#### Sky Kiwi

##### Pirate Master

**If you don't care about the science behind it all, just go to the bottom. The words/numbers in RED are the important ones. You might also want to read the "General Notes" section at the bottom.**

Hi there! You probably know me as "that one guy who filled a few threads with a whole lot of math". Well I'm here to put it in its own thread now.

Disclaimer: I haven't fully tested SvS yet. All this is PvE.

The first thing you need to know is how cannonball damage works. This is important because it means all the end result numbers can be in terms of

**percent average damage relative to an ordinary broadside.**Even against all enemy ships, at all times, these damage ratios remain persistent. Hunters receive 8% less damage and Warships receive 24% less damage. This was tested at notoriety 42, and max sailing/cannon level. These percentages go down at higher levels, which I have just confirmed (but still working on details), but the important part remains: the percentage is consistent across different ammo types. Additionally, ships with armour remaining take 50% less damage when hit on that side. Again, this number is persistent.

Why does that matter so much? Well, let's take for example round shot vs fury shot. Fury is known to be

*exactly twice as strong as Round Shot*. The importance of what I said above is that it doesn't matter if you shoot a Navy Ferret with no armour, or a Battle Royale with full armour - Fury still does twice as much damage.

With that said, the next step is knowing your damage values. You may have seen this thread where I went very overboard on obtaining various numbers and explaining my math. If you want to delve deeper into what happens next, read through the conversations that happened there.

I obtained my damage values through a thoroughly controlled method. I would fire each of my three relevant shots (in this case round, thunder and explosive) against the same type of ship while armoured, then again while not armoured. I repeated this process for hunters, and then warships. Once I had determined how it all correlates together, I no longer had to test the same ammo types against three different ships, I merely had to compare against round shot to the other ammunition types against any particular ship. As said before, for examples of numbers and a higher detail explanation, see the thread linked above. For ammo types I don't have, I recruited some helpful forum members to provide me with their exact damage values for me to do my math with (thanks @WilyJaymes and @DR1F73R).

All the cannonball types (that are relevant to us) have clean multiple values of round shot's damage. So for the purpose of everything in this thread,

**we are going to use the relative damage to round shots**. In other words, the values below show "how many round shots it takes to do the same amount of damage." These are the values found below:

**Ammo Type Damage Amount:**

**Round Shot: 1**(duh)**Firebrand: 1.25****Thunderbolt: 3****Explosive: 12****Fury: 2**

Using these numbers in this format makes it very easy to compare special hull broadsides average damage values. The way to do this is simple. You multiply each cannonball's damage value by the chance of them obtaining it, and add them together. For example, on a Storm Chaser IV, you would use

**((1 * 0.85) + (3 * 0.15)).**For a regular broadside, it would be

**(1 * 1)**, which is obviously just 1. So remember, 1 is 100%. This allows us to obtain the average broadside damage values for each hull type.

**Copperhead****IV:**(1 * 0.95) + (12 * 0.05)**= 1.55**=**155%****V:**(1 * 0.90) + (12 * 0.10)**= 2.10**=**210%****VI:**(1 * 0.85) + (12 * 0.15)**= 2.65 =****265%****Additional Notes:**Copperhead has the highest*average damage*per broadside, however because of the nature of its low percentage but high hitting ammo it can vary wildly. Some broadsides will have absolutely no explosives, resulting in a meager 100%, while others might have an extra one or two in there, going as high as 400%. So Copperhead is commonly known as a high risk, high reward broadside ship. Additionally,*when your broadsides do not lock on,*the heavier weight of explosive ammo gives them less range.

**Skull and Bones**(1 * 0.85) + (2 * 0.15)**IV:****= 1.15 = 115%**(1 * 0.67) + (2 * 0.33)**V:****= 1.33 = 133%**(1 * 0.50) + (2 * 0.50)**VI:****= 1.50 = 150%**

**Fortune Hunter**(1 * 0.85) + (1.25 * 0.15)**IV:****= 1.0375 = 103.75%**(1 * 0.70) + (1.25 * 0.30)**V:****= 1.075 = 107.5%**(1 * 0.55) + (1.25 * 0.45)**VI:****= 1.1125 = 112.25%**

**Firestorm**(1 * 0.80) + (1.25 * 0.20)**IV:****= 1.05 = 105%**(1 * 0.60) + (1.25 * 0.40)**V:****= 1.10 = 110%**(1 * 0.40) + (1.25 * 0.60)**VI:****= 1.15 = 115%**

**Storm Chaser**(1 * 0.85) + (3 * 0.15)**IV:****= 1.30 = 130%**(1 * 0.70) + (3 * 0.30)**V:****= 1.60 = 160%**(1 * 0.55) + (3 * 0.45)**VI:****= 1.90 = 190%****Additional Notes:**When your broadsides do not lock on, thunderbolt ammo's lighter weight makes the shots travel significantly further.

**General notes:**

- Ammo range/speed does not matter if your broadsides lock on - all shots will travel at the same arc and speed.
- Firebrand burning effect is not working at this time, and when it does it does not stack. However, because of this, the firebrand's base damage is increased. In POTCO,
*firebrand actually did less base damage than round shot,*making the firebrand hulls have lower average damage than regular boardsides! - All skill points up to 5 increase every ammo type by the same percentage. The values above are true only if your round shot and special shot skills are the same skill level, otherwise you will see variance.
- Barrage
**does**affect broadside damage, but equally across all ammo types (in percentage), therefore not changing the results of these equations. - The broadside skills from sailing increase all ammo types equally in percentage, therefore not changing any of the values shown above.
- No matter what hull you're on,
**a good crew will always be your main damage output.**Some of these numbers may seem very extreme, but your broadsides will never be as powerful as a deck of strong gunners. A lucky Copperhead with a poor crew will not out-damage a Fortune Hunter with a strong crew. - The formula for enemy Hunter/Warship damage taken multiplier is
**1 - ((EnemyLevel - (PlayerNotorietyLevel + 5)) * 0.02)**. In layman terms, this means**"For every level the enemy is above (your notoriety level + 5), the enemy takes 2% less damage"**. This means for a Notoriety 50 pirate, Warships (level 59-61) take 8-12% less damage. At Notr30 they take 52% less damage! However, this damage reduction applies equally across all ammo types. I am unsure if normal ships follow this rule.

On a side note, I have a buff suggestion for firebrand (and therefore fortune hunter and firestorm hulls) coming soon, with an additional firestorm buff on top of that. I also think Skull and Bones could use a bit of a buff.

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