While playing the Overlord in our Descent:RtL campaign with custom-made heroes using Kevin Wilson's create-your-own-hero rules (you can read a detailed campaign diary at http://www.compoundeye.net/descent/), I had a very hard time killing any hero. I seemed to be nearly unable to penetrate their high armor (one with armor 6, two with armor 5, one at 4). I kept reading on the net that I simply should attack them again and again, slowly wearing them down until they would finally die. Only - it didn't work, and I didn't really know why.
So while carrying around our 7-month-old daughter when she had problems falling asleep, I thought about the problem of monster damage and hero armor. What follows is a statistical analysis, which I hope some of you may find insightful. If you don't want to work yourself through the figures and statistics, you can skip the next section and simply read the "Conclusion and Summary" at the end.
The first important thing to note is that damage in Descent is rolled with multiple dice. Because of this, the amount of damage rolled is not uniformly, but normally distributed. What that means is that the average amount of damage will be rolled a lot more often than minimum or maximum damage. Consider rolling two "normal", six-sided dice - you will roll a "7" a lot more often than a "2" or "12". This effect becomes stronger the more dice are rolled for an attack.
Let's have a look at some of the more common combinations of two dice on copper level and their probabilities of rolling a certain amount of damage.
On the y axis, the probability of rolling 0-7 damage (on the x axis) is shown for red/green (razorwings, blood apes), red/yellow (beastmen), blue/green (skeletons) and white/green (banespiders) dice. No pierce, damage boni or other effects are considered, only raw die rolls. Also note you will always have a 16.7% chance of getting a miss result.
If you look at the graphs from damage 1 upwards, you can see the bell curves of the normal distribution: Minimum and maximum damage is less probable than average damage. Because the Descent dice are labeled differently than "normal" dice, the bell curves are skewed, with their maximum moved slightly towards the right. But for all except the red/green die combination, the graphs have their maximum at 3 and 4 damage respectively, and decrease for higher values. I'll come back to that again later.
So what does this mean? Since minimum damage and, more often than not, average damage will be unable to penetrate average (4) to high (5+) hero armor, the Overlord wants to roll near-maximum damage to be able to do any damage at all - only that this will happen far less often than rolling average damage. There's one direct consequence:
If as the Overlord you're adding power die boosts, upgrade black to silver to gold dice first before adding another black power die.
The average damage rolled will be the same, but by keeping the number of dice rolled at a minimum, you will increase the chances of rolling near-max damage - which you will need, at least as an Overlord facing a high-armored hero.
As a hero, you want to do the same if you worry about not being able to penetrate a monster with high armor, but this will be rare. So you have to decide:
If as a hero you need near-max damage, upgrade black to silver to gold dice first before adding another black power die. However, if only a medium amount of damage is needed, minimum damage would not be enough and maximum damage would be overkill, add more black power dice before upgrading.
Another consequence is that monsters with lots of dice look more scary than they often are. Example: A master giant rolls a red, green, yellow, yellow, black die. Five dice! Impressive, right? No, not really. The odds for him to roll his max damage of 10 is only 0.3%, and he will mainly roll his average damage of 5.5 - nice, but disappointing for a creature labeled "giant".
Average Monster Damage
The above analysis on dice in general was kind of theoretical, since many monsters have damage boosts like pierce or +damage. So let's have a look at average monster damage against hero armor values for typical copper monsters.
What you can see is how much damage a monster deals on average to a hero with armor values between 0 and 6. The graphs for the skeleton and hellhound start as a straight horizontal line because their pierce ability will negate low values of armor. Additionally, no graph is linear because of the normal distribution of damage. As expected and experienced by us all, the beastmen do best because of their flat-out +2 bonus damage, and the hellhound on the other end of the spectrum is unable to penetrate even an armor of 5.
This figure is not very exciting, except that you should note that the average damage falls below 1 for all monsters (except for beastmen) somewhere between armor 3 and 4, and decreases to a value of nearly 0 for armor 5 and 6. Remember the bell curves from the first figure, and you know why it is that way.
Average damage is the value mostly calculated and cited in reference sheets, and hey, even an average damage of below 1 is still damage, right? As long as you will be able to throw enough monsters at the heroes, they will die and all is well, correct?
Not really. What these figures don't tell you is that most attacks against heroes of armor 5 and above fail to do any damage at all. "Average damage" is misleading in a game like Descent, where a monster will either deal at least one wound, or none at all - in which case the attack is completely wasted and does nothing. So instead of calculating average damage, let's have a look at how many monsters are needed to deal any damage at all to a hero.
What this figure tells you is how many monsters you have to throw against a hero with armor between 0 and 6 until you can expect to have dealt at least one wound. The interesting thing here is that this value increases exponentially for higher values of armor, and that this increase starts to ramp up considerably going from armor 4 to 5, and even more so from armor 5 to 6.
Let's take a closer look at the best monster of the bunch by far: The beastman. To be able to do any damage at all to a hero with armor 3, you need 1.38 beastmen on average - that sounds fair. Now add one point of armor, and suddenly you already need 1.8 beastmen to do at least one wound - but this is still okay. But increase the hero's armor to 5, and suddenly you need 3.6 beastmen on average to be able to do any damage at all, and against a hero with armor 6, already 18(!) beastmen are needed - for one measly wound!
Keep in mind that these numbers are for at least one wound only - to kill a hero with armor 6 and 12 wounds, you'd need 216(!) beastmen on average. As you can see, the jump from armor 5 to 6 brings the most dramatic increase in protection for a hero. For all other monsters, this most rewarding jump is from armor 4 to 5. With armor 4, it will be a challenge for the Overlord to kill you, but it can be done with enough monsters - Descent essentially is a war of attrition. However, by increasing your armor from 4 to 5, all of a sudden it is nearly impossible for the Overlord to kill you - he can still wound you from time to time, but without damage boosts like Command or a huge amount of luck, he cannot realistically expect to kill you before you drink a healing potion or go to the temple.
If as a hero you want to tank, it is a lot more worthwhile to increase your armor from 4 to 5 (or even 6!), than to 3 or 4.
Increasing your armor to 4 reduces the average damage you receive considerably, but as soon as you reach 5 or even 6, it's no longer about average damage, but about if you can get killed at all (not counting Traps, Command etc. of course).
Now you know why all Overlords hate Nanok, and why for nearly all other starting heroes, it is easily possible to get to armor 4 with starting equipment, but it's really hard to get to armor 5 or above if you don't want to leave your fellow party members naked. This actually preserves game balance! Because of this, I also consider the Defender ability of Kevin Wilson's "Create Your Own Hero" rules broken, as it essentially gives you that important increase from armor 4 to 5 to the whole party for free. The depressing results can be read about in my diary...
Conclusion and Summary
* Because damage is determined by rolling multiple dice, you have higher odds for average damage than for minimum or maximum damage. This effect is stronger the more dice are rolled for an attack.
* As an Overlord, you are more interested in doing max damage than average, because more often than not only max damage will do any damage at all against high-armored heroes. Because of that, prefer monsters with fewer, but better dice over those with more, but weaker dice. In encounters, always upgrade existing power dice before adding new one.
* As a hero, you have two options. If you want to kill a wounded monster where average damage is enough, add more power dice. If you need max damage, to penetrate high armor or kill a healthy foe for example, upgrade your existing power dice first instead.
* Increasing a hero's armor in the lower ranges reduces average damage taken from monsters considerably. For the tanks however, higher armor ratings are more powerful because for them it's not about average damage taken, but if they take damage at all. Increasing the armor from 4 to 5 is the most rewarding step on copper level in that regard, and increasing it to 6 makes a hero nearly invulnerable to most monsters in practice.
I hope you found this analysis enlightening in some way. Please feel free to comment!
Arnold Vincent Canaria
Very interesting, albeit depressing for OL players. This information can help me though when figuring out what option to take when throwing monsters at the heroes in different situations (e.g. early game, mid armor, high armor, etc.), if ever to go that route at all. Then again, monsters are still good at leaving cumbersome ongoing effects on Heroes.
Quite straightforward, but a sound conclusion. To supplement your findings, I'll add that I once did a quick rough analysis that showed that Hero toughness against copper and silver monsters effectively doubles at every point of armor above 4, which makes sense when you consider how the dwarves have 1 more armor than the other tanks, but half the Wounds.
Thanks for working this up, it's useful information.
I'd actually been looking around for some analysis of the dice results to evaluate the utility of Aim. So far the only good use we can see for it is long range, high armor, or maybe a power potion. Battle seems better in most other usual cases - note that this is vanilla, not RtL. I'd imagine with Silver/Gold power dice, power potion + Aim gets a lot nastier.
Does anyone know of some statistical breakdowns of damage comparing aim to battle?