragon: An Analysis of Survival Instincts

 

                                                                                                                             Now that's a monster (miniset.net)  

Anyone who’s ever played against a Nazgul on Fell Beast knows the terrifying power of flying monsters. Able to hit from any angle they want to line up devastating Hurls or butcher support characters, they are a nightmare to plan against. Ringwraiths and Eagles, however, have always been balanced by having a measly 2 Attacks, making them very reliant on getting the charge and a little unreliable at winning combats. Dragons, on the other hand, laugh at such measly constraints. F7, A4 and S7 make a Dragon one of the most dangerous models in the game, especially when they’re upgraded with those near-mandatory Wings.  Very few models can hope to outfight one, and outrunning or hiding from them is practically impossible. The catch? They are all too prone to using those expensive wings to fly themselves off the table after taking a wound, due to their deceptively named Survival Instincts. Being required to pass a Courage test after taking a Wound or disappear from the battlefield, they can end up wreaking havoc on their player’s nerves every time a stray Orc Tracker takes aim at their 300-point model.

                                     Just look at that face, he's practically mocking me (The Lord of the Rings: Armies of Middle Earth)

I thought that any real analysis of the Dragon would therefore need to start by figuring out how long it’s likely to stick around on the battlefield. It has 7 Wounds, so it can theoretically take a few hits, but how many can it reliably take before it runs away? This turned out to be quite difficult to calculate, because while it’s easy to work out the probability of a model passing a Courage 4 test, it’s much harder to do so when there are Will Points involved (the Dragon has 3, which you should almost never spend on anything except Courage tests). It’s pretty much certain to pass the first test if it throws enough Will at it, but its odds of passing the second depend on whether it had to spend Will on the first, and so on.

                                                                  Me trying to use Pythagoras and the volume of a cone to solve a probability question

In the end, I wrote an Excel program to brute force it all, working out the average number of Wounds the Dragon could take before it would have burnt through all its Will and failed a test, and was quite shocked by some of the results. Indeed, diving deeper into the numbers made me look at the Dragon, and some of its upgrades, in a totally different way. The spreadsheet is attached at the bottom if you want to play around with it, but I’ll summarise all the most interesting results here.

                                                                            My poor laptop was really struggling by about row 19000

I’ll start with the assumptions I worked on. I assumed that you weren’t spending Will points on anything other than Courage tests, but that you probably needed your Might points for winning duels and calling Heroic Strikes/Combats. I also assumed that your Courage wasn’t depleted by anything like a nearby Harbinger of Evil, or boosted by a War Horn. I later looked at the effect of departing from those assumptions, but I’ll come to that near the end. Finally, I assumed there wasn’t anything weird like Mighty Blow or Drain Soul going on, for obvious reasons.

                                                       How many Wounds can a Dragon survive from this guy? Uh, one. (SKOLD painting)

The first big takeaway is that within those parameters, a Dragon will survive an average of ~4.7 Wounding Strikes. This means that it is effectively fairly equal to a Monster with 6 Wounds like a Cave Drake. This number was actually substantially higher than I expected, especially when you take into account Fate. If you’re spending Might to boost Fate rolls of a “3” (a generally more efficient use of Might than saving it to pass Courage tests, I later found), then you’re pretty-much equivalent to an 8 Wound monster, which is shockingly tough. I had always expected that anything more than a couple of hits would be the end for our scaredy little monster, but that’s apparently not the case.

                                                            This Dragon looks very smug about being underestimated (David Demaret)

Of particular relevance from this is that it makes the “2 additional Wounds” half of Tough Hide substantially better than I had first thought. Indeed, when I ran the numbers on it, it turns out that a Dragon with this upgrade can take around 0.9 Wounds more on average, a fairly relevant amount. When I then factored in To-Wound probabilities I discovered that a Dragon with Tough Hide will survive well over twice as many S4 hits, and almost 3.5 times as many S2 or S3 hits (such as those from most bows) as one without the upgrade. It also makes you immune to Thrown Stones from Hobbits, but I’m not sure how often a 12” Move Dragon takes hits from weapons with an 8” range. I had always dismissed Tough Hide as a bit overpriced for what you get, but increasing your durability several times over is quite possibly worth the 17% increase in cost. If you’re fielding a Dragon, you’re putting a lot of eggs in one basket already, so it does potentially make sense to reinforce that basket a bit.

                                                                    Anything to reduce the likelihood of this happening (Paolo Puggioni)

I’ve talked a lot about how resilient the Dragon is, and we already know how good it is at killing things. So should we all be bringing them to our next big tournament?

It turns out that there are actually quite a lot of difficulties with that plan. For one, these numbers are averages. While a Dragon is basically guaranteed to survive one Wound, there is a very genuine possibility that it dies to the second, no matter how many points you invested in its survival. In fact, there's a full 1/6 chance of it surviving no longer than a W3 character, which isn't great for something so expensive. The one certainty, of course, is that it will fail its Courage test at an absolutely critical moment in order to amuse the dice gods on their thrones of tears.

                                                        Gotta say, this wasn't what I was expecting when I searched "Throne of Tears"

The numbers also revealed some worrying weaknesses to magic. I had set the Courage value of the Dragon and the number of Will/Might points available for Courage tests as variables within the spreadsheet, and lowering these numbers had a huge impact on our scaly friend’s odds of sticking around. A single Drain Courage spell, cast on a 2+ by many Evil spellcasters, was equivalent to doing ~ 1.2 wounds worth of damage. That means that a humble Ringwraith can use this spell to reduce the expected lifespan of the Dragon by more than Sauron himself could do with Chill Soul! The effect is actually even stronger if you’ve taken Tough Hide, reducing your lifespan by about two whole Wounds. Even just standing around within 12” of the Dragon to activate your Harbinger of Evil rule will increase the chances of it turning tail and fleeing by a horrifying amount.

                                                                                        Yeah, I'd probably be running too (John Howe)

Furthermore, it’s not like you can afford to spend Will points to resist spells (beyond your “free” one from Resistant to Magic), because every Will point you lose drops the number of hits you can expect to survive by almost a whole Wound. If you get hit with Drain Courage, lose a couple of Will to Sap Will, and then take a Wound while within 12” of a Harbinger of Evil, you’re as likely as not to flee the field immediately. Fate points can save you from a few hits, but the big takeaway from this is that you should be absolutely terrified of Ringwraiths. In fact, I would go so far as to say that you should never bring a Dragon to a tournament that isn’t Good versus Evil. Ringwraiths —and other Evil spellcasters like Sauron, the Necromancer, and even the Mouth of Sauron— are such a ridiculously hard counter that I don’t think it’s worth the risk. If you do happen to end up facing one, your best bet is to try and kill it immediately; all it takes is a couple of turns of spellcasting and your Dragon will be ready to turn tail and flee the second you lose a combat. If you end up facing The Nine, shake hands and wish your opponent well. You aren’t winning that one.

                                                                                Ready to send your Dragon flying for the hills

Oh, and if you were still contemplating the option to Breath Fire, take this as your notice to cease and desist. Spending all your Will on incinerating the enemy might be fun, but it literally halves the number of Wounds you can take. Relative to spending those points on Tough Hide, you are making your Dragon around 4-6 times (!) easier to kill; not great when you’re investing half your army into this thing. It’s possible that you may get 50 points worth of value out of the threat afforded by the upgrade, especially supplemented by one or two fireballs against choice targets. But know that every use of the expensive upgrade is dramatically reducing the lifespan of your centrepiece model.

                                                                            Breathing Fire isn't as fun when you can only do it a couple of times

On the other hand, the stats do show that fitting in a War Horn in an allied contingent boosts your lifespan by more than an entire Wound, and makes it much more likely that your Dragon will fight it out to the end. So if you were looking to include some Black Númenóreans alongside your Dragon, then go ahead, the stats back it up. And if you somehow find a way to restore lost Will points to a Dragon, then enjoy your tournament wins, you’ve earned them.

                                                                                            See if you can get this guy to swap sides for a bit

What’s the big conclusion from all of this? Is a Dragon worth fielding? I think we can definitely rule out matches where you might face an Evil force, because a single Ringwraith can reliably take out your hyper-expensive killing machine with just a couple of spells. But in Good versus Evil tournaments, a Tough Hide/Fly Dragon or one with just Fly could be quite interesting. It’s almost as tough as the Balrog, hits substantially harder and is much more mobile. On the other hand, it loses out on the Fiery Lash, F10, and the free Heroic Combat, and it’s vastly more vulnerable to magic. It also doesn’t buff your Goblins at all, and doesn’t have a Legendary Legion based around it. But those trade-offs could potentially be worth it to get Fly and Monstrous Charge, both of which hugely increase the amount of damage it can do to your opponent. I think I’d almost always take it with Tough Hide, having seen these numbers; it’s simply too big a part of your list not to take the vastly increased resilience. Wyrmtongue is nice, but it doesn’t help if your enemy shot you out of the sky with Elf bows on Turn 3. I’d also possibly consider running it with just Fly in smaller games, though it requires you to play a bit cagier with your centrepiece. Finally, if you do take it, I recommend a daily sacrifice of a lamb and three ducks to the dice gods. Or Morgoth, whoever you think is a safer bet.

                                                                             Definitely the safer bet (Thomas Rouillard)

If you’re interested in diving deeper into the spreadsheet linked below and playing around with it, the cells coloured in blue are variables you can adjust (Courage, number of Will/Might to spend, starting Wounds for the Dragon), while the cells coloured in red are the outcomes. These are in terms of Effective Wounds, so if it has six Effective Wounds then it ran away after taking the sixth Wound. To the right of these results is a neat little frequency table in red, showing the probability of it disappearing after taking a given number of Wounds. There’s also a second sheet which applies the same maths to Shelob, who, as it turns out, is almost certain to survive until she’s taken 6 Wounds. If you have no interest in spreadsheets, then feel free to take me at my word, and I hope you found this interesting anyway.

 Until next time, may your Dragons always pass their Courage tests!

https://docs.google.com/spreadsheets/d/1Mp9CgEy500bBxPMY_R828_nJTt-hzljJ3TsD94OTpWw/edit?usp=sharing