Bad maths indeed.
Never use cannons. Always use volley guns.
Volley guns never hit anything beyond 24". Empire Cannons have range 72". They have different roles. Volley guns are short range all-arounders, cannons are there to counter monsters and enemy war machines. Volley gun simply doesn't do what a cannon does. And vice versa.
let's do math. To start with, there's the chance of misfire. Any gunpowder weapon that misfires has a 50% chance of being rendered useless for the rest of the game and a 1/6 chance of being killed outright, so misfires are terrible. A cannon has a 1/6 chance of misfiring every time it shoots. A volley gun has a 1/24 chance of misfiring.
Did you read the cannon and volley gun rules before writing this? Especially, did you read the Misfire Table, Page 74 of the 9th Age v1.0.0 basic rule book?
The chance for Breakdown (useless for the rest of the game) is 1/3. Not 50% but 33.3 %.
In the 9th Age, apart from some rare and dangerous artillery pieces, artillery is never 'killed outright' by the misfire table. Contrary to previous editions, misfire doesn't have a chance of autodestroying artillery, so doesn't give points to the enemy.
The chance of Volley Gun misfiring is 7.4 %. Yes, that's less than the cannon 16.7 % (1/6), but significantly more likely than 1/24 (ca. 4 %) would be.
A cannon that is not shooting at a large target will hit 50% of its shots. This means you will get three hits on average every game. Sometimes more, sometimes less. Assume the target is a large target, and flying, the ideal cannon target. The cannon still hits only 1/3 of the time, and averages (barring the roll of a 1 to wound) 4 wounds. So over the course of a game you can expect to kill a single monster with a cannon. Okay, that's worth 100 points.
A cannon that is not shooting at a large target will hit 50 % at short range, and 33.3 % at long range. Assuming it's not used by an Artificer (Engineer). It's hard to say if the enemy comes into close range or not. Many players are afraid of cannons, so often the enemy doesn't come close enough, so 33.3 % or two hits is likely.
This still has a real threat of removing more than 100 pts value from the enemy. Few of ordinary Empire units can hope for 100 % or better payback. It's a gamble, as games often are, but a gamble worth taking. Especially for Empire, which has problems to deal with enemy monsters.
Large makes hitting
easier, so doesn't
reduce the probability of hitting! At close range, you hit 66.7 % of the time, at long range, you hit 50 % of the time. Not 1/3 (33.3 %).
There are many single model multiwound flying units in the game. Cannons work superbly against them, at ranges much longer than Volley Guns can ever achieve.
A volley gun shooting that same target, let's assume long range, will average 20 shots, hitting on 5's so 6-7 hits, wounding on 4's (unless your opponent is fielding a dragon) so 3 wounds. Average is 18 wounds over those same six turns.
To start with, the long range of the Volley Gun is 12.1"-24". At this range, the cannon always shoots at short range.
At long range, a Volley Gun without an Artificer (Engineer) that doesn't misfire can hope for 5-6 hits. Overall, 5 hits is the average. Strength 5 let's you wound T4 guys on 4's. Cannons usually target T5/T6 monsters or T7 war machines. So the comparison is weak and/or partial. I'd say against typical cannon targets the Empire Volley Gun can hope for 1-3 Wounds at long range, and that assumes that they come within 24". The average Wound total over 6 turns is perhaps 12. Strength 5 and AP (-2) may still leave a chance for armour save on a 6. So it could be 10 wounds.
But in general, getting enemy monsters or war machines within 24" of your Volley Gun is very, very unlikely. If they come that close, they usually charge into combat, preventing the use of ranged weapons against them. Thus, even if a cannon can hope to hit a large target only twice or thrice in a game, dealing on the average 6-9 Wounds (8-12 against flyers) over the whole game, a Volley Gun probably rarely has the chance to even try.
Let's talk units.
This part was better. I agree Cannons just don't work against units, and I think the feeling of the game is flawed there.
Then again, the 9th Age designers really wanted to profile different troop types and units, so having clear and different targets for cannons and volley guns probably goes along the design intent.
Another interesting comparison is Volley Guns to Handgunners (for the similar point cost). Volley Gun is always more efficient, but you need to consider the reliability of the Handgunners (no misfires), and their much larger total Wounds. They can even do some cc fighting, and can carry a standard to play the objective game. Again, I'd say the two unit choices have a clearly different role on the battlefield, and you should choice your unit according to what you want to do. Neither is universally better than the other.
-Z