Discussion Why I don't think lvl4 Copperhead has 5% explosives (case study)

[Chris Phantomsteel]

A few first words
So a few days ago I decided to grind out a lvl4 copperhead war brig, and my first reaction was that is was really nice, since it can almost one-shot any ship that isn't a hunter or warship if there was an explosive round loaded. IF. Over the course of time I found the number of explosives to be ridiculously low, and since I have time today I decided to sacrifice around 2 hours to do some basic statistics study.



How did I do this?
I took my war brig, out to somewhere far from any other ships in order to fire broadsides as a test. I would stay away from other ships in order to clearly distinguish what rounds are explosives and what rounds aren't. See screenshot for example:

The rounds that went farer were normal ones, the one that landed less far is an explosive. Pretty self explanatory.

Afterwards I would take the statistics and put everything in a google excel sheet, which I will link at the end.

I didn't really bother to make a video as a proof, because it would take away way too much space for my computer. You'll just have to assume I'm not lying with the statistics. If you think I am lying, feel free and stop reading here.



First things to note
A war brig has 24 broadsides. Copperhead lvl4 supposedly gives you 5%. So that means that for every broadside, you should expect around 24*0.05=1.2 explosives.



The statistics
After going through 200 broadsides and noting down the number of explosives for each and every single broadside, my assumptions were quite true.

At a sample rate of 200, the average percentage of explosives was 2.29% and the average number of explosives was 0.535. Pretty astonishingly bad, but it was what I assumed before.

Here is a recap:

The sheet should be self explanatory, because only basic statistical calculations are made.

So why did you make different sample sizes? Because it can show me if my assumptions CAN be valid or not. At a small sample size, you can easily not get the percentage you're supposed to get. But as the sample size increases, the average still isn't near what it is supposed to be.

I also made sure that I was correct by making a chart that is visible. Until the sample size is around 50, the numbers aren't very stable, but that's normal. However, if the percentage was really 5%, this chart should be approaching 5 for the average percentage and 1.2 for the average number of explosives as the sample size increases. In this case, the chart stagnated at around the sample size of 75. At the sample size of 200, this was still similar. So it won't be approaching 5% even if I continue.

So, according to basic statistics, lvl4 Copperhead does NOT give you a 5% explosive chance for your broadsides. The bad thing is that the statistics that I had show that it's not even half of 5%.



So what am I trying to prove here?
With this, I want to show that something's not right. I'm not blaming anyone, but maybe it should be looked into by the developers because I honestly believe something is wrong here, especially with the numbers shown to me.

I might do this with a maxed out copperhead war brig again if I find a time to not do anything else that's useful in my life.

Please comment if you have any opinions/ideas on where I may have made a mistake.

Here is a link to the google docs to see exactly what I did: https://docs.google.com/spreadsheets/d/1SAbeHuKApFZIXG1Nc-mi1Nk1o-Fi0GmMMrQw0lkOh7c/edit?usp=sharing

 

[Driftarr]

This is me asking what may be obvious to everyone else. But does saying that a level 4 copperhead has a 5% chance of having explosive broadside mean every single shot has a 5/100 chance of being explosive? Meaning every shot from your 12 cannoned port-broadside has a 5 in 100 chance. rather than grouping the 5% chance over the 24 shots collectively?

Maths are not my strong suit but I feel like if the consistent statistics are showing lower than 5% to the favorability of getting explosive shot at lv 4 copperhead. It's because every single shot undergoes a 'roulette' if you will, of possible outcomes where getting a special shot is extremely unlikely as there's a 95% chance of it landing on round shot every single time. If this was across the 24 broadsides as a whole you would maybe see more consistent numbers.

Just to add, I have a level 6 firestorm war sloop. Now firestorm is one of the oddballs in ship types for the fact that it's special ammo rates are higher than round shot's, being at 60% Firebrand chance. But because I think that every shot individually has a 60% chance of special, more times than not, I get firebrand in every shot. I would almost wager to say if I spent two hours tracking the special ammo my firestorm puts out, that the number would be closer to 75-90% Firebrand over the course of a lengthy test.

 

[Chris Phantomsteel]

This is me asking what may be obvious to everyone else. But does saying that a level 4 copperhead has a 5% chance of having explosive broadside mean every single shot has a 5/100 chance of being explosive? Meaning every shot from your 12 cannoned port-broadside has a 5 in 100 chance. rather than grouping the 5% chance over the 24 shots collectively?

Maths are not my strong suit but I feel like if the consistent statistics are showing lower than 5% to the favorability of getting explosive shot at lv 4 copperhead. It's because every single shot undergoes a 'roulette' if you will, of possible outcomes where getting a special shot is extremely unlikely as there's a 95% chance of it landing on round shot every single time. If this was across the 24 broadsides as a whole you would maybe see more consistent numbers.

Just to add, I have a level 6 firestorm war sloop. Now firestorm is one of the oddballs in ship types for the fact that it's special ammo rates are higher than round shot's, being at 60% Firebrand chance. But because I think that every shot individually has a 60% chance of special, more times than not, I get firebrand in every shot. I would almost wager to say if I spent two hours tracking the special ammo my firestorm puts out, that the number would be closer to 75-90% Firebrand over the course of a lengthy test.

Did you mean 24 cannoned port-broadside?

If every shot has a 5/100 change of being explosive, then it's 0.05, afterwards multiplied by the number of shots per broadside with is 0.05*24 = 1.2
If we group the 5% chance to the 24 shots directly, it is the same which is 1.2.
Statistically, both situations you mentioned aren't any different from each other.

I understand that every shot has a very low percentage of being explosive and 95% chance of being normal. However, there are no differences (or shouldn't be, in this case) a difference between each shot being calculated as explosive or not, with the same process being done 24 times OR if the percentage was applied to the whole broadside. And even with the numbers being ridiculously low, there should not be such a large difference between statistics and the supposed percentage. 2.29% is a huge difference compared to 5%. The numbers on the graph show that as the sample size increases, the percentage is consistently at around 2.25%. If it was supposed to be 5%, then the graph should have at least shown some sort of increase, which at even the sample size of 200 didn't show.

 

[DatgdMadooko]

Hate to burst your bubble, but you have made a crucial error. You are just a tad bit wrong when you say that the war brig has 24 broadside cannons. The war brig has 24 broadside cannons split across both sides of the ship, meaning when you fire a single broadside, only 12 cannon rounds will be fired.

So the data you have collected is actually in favor of the 5% explosive chance. Your 2.29% that you found becomes 4.58% when you correctly account for the number of broadside cannons on a single side of a ship.

EDIT: I looked at your spreadsheet, and the 2.29% you referenced is actually 2.229%. This turns the adjusted 4.58% into 4.458%.

EDIT 2: Also what are we even talking about? The war brig has 22 total broadsides, meaning it only fires 11 cannons on each side. This turns the 4.458% into 4.86%! Lol what are we even doing...

Here's what the spreadsheet should read:

 

[Chris Phantomsteel]

Hate to burst your bubble, but you have made a crucial error. You are just a tad bit wrong when you say that the war brig has 24 broadside cannons. The war brig has 24 broadside cannons split across both sides of the ship, meaning when you fire a single broadside, only 12 cannon rounds will be fired.

So the data you have collected is actually in favor of the 5% explosive chance. Your 2.29% that you found becomes 4.58% when you correctly account for the number of broadside cannons on a single side of a ship.

EDIT: I looked at your spreadsheet, and the 2.29% you referenced is actually 2.229%. This turns the adjusted 4.58% into 4.458%.

EDIT 2: Also what are we even talking about? The war brig has 22 total broadsides, meaning it only fires 11 cannons on each side. This turns the 4.458% into 4.86%! Lol what are we even doing...

Here's what the spreadsheet should read:
View attachment 92708

This clears up a lot of things. About the broadsides though, the wiki says 22 and ingame it shows 24 for me?

 

[DatgdMadooko]

I knew there was some sort of confusion about the number of broadsides! The wiki says 22, the shipwrights (when purchasing a ship) say 22, but I suppose in the ship menu (H), it says 24? If that's the case, then we definitely discovered something that should be changed.

 

[Chris Phantomsteel]

I knew there was some sort of confusion about the number of broadsides! The wiki says 22, the shipwrights (when purchasing a ship) say 22, but I suppose in the ship menu (H), it says 24? If that's the case, then we definitely discovered something that should be changed.

And so my thread wasn't useless after all :^)

EDIT: Counted in game, counted 12

 

[DatgdMadooko]

And so my thread wasn't useless after all :^)

Yes but not just for the practical reason of finding a mistake in the game. You have also demonstrated that it's ok to be wrong, which is a mark of good character.

 

[Sky Kiwi]

Guys, the War Brig has 12 broadside cannons per side. The 24 count is total broadsides - ie, both sides.

This means there's an average of 0.6 explosives per broadside (12 * 0.05). You got 0.535, which is indeed lower but not so much it's controversial. That difference is most likely just chance.

As for your "percentage of explosives" calculation of 2.29%, since the dividing number (number of cannonballs fired) is half what you thought it was, that means your percentage should be doubled, up to 4.58%. Again, most likely just chance.

 

[DatgdMadooko]

your percentage should be doubled, up to 4.58%

That's what I said. We did further investigation as well, and found there is an inconsistency in the game.

At a shipwright, when purchasing a war brig, we see this:

Note the number of broadsides is 22.

When you have purchased the war brig, by pressing H, we see this:

Note the number of broadsides is 24.

I don't own a war brig, so I can't confirm which is correct. But if I remember anything from my POTCO days, it was that the war galleon had more broadsides than any other ship (24).

So assuming the war brig only has 22 broadsides, and thus only fires 11 cannons on a single broadside, the observed chance (observed by @Chris Phantomsteel) of firing an explosive round with L4 copperhead is 4.86%, which is what we expect.

 

[Sky Kiwi]

That's what I said. We did further investigation as well, and found there is an inconsistency in the game.

At a shipwright, when purchasing a war brig, we see this:
View attachment 92723
Note the number of broadsides is 22.

When you have purchased the war brig, by pressing H, we see this:
View attachment 92724
Note the number of broadsides is 24.

I don't own a war brig, so I can't confirm which is correct. But if I remember anything from my POTCO days, it was that the war galleon had more broadsides than any other ship (24).

So assuming the war brig only has 22 broadsides, and thus only fires 11 cannons on a single broadside, the observed chance (observed by @Chris Phantomsteel) of firing an explosive round with L4 copperhead is 4.86%, which is what we expect.

Yeah this inconsistency was noticed quite some time ago. The wiki is/was unhelpful in the same area. As both a War Brig owner and "a guy who googled images of War Brigs and counted them just to be sure" (my official title, btw), I can guarantee to you it's 24 (12 on each side). Same as a War Galleon, which I always thought was stupid.

 

[GoGud]

So basically we discovered that the War Brig is even more overpowered than we thought :thinking:

 

[Mathias]

The number of broadsides you see is the total number. The war brig has 24 broadside cannons, but 12 broadside cannons per side.

Also, most games with RNG factors use code like the following:

If (X <= Y) {hit} where X is a randomly generated number and Y is rate. Let's say the random numbers chosen for your twelve broadsides on a copperhead 4 are 20, 50, 2, 34, 4, 85, 75, 3, 89, 5, 12, 48, you'd be firing 4 explosive rounds, 5 if you had copperhead 6 with its 15% chance.

And BTW, for your programmers out there, this is a gross oversimplification.