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INTRODUCTION:
Many of us like to play with big, flying monsters. For a Wood Elf player, that means a highborn on a dragon! A common question that appears on these boards is "How exactly should I equip my highborn dragon rider?" There are a number of viable combinations, each of which serves a different purpose. Some tend to emphasize protection from shooting, others emphasize close combat defense, and still others try to maximize close combat offense. But what should you prioritize when facing off against a given opponent?
What follows will be a detailed analysis that covers most projectiles likely to be hurled in the general direction of your precious dragon rider. By examining the numbers in detail, I hope to figure out a few things:
- How threatening is missle fire in general?
- What types of missile fire are the biggest threat?
- Should you choose items that protect the rider, the dragon, or both?
- How much of a risk are you running ignoring ranged defense to focus on close combat?
First I will examine war machines, which will require some creative thinking in figuring out how likely certain things are to hit you. Cannons and stone throwers, for example, use unique firing methods that you can't just use d6 probabilities to capture easily.
Having done that, I will calculate expected values for each weapon against your dragon under a number of battlefield conditions. For now I'll assume that the dragon isn't in cover.
Finally, I'll look over the numbers for general trends and attempt to answer some of the key questions asked above.
DETERMINING CHANCE TO HIT:
My math on this might be a bit off. Feel free to correct me.
When shooting at a monster with a 50mm base, it's optimal to guess 9-10" short of the target, which gives you 19 possible combinations of artillery rolls that will result in a hit [(10, X ), (8, X ), (6, not 2 ), (4, 6 ), (4, 8 ), (4, 10 ), (2, 8 ), (2, 10 )]. If shooting at a chariot base, then it becomes optimal to guess 8" short of the target, as there will be 21 possible combinations that will result in a hit [(10, X ), (8, X ), (6, X ), (4, not 2 ), (2, 8 ), (2, 6 )]. X in both cases indicates any numerical (non-misfire) roll.
Of course, if we factor in runic cannons then we need to adjust our numbers. A cannon with the rune of forging gets to reroll misfires. So for a monster base, there is a 52.8% chance to hit outright and a 30.6% chance of a reroll, which itself will result in a 52.8% chance to hit for a total chance to hit of 69%. For a chariot base, there is a 58.3% chance of hitting outright and a 30.6% chance of a reroll, which itself will succeed 58.3% of the time for a total chance to hit of 76.1%. Remember, if EITHER artillery die rolls a misfire you have to reroll the artillery dice according the wording in the dwarf rulebook.
So, in sum (assuming optimal guessing, and in the case of the chariot assuming the cannon is firing defilade. If the cannon is firing enfilade, treat a chariot base as a monster base):
A Normal cannon hits a monster base 52.8% of the time and a chariot base 58.3% of the time.
A Rune of Forging cannon hits a monster base 69% of the time and a chariot base 76.1% of the time.
Note that real players will not get results this good because they will likely have some degree of error in their guessing.
A cannonball that hits will have a 2+ to wound either target and ignores regular armor, dealing either d3 or d6 wounds depending on cannon type and/or the presence of a dwarven master engineer.
Bolt throwers are even easier, as they hit reliant on the users BS. DE and HE bolt throwers will be hitting on 2+ or 3+ depending on range. Dwarf bolt throwers will be hitting on 2+, 2+/3+ or 3+/4+ depending on the presence of a master engineer, engineer, or no engineer respectively. O+G Spear Chukkas will hit on a 3+/4+. Lizardmen giant bows will hit on a 3+/4+ if a crew member is firing and a 2+ if the chief is firing (assuming the chief is allowed to fire, this is subject to some debate).
Stone throwers are a bit more difficult because I am slightly unclear on how the rules for them work. If using the small template, no matter what your monster or chariot base won't be completely covered. If using the large template (not sure off hand if any stone throwers do this), then the monster base might be completely covered on a direct hit whereas the chariot base will never be completely covered. So assuming we are using the small template, then no matter what a grudge thrower will still need to roll on a 4+ to hit your model. My question is whether both rider and dragon roll roll 4+, whether both are hit on a single roll of 4+, or whether the hit is randomized after a single roll of 4+. Furthermore, do both rider and dragon count as being under the center of the template if the center of the template is over any portion of the model's base? Also, do ridden monsters count as a "single model" for purposes of autohits when under the center of the template?
Anyway, I'm going to have to fudge a little bit with the scatter calculations but this will give at least a close ballpark estimate. An optimal guess will place the center of the template at the center of the base. 27.78% of the time, a roll of hit along with a number will result in a direct hit. 16.67% of the time, a misfire will result. The rest, there will be some scattering in a random direction. A roll of 2 on the artillery die is going to still result with the template in contact regardless of the base type of the dragon and the direction of the scatter, seeing as it will only result on .5" of effective movement in any given direction (given the 1.5" radius of the small template). A roll of 4" on the scatter will result in 2.5" of effective movement in a random direction, which will always result in a miss, seeing as the greatest possible distance from the center of the model to the corner of the model is 2.2" (in the case of a chariot base). So even with an optimal directional roll from the scatter die, it'll still miss. With the larger template, however, things get a bit trickier. A roll of 2" will result in a partial for a monster base no matter the direction, and a roll of 4" will result in a miss. For a chariot base, however, if the template scatters toward any of the four corners of the base, then a roll of 4" will result in a partial. The problem is that I'm not entirely sure how large the window of arc is toward each corner that will still result in a hit. I'll guess and say 45 degrees, which is probably a reasonable estimate. That means that if an arrow and a 4 are rolled, then there will be a 50% of a partial with the large template against a chariot base. If a 6+ is rolled on the scatter it'll be a miss no matter what.
A stone thrower with no template will miss with any scatter at all against a monster base, and will nick a corner of a chariot base about 50% of the time on a roll of 2" scatter, but miss on any scatter greater than 2".
So, boiling that down:
Using no template against a monster base: [(Hit, X)] will result in a direct hit.
Using no template against a chariot base: [(Hit, X)] will result in a direct hit and [(Arrow, 2)] will result in a direct hit about half the time.
Using a 3" template against a monster or chariot base: [(Hit, X), (Arrow, 2)] will result in a partial hit.
Using a 5" template against a monster base: [(Hit, X)] will result in a direct hit and [(Arrow, 2)] will result in a partial hit.
Using a 5" template against a chariot base: [(Hit, X), (Arrow, 2)] will result in a partial hit and [(Arrow, 4)] will result in a partial hit about half the time.
Therefore, assuming perfect guessing:
No template against a monster base: 27.8% chance of a direct hit.
No template against a chariot base: 33.5% chance of a direct hit.
3" template against monster or chariot base: 38.9% chance of a partial hit.
5" template against a monster base: 27.8% chance of a direct hit, 11.1% chance of a partial hit.
5" template against a chariot base: 44.5% chance of a partial hit.
However, that assumes that ridden monsters don't count as a "single" model if under the template hole. If they do, then the following numbers apply instead:
3" template against monster base: 27.8% chance of direct hit, 11.1% chance of partial hit.
3" template against chariot base: 33.4% chance of direct hit, 5.56% chance of partial hit
5" template against a monster base: as above.
5" template against a chariot base: 33.4% chance of direct hit, 11.1% chance of partial hit
But wait! A grudge thrower with the rune of accuracy gets to re-roll the scatter die. Therefore, the 44.4% chance of the time that the shot would miss because of scatter we have to factor in a re-roll. If the artillery die came up a 2 or misfire, the reroll won't matter (and thus you wouldn't even bother rerolling.) A 4, 6, 8, or 10, will then result in a hit 1/3 of the time on the reroll.
Thus a dwarven grudge thrower with a rune of accuracy has a 53.7% chance of a partial hit at S4(8 ).
The numbers, of course, are different if the ridden monster counts as a "single model." In this case, if it is a monster base then we'll assume the player will re-roll if he doesn't get a direct hit. So if the artillery die comes up as misfire it doesn't matter but any number will result in a reroll of a non-hit scatter die. All rerolls that come up hit will get a direct hit and rerolls of an arrow paired with "2" on the scatter die will result in a partial. So there is a 46.3% chance of a direct hit and a 7.4% chance of a partial hit. Against a chariot base, you'll re-roll any non-misfire, non-hit, non-scatter 2 toward the corner result (IE: all arrow + 4, 6, 8, 10 and half of arrow + 2). Of these rerolls, all that come up hit will result in a direct hit, rolls of an arrow paired with a 2 will result in a direct hit if they scatter to the corner and a partial if they scatter to the side. Thus a 51.91% of direct hit and a 1.85% chance of partial hit is achieved.
Because of the manner in which it is fired, I can't calculate the odds of being hit by a warp lightning cannon as it depends on the exact range, which will vary widely depending on the situation. I am also unsure as to whether both rider and mount are hit if the model is hit or if the shot is randomized instead.
The hellstorm rocket battery is also rather difficult to calculate because it combines the cannon and mortar shot mechanics, so there is a random element to where the template is initially placed as well as the mortar scatter. That said, the rocket battery isn't particularly dangerous to your dragon and rider as it is relatively lower strength, doesn't outright ignore armor, and only causes one wound.
The hellblaster volley gun will take a bit of work to calculate. There is a 2.78% chance that the first barrel will misfire and cause the gun to go nuts and fire 30 shots. There is a 2.78% chance that the first barrel won't fire at all but the rest will. There is an 11.1% chance that no barrels will fire. In all other cases (ie: 83.3% of the time), the first barrel fires an average of 6 shots and you move on to the second barrel. Now there is a 2.78% chance that the second barrel will misfire and the gun will go nuts, firing an additional 20 shots. There is a 2.78% chance that the second barrel won't fire but the third barrel will. There is an 11.1% chance that neither the second nor third barrel will fire. In all other cases, the second barrel fires an average of 6 shots and you move on to the third barrel. The third barrel has a 2.78% chance of going nuts and firing 10 shots, a 13.89% chance of firing nothing, and the rest of the time it will fire 6 shots on average.
So we have a:
2.78% chance of 30 shots (misfire)
11.1% chance of jam
.078% chance of nothing + 20 shots (misfire)
.0021% chance of nothing + nothing + 10 shots (misfire)
.309% chance of nothing + jam
.011% chance of nothing + nothing + nothing/jam
.321% chance of nothing + 6 shots (average) + nothing/jam
.064% chance of nothing + 6 shots (average) + 10 shots (misfire)
1.93% chance of nothing + 6 shots (average) + 6 shots (average)
2.31% chance of 6 shots (average) + 20 shots (misfire)
9.26% chance of 6 shots (average) + jam
.064% chance of 6 shots (average) + nothing + 10 shots (misfire)
.321% chance of 6 shots (average) + nothing + nothing/jam
1.93% chance of 6 shots (average) + nothing + 6 shots (average)
1.93% chance of 6 shots (average) + 6 shots (average) + 10 shots (misfire)
9.65% chance of 6 shots (average) + 6 shots (average) + nothing/jam
57.9% chance of 6 shots (average) + 6 shots (average) + 6 shots (average)
That adds up to a total expected value o 14.71 shots per turn. I'm not sure if this is affected by the to-hit penalty for multiple shots or not. If not, it'll hit on a 3+/4+ depending on range. If so, it'll be 4+/5+.
Luckily, the dwarf organ gun is MUCH easier to calculate, and simply fires an average of 5 hits per turn.
Razordons and Leadbelchers are similarly easy, firing an average of 5 shots per turn, hitting on 3+.
If I'm not mistaken, this should cover every war machine in the game with the exception of war machines which fire templates, which are not very likely to be fired at a dragon on anything resembling a regular basis due to their short range and relatively poor performance against large single models.
EXPECTED VALUES:
Now I'll consider the expected value of the actual damage caused to your dragon and rider with a basic equipment loadout. I will calculate the values for stone throwers (orc rock lobba, goblin doom diver, brettonian trebuchet, gnoblar scrap launcher, chaos hellcannon, empire mortar, dwarf grudge thrower, tomb king screaming skull catapult) once I am clearer on how the hits are counted.
First let's discuss equipment loadouts. I'll assume you'll always have at least light armor and a shield for a 5+ armor save on the rider, a 3+ scaly skin save for the dragon, and no wards. Helm of the hunt or enchanted shield improves the rider's armor save to 4+. Oaken armor provides the rider with regeneration. Glamourweave provides the rider with a 4+ ward save against war machines. SotCM provides both rider and dragon with a fragile 3+ ward save. Amaranthine brooch protects the rider with a 3+ ward save that won't help against runic war machines. The Rhymer's harp provides a 5+ ward for rider and mount.
Great Cannon: 52.8% chance to hit vs. monster base, 58.3% chance to hit vs. chariot base, striking the rider on a 5+. Regardless of which part is hit, the cannon will wound on 2+ with no armor save, multiplying to d6 wounds. Thus this will do .513 wounds to the rider and 1.027 wounds to the dragon per shot on average (monster base), or .567 wounds to the rider and 1.134 wounds on average to the dragon per shot on average (chariot base). Then apply your ward/regeneration saves from gear to further modify that number.
Runic Great Cannon: 69% chance to hit vs monster, 76.1% chance to hit vs. chariot base, striking the rider on a 5+. Regardless of which part is hit, the cannon will wound on 2+ with no armor save, multiplying to d6 wounds. Thus this will do .671 wounds to the rider and 1.342 wounds to the dragon per shot on average (monster base), or .74 wounds to the rider and 1.48 wounds on average to the dragon per shot on average (chariot base). Then apply your ward/regeneration saves from gear to further modify that number.
Small Cannon: 52.8% chance to hit vs. monster base 58.3% chance to hit vs. chariot base, striking the rider on a 5+. Regardless of which part is hit, the cannon will wound on 2+ with no armor save, multiplying to d3 wounds. Thus this will do .293 wounds to the rider and .586 wounds to the dragon per shot on average (monster base), or .324 wounds to the rider and .648 wounds on average to the dragon per shot on average (chariot base). Then apply your ward/regeneration saves from gear to further modify that number.
Runic Small Cannon: 69% chance to hit vs monster base, 76.1% chance to hit vs. chariot base, striking the rider on a 5+. Regardless of which part is hit, the cannon will wound on 2+ with no armor save, multiplying to d3 wounds. Thus this will do .383 wounds to the rider and .767 wounds to the dragon per shot on average (monster base), or .423 wounds to the rider and .846 wounds on average to the dragon per shot on average (chariot base). Then apply your ward/regeneration saves from gear to further modify that number.
Bolt Thrower (Orc): Hits on 3+ at short range, 4+ at long range, striking the rider on 5+. Wounds the rider on 2+ and the dragon on 4+ with no armor saves and multiplies to d3 wounds. Thus this will do .37 wounds to the rider and .44 wounds to the dragon per shot on average (short range), or .28 wounds to the rider and .33 wounds on average to the dragon per shot on average (long range). Then apply your ward/regeneration saves from gear to further modify that number.
Bolt Thrower (Elf): Hits on 2+ at short range, 3+ at long range, striking the rider on 5+. Wounds the rider on 2+ and the dragon on 4+ with no armor saves and multiplies to d3 wounds. Thus this will do .46 wounds to the rider and .56 wounds to the dragon per shot on average (short range), or .37 wounds to the rider and .44 wounds on average to the dragon per shot on average (long range). Then apply your ward/regeneration saves from gear to further modify that number.
Bolt Thrower (Dwarf): Hits as an Orc bolt thower if no engineer. Hits as an elf bolt thrower with an engineer. Hits as an elf bolt thrower at short range regardless of range with a master engineer. Note that runes can be used to improve the strength of the attack, which will have no effect on the expected value vs. the rider but will increase the expected value vs. the dragon.
Bolt Thower (Lizardmen): I'm only going to bother with the "shot by crew" scenario for now. Hits on a 3+ at short range and a 4+ at long range, although this may be further reduced if the stegadon moves and shoots, poisoning on a 6 to hit and then striking the rider on 5+. If non-poison, it will wound the rider on a 2+ and the dragon on a 5+ with no armor saves, multiplying to d3 wounds. Thus this will do .389 wounds to the rider and .44 wounds to the dragon per shot on average (short range), or .296 wounds to the rider and .368 wounds on average to the dragon per shot on average (long range). Then apply your ward/regeneration saves from gear to further modify that number.
Hellblaster (if it takes no penalty for multiple shots): Averages 14.71 shots per barrage. Hits on 3+ at short range, 4+ at long range, striking the rider on 5+. Wounds the rider on 2+ and the dragon on 5+ with -3 armor saves. Thus this will do 2.72 wounds to the rider and 1.82 wounds to the dragon per barrage on average (short range), or 2.04 wounds to the rider and 1.36 wounds on average to the dragon per barrage on average (long range). Then apply your ward/regeneration saves from gear to further modify that number.
Hellblaster (if penalty for multiple shots): Averages 14.71 shots per barrage. Hits on 4+ at short range, 5+ at long range, striking the rider on 5+. Wounds the rider on 2+ and the dragon on 5+ with -3 armor saves. Thus this will do 2.04 wounds to the rider and 1.36 wounds to the dragon per barrage on average (short range), or 1.36 wounds to the rider and .91 wounds on average to the dragon per barrage on average (long range). Then apply your ward/regeneration saves from gear to further modify that number.
Organ Gun: Averages 5 hits per turn, striking the rider on 5+. Wounds the rider on 2+ and the dragon on 5+ with -3 armor saves. Thus this will do 1.39 wounds to the rider and .93 wounds to the dragon per barrage on average. Then apply your ward/regeneration saves from gear to further modify that number.
Razordon: Averages 5 shots per turn, hitting on 3+ and striking the rider on 5+. Wounds the rider on 3+ with normal saves and wounds the dragon on 6+ with normal saves. Thus will do .49 wounds per turn to the rider and .12 wounds per turn to the dragon, on average. Then apply your ward/regeneration saves from gear to further modify that number. Note: Ogre Leadbelchers produce numbers very similar to these, albeit slightly better due to the fact that they are armor piercing.
BONUS: Some regular shooting numbers! All numbers are average unsaved wounds per shot assuming LA + shield and no further gear.
BS 3 guns/xbows: .148 wounds to rider (short), .111 wounds to rider (long), .049 wounds to dragon (short), .037 wounds to dragon (long).
BS 4 guns/xbows: .185 wounds to rider (long), .148 wounds to rider (long), .062 wounds to dragon (short), .049 wounds to dragon (long).
BS 3 bows: .074 wounds to rider (no penalty), .056 wounds to rider (-1 to hit), .37 wounds to rider (-2 to hit), .025 wounds to dragon (no penalty), .019 wounds to dragon (-1 to hit), .012 wounds to dragon (-2 to hit).
BS 4 bows: .093 wounds to rider (no penalty), .074 wounds to rider (-1 to hit), .056 wounds to rider (-2 to hit), .031 wounds to dragon (no penalty), .025 wounds to dragon (-1 to hit), .019 wounds to dragon (-2 to hit).
BS 4 rxbows: .19 wounds to rider (-1 penalty), .14 wounds to rider (-2 penalty), .074 wounds to dragon (-1 penalty), .056 wounds to dragon (-2 penalty).
That covers the majority of mundane shooting that you are likely to run into, although it does not cover rare encounters such as slings, poison darts, javelins, gnoblar sharp stuff, and glade guard longbows at short range.
CONCLUSIONS:
In general, ranged weapons aren't as big of a threat to a dragon rider as I expected, with one major exception: the hellblaster volley gun, which has respectable chance of tearing your rider to ribbons in a single barrage. Even if it fails to kill in one volley, it'll do pretty heinous damage.
Beyond the hellblaster, cannons are the next greatest threat. The interesting thing about cannons is that they wound the dragon at exactly double the rate that they wound the rider. As the dragon has 6 wounds and the rider has 3, against cannons it is equally important to protect the dragon as it is the rider. Thus if you are expecting to face a lot of cannons, you might want to invest in the SotCM or Rhymer's Harp. If you only protect the rider, the enemy is likely to tear the dragon out from under you. Granted, it will still take quite a lot of cannon fire to bring your rider and dragon down. One or two cannons aren't likely to kill your model before you swoop in and rip them to shreds.
Bolt throwers, on the other hand, only wound the dragon slightly faster than they do the rider. As a result, it's much more important to protect the rider than it is the dragon as you're more likely to lose him early. An item like the amaranthine brooch (but beware of runic weapons) or glamourweave may be a good purchase here. Also mind that dwarf bolt throwers with multiple +strength runes on them are going to act a lot more like small cannons than bolt throwers. Once the bolt thrower hits S8, it's hits are indistinguishable from small cannon shots, so you should treat those models as small cannons with respect to your dragon.
Against multi-shot weapons like the hellblaster and organ gun, this effect is even more pronounced. These weapons struggle to dent the dragon's thick, tough hide but turn your elf into paste right quick. Against these types of weapons, protecting the rider is imperative
Against mundane missile weapons like bows, handguns, and repeater crossbows, the rider is in much more danger than the mount. Typically these weapons wound the rider around three times faster than they do the mount. So if you are expecting a lot of basic missile troops, you should be sure to protect the rider. Protecting the dragon isn't nearly as important.
A note about stone throwers: I'm still not quite sure how these affect your dragon rider. If hits are randomized, then they basically act like cannons only less accurate, and thus you should seek to protect both dragon and rider against them. If they hit BOTH targets rather than randomizing, then they will kill your rider MUCH faster and thus you need to emphasize protecting the rider. Note that stone throwers in general are less of a threat than cannons because they are less likely to hit, are less likely to target your dragon, and generally have a minimum guess range that you can fly inside fairly easily.
So, in summary:
- Ranged weapons in low to moderate numbers are not particularly threatning, with the exception of the Hellblaster.
- Against cannons and high strength runic bolt throwers, you want to protect both dragon and rider
- Against other bolt throwers it's better to protect the rider
- Against multishot war machines and mundane missile fire, it's MUCH better to protect the rider and you probably shouldn't worry too much about the dragon
- Against grudge throwers, it depends on if they randomize or if they hit both rider and mount. If they randomize, treat them like inaccurate cannons. If they don't, then treat them like multishot war machines with respect to how you choose to protect yourself
- If you're only going to be facing one or two war machines and a smattering of missile troops, you can safely emphasize close combat offense/defense at the cost of ranged defense.
whoa.
Yikes, math hammer taken to the extreme. Glad I didn't do it
Rep just for the effort.
SirKently
I am right 94% of the time, why worry about the other 3%.
Hehe, I like theorycrafting and playing math-hammer... sometimes I get started though and it ends up going to an extreme! Thanks for the reps all!
0.0
-.-
0.0
well ok!
that was awesome
midvalley
Bloomin heck! nice work, i want to get myself a dragon just because of the post
this would be a nice entry in the tatica...