Cannon accuracy

Every ball in a broadside is rolled separately. The game works out one chance to hit for the battery, then each gun rolls against it. This page walks through that sum. If you would rather just see the answer, use the hit chance calculator.

The short version

chance = 100 - target's defense + your accuracy      (as a percentage)
chance = chance x range fall-off
chance = chance + target size bonus or penalty

The first line is allowed to go over 100. That surplus is not wasted: it is what survives the range fall-off in the second line. Only the final answer is limited to between 0% and 100%.

Step 1: defense against accuracy

Defense is on every ship page, one number each for bow, stern, sides, sails and crew. Which one counts depends on what your shot is aimed at and where you are standing:

Round shot aims at the hull, so the game uses the defense of the side facing you: bow, stern or side.
Bar and chain shot aim at the sails. Grape and canister aim at the crew.

Each point of defense is one percentage point off your chance to hit.

Accuracy is everything added back on:

Source	Typical size	Notes
Your cannon	+40 point blank, about +55 to +70 at mid range, more beyond	Listed on each cannon page under Accuracy by range. It slides smoothly between the three marks.
Your shot type	0, or -1 for chain	Shot barely changes accuracy. What it changes is range — see Step 3.
Captain skills and fittings	varies	Anything that says Accuracy. Some only apply to hull, sail or crew shots, or to one range band.
Night	-10	Dawn, day and dusk are all normal.
Target on battle sails or furled	-15	Only when you are shooting at her sails. Less canvas is a smaller target.
Movement	0 or worse	See below.

Step 2: movement

Shooting from a moving deck at a moving target is harder. Three things are added together:

Your own speed: -2 per knot you are sailing (never worse than -50). At 10 knots that is -20.
The target crossing your guns: up to -10. It is measured by how fast your gunners must swing the barrels to follow her. No penalty inside 60 m; full effect from 200 m out. A ship sailing straight toward or away from your broadside barely counts.
Target Tracking: a bonus that pays those penalties off. Every ship has some built into her deed, from about +12 to +30 (shown on the ship page under How to get it), light cannons add a few more, and some fittings and skills add to it.

The total can never go above zero. Target Tracking only ever cancels movement penalties; it never adds accuracy on its own.

In practice your ship’s own tracking covers normal battle speeds. A ‘Lexington’ Brig has +20, which pays for about 8 knots plus a crossing target. You only start losing accuracy when you are sailing faster than your tracking covers: that same brig at 14 knots is down 11.

Step 3: range fall-off

Every cannon has a mid range and a maximum range (see its cannon page). The shot you load shortens both:

Shot	Reach compared with round shot	A 12lb Cannon (390 m mid / 700 m max) becomes
Round	100%	390 m / 700 m
Bar	90%	351 m / 630 m
Chain	70%	273 m / 490 m
Grape	60%	234 m / 420 m
Canister	55% mid, 50% max	215 m / 350 m

Beyond the shortened maximum the guns will not fire at all. So anti-sail and anti-crew shot are close-range tools: with chain loaded, “mid range” for that 12-pounder is 273 m, not 390 m.

The chance from steps 1 and 2 is then multiplied by a fall-off, measured against those ranges:

Where the target is	Multiplier
Point blank	x 1.00
Halfway to mid range	x 0.80
At mid range	x 0.57
A quarter of the way from mid to max	x 0.27
Halfway from mid to max	x 0.13
At maximum range	x 0.03

So accuracy slides gently down to mid range, then drops off a cliff. This is why your cannon’s accuracy bonus grows so much at long range: it is fighting that cliff, and only partly winning.

The practical lesson: your cannon’s mid range is the most important range number it has. Inside it you hit most of the time. Much beyond it you are mostly making splashes. Light guns have a longer mid range than heavy guns, so small ships can out-range big ones in practice even though every ship gun shares the same maximum.

Step 4: the size of the target

Big ships are easier to hit and small ships are harder. This is added after range fall-off, so it still matters at long range.

Target’s length	Adjustment	Extra beyond 400 m (full at 550 m)
Up to 5 m	-8%	-6%
5 to 10 m	-7%	-6%
10 to 15 m	-6%	-6%
15 to 20 m	-5%	-6%
20 to 25 m	-4%	-6%
25 to 30 m	0	-4%
30 to 35 m	+8%	0
35 to 40 m	+16%	+4%
40 to 45 m	+20%	+4%
45 to 50 m	+24%	+4%
50 to 55 m	+28%	+4%
55 to 60 m	+32%	+4%
Over 60 m	+36%	+4%

A ship’s length is on its page. Because this is added at the end, it sets a floor: a 45 m frigate is at least 20% likely to be hit by anything that can reach her, while a 17 m sloop at long range is very nearly untouchable.

Worked example

You are in a ‘Lexington’ Brig (Target Tracking +20) with 12lb Cannon (mid range 390 m, maximum 700 m), sailing at 8 knots, firing round shot into the side of another ‘Lexington’ Brig (defense 39, length 27 m) as she crosses your beam.

	100 m	250 m	390 m	550 m	700 m
Start	100	100	100	100	100
Her side defense	-39	-39	-39	-39	-39
Cannon accuracy at that range	+47	+58	+68	+160	+247
Movement: speed -16, crossing up to -4, tracking +21	0	0	0	0	0
Before range	108	119	129	221	308
Range fall-off	x 0.91	x 0.74	x 0.57	x 0.12	x 0.03
Size (27 m)	0	0	0	-4%	-4%
Chance each ball hits	98%	88%	73%	23%	5%

Three things to notice:

Movement costs this brig nothing. Her own +20 tracking (plus +1 from the guns) covers 8 knots and the crossing target. Push on to 14 knots and every column loses 11 before range, which costs 8% at 250 m but only about 2% at 550 m.
The cannon’s long-range bonus is doing real work. Accuracy climbs from +68 at mid range to +247 at maximum precisely because the fall-off is so brutal. Without it the 550 m shot would be about 12% instead of 23%.
It still is not enough. Three balls in four miss at 550 m, while at 250 m nearly nine in ten hit.

Same shot, different targets

Now hold everything the same and change only what you are shooting at:

Target	Side defense	Length	At 250 m	At 550 m
‘Jamaica’ Sloop	43	17 m	80%	15%
‘Lexington’ Brig	39	27 m	88%	23%
‘Alexander’ Fourth Rate	18	40 m	100%	49%

At 550 m the fourth rate is more than three times as easy to hit as the sloop, and almost all of that gap is size. Her 25 points of lower defense are worth only about 3% out there, because defense is crushed by the same fall-off as everything else. The size adjustment (+20% for her, -11% for the sloop) is added after the fall-off, so it keeps its full value at any range.

What this means in a fight

Fight inside your mid range. Know the number for the guns you carry.
Defense matters most up close. A point of defense removes a full 1% at point blank, about 0.6% at mid range, and almost nothing at long range, because it is multiplied by the same fall-off as everything else.
Accuracy bonuses work the same way. +10 accuracy is worth +10% at point blank but only about +1% near maximum range. Size, on the other hand, is added at the end and keeps its full value at any distance.
Know how fast you can shoot from. Halve your Target Tracking: that is roughly the speed in knots you can sail with no accuracy loss. Above it, each extra knot costs 2. Fast ships with low tracking feel this most; drop to battle sails before an important broadside.
Load the right shot for the distance. Chain and grape cut your gun’s range to 70% and 60%. If you are beyond that shortened mid range, round shot will hit far more often.
Small ships should stay at range against big ones. Past 400 m the size table works doubly in their favour.
Shooting sails? Do it while she is under full sail. Once she drops to battle sails your sail shots lose 15.
Night fights are sloppier for everyone: -10 all round.

Grappling uses a different sum

Boarding has its own chance, explained in Grappling and boarding.