Thoughts after poking at the data for a short while:
The most notable thing, to me, is that plausible extrapolation of the distribution of damage from the encounter types listed is far from being sufficient to explain how many ships are lost. Crabmonsters don’t usually do a lot of damage and it looks as if maybe 1% of crabmonster encounters are terminal. Demon whales are the most unclear—the PDF is still increasing at 100% damage—but it looks as if maybe 100% is approximately the peak, in which case we should expect about as many sinkings as we’ve seen non-sinkings. Harpies are never known to do >24% damage. Krakens are never known to do >78% damage. Merpeople seem like they have a bit of a right tail, but there’s no way to know how far it extends. It doesn’t look as if it’s likely to account for a huge numbre of sinkings. Nessie has what looks like a normal-ish distribution whose right tail extends a bit beyond 100% but I wouldn’t expect more than a few percent of encounters to result in sinking. Pirates are never known to do more than 64% damage. Sharks are never known to do more than 56% damage. Water elementals are always between 74% and 85%. These seem like we might have maybe 10-20 sinkings from crabmonsters, 330 from demon whales, a couple of hundred from merpeople, 25ish from Nessie, and none from anything else. But actually there are 2367 sinkings.
This suggests that most of the sinkings come either from encounters that are way beyond the known distribution of damage, or from entirely different types of encounters we don’t have a record of.
For the first option, maybe the demon whale distribution keeps growing rightward for a while longer. Not terribly implausible. Maybe the merpeople have a really long right tail. The water elemental distribution is pretty weird; maybe there are other types of water elemental with similarly narrow distributions living beyond 100%. For the second option, maybe sometimes the gods get angry and smite ships with lightning so that everyone dies, or maybe there’s some horribly dangerous geographical feature that isn’t on the maps because once you get close enough to see it you’re already doomed. Or maybe sometimes the captain or crew decides that they can sail far off course, sell the cargo, keep the proceeds, and live happily ever after.
What can we do about all these? We can completely stop merpeople attacking. Maybe merpeople are a lot of the mystery sinkings. Might be worth it. We can bring krakens and demon whales down by 2% per oar, and weirdly this stacks additively, so buying 50 oars might be worth it since demon whales are our leading “in-sample” candidate to explain the sinkings. Except that we top out at 20 extra oars. Better than nothing, probably worth it. Shark repellent is a terrible idea because sharks are among the nicer encounter options. Rifles for harpy protection seem dumb since harpies are never known to do much, but if we’re battling unknown unknowns something that offers to prevent all damage done by harpies is tempting. (Though it’s hard to know how we could actually know that they will prevent all damage even in hypothetical cases where the harpies do >4x more damage than they have ever done to any ship that’s returned to tell the tale.) Water elementals are pretty common and the foam swords will always save a lot of damage when they attack—and if indeed there are currently-unknown super-water-elementals doing >100% damage, they might save us.
As for the completely unknown unknowns, maybe we can bring a priest or institute big rewards for foiling mutinies, or something.
(Perhaps I should take the name of the ship as a hint that we’re facing the first kind of scenario rather than the second.)
Since my top priority is to survive, I buy off the merpeople (45gp) and fill up on extra oars (20gp). Now I could get rifles (35gp) just in case there are occasional super-harpies, but it’s not clear that that’s more likely than occasional super-elementals so I’ll get the foam swords instead (15gp) since that does much more to reduce damage in the non-fatal cases. I have 20gp left, with which I can halve crabmonster damage (saving, by eyeball, maybe 20% damage on average in the 4% of cases when they attack) or knock 20% off Nessie-and-pirate damage (saving, by eyeball, maybe 16% of damage in 4% of cases when Nessie attacks, plus maybe 12% of damage in 20% of cases when pirates attack); the latter is clearly better damage-wise and might be better sinking-wise too. So: tribute to the merpeople, max extra oars, foam swords, two cannons.
But I am still painfully aware that I don’t know where those sinkings are really coming from, and if there were some way to get more information about that (e.g., fit some ships with lifeboats) it would be a hell of a good idea to do it first.
I didn’t see any obvious sign of large seasonal or directional effects. There are some long-term drifts; e.g., pirates seem to be becoming less common, harpies, merpeople, sharks, and maybe krakens seem to be becoming more common. I don’t think these effects are large enough to change the decisions above. I haven’t looked for correlations (e.g., maybe when a ship has been attacked by pirates it becomes more or less likely that the next ship going the same way will be). I do have more detailed notes on what the damage-distributions look like for the various kinds of encounter, but the level of detail above seems sufficient. (They don’t appear to vary much with month, year, or direction.)
[EDITED to add:] Hmm, but buying off the merpeople might be risky? It would mean more attacks by other things that might turn out to be potentially ship-sinking. In particular, more demon whales, and our best demon whale countermeasure isn’t very good. I’m not terribly sure that paying the merpeople is actually wise.
Thoughts after poking at the data for a short while:
The most notable thing, to me, is that plausible extrapolation of the distribution of damage from the encounter types listed is far from being sufficient to explain how many ships are lost. Crabmonsters don’t usually do a lot of damage and it looks as if maybe 1% of crabmonster encounters are terminal. Demon whales are the most unclear—the PDF is still increasing at 100% damage—but it looks as if maybe 100% is approximately the peak, in which case we should expect about as many sinkings as we’ve seen non-sinkings. Harpies are never known to do >24% damage. Krakens are never known to do >78% damage. Merpeople seem like they have a bit of a right tail, but there’s no way to know how far it extends. It doesn’t look as if it’s likely to account for a huge numbre of sinkings. Nessie has what looks like a normal-ish distribution whose right tail extends a bit beyond 100% but I wouldn’t expect more than a few percent of encounters to result in sinking. Pirates are never known to do more than 64% damage. Sharks are never known to do more than 56% damage. Water elementals are always between 74% and 85%. These seem like we might have maybe 10-20 sinkings from crabmonsters, 330 from demon whales, a couple of hundred from merpeople, 25ish from Nessie, and none from anything else. But actually there are 2367 sinkings.
This suggests that most of the sinkings come either from encounters that are way beyond the known distribution of damage, or from entirely different types of encounters we don’t have a record of.
For the first option, maybe the demon whale distribution keeps growing rightward for a while longer. Not terribly implausible. Maybe the merpeople have a really long right tail. The water elemental distribution is pretty weird; maybe there are other types of water elemental with similarly narrow distributions living beyond 100%. For the second option, maybe sometimes the gods get angry and smite ships with lightning so that everyone dies, or maybe there’s some horribly dangerous geographical feature that isn’t on the maps because once you get close enough to see it you’re already doomed. Or maybe sometimes the captain or crew decides that they can sail far off course, sell the cargo, keep the proceeds, and live happily ever after.
What can we do about all these? We can completely stop merpeople attacking. Maybe merpeople are a lot of the mystery sinkings. Might be worth it. We can bring krakens and demon whales down by 2% per oar, and weirdly this stacks additively, so buying 50 oars might be worth it since demon whales are our leading “in-sample” candidate to explain the sinkings. Except that we top out at 20 extra oars. Better than nothing, probably worth it. Shark repellent is a terrible idea because sharks are among the nicer encounter options. Rifles for harpy protection seem dumb since harpies are never known to do much, but if we’re battling unknown unknowns something that offers to prevent all damage done by harpies is tempting. (Though it’s hard to know how we could actually know that they will prevent all damage even in hypothetical cases where the harpies do >4x more damage than they have ever done to any ship that’s returned to tell the tale.) Water elementals are pretty common and the foam swords will always save a lot of damage when they attack—and if indeed there are currently-unknown super-water-elementals doing >100% damage, they might save us.
As for the completely unknown unknowns, maybe we can bring a priest or institute big rewards for foiling mutinies, or something.
(Perhaps I should take the name of the ship as a hint that we’re facing the first kind of scenario rather than the second.)
Since my top priority is to survive, I buy off the merpeople (45gp) and fill up on extra oars (20gp). Now I could get rifles (35gp) just in case there are occasional super-harpies, but it’s not clear that that’s more likely than occasional super-elementals so I’ll get the foam swords instead (15gp) since that does much more to reduce damage in the non-fatal cases. I have 20gp left, with which I can halve crabmonster damage (saving, by eyeball, maybe 20% damage on average in the 4% of cases when they attack) or knock 20% off Nessie-and-pirate damage (saving, by eyeball, maybe 16% of damage in 4% of cases when Nessie attacks, plus maybe 12% of damage in 20% of cases when pirates attack); the latter is clearly better damage-wise and might be better sinking-wise too. So: tribute to the merpeople, max extra oars, foam swords, two cannons.
But I am still painfully aware that I don’t know where those sinkings are really coming from, and if there were some way to get more information about that (e.g., fit some ships with lifeboats) it would be a hell of a good idea to do it first.
I didn’t see any obvious sign of large seasonal or directional effects. There are some long-term drifts; e.g., pirates seem to be becoming less common, harpies, merpeople, sharks, and maybe krakens seem to be becoming more common. I don’t think these effects are large enough to change the decisions above. I haven’t looked for correlations (e.g., maybe when a ship has been attacked by pirates it becomes more or less likely that the next ship going the same way will be). I do have more detailed notes on what the damage-distributions look like for the various kinds of encounter, but the level of detail above seems sufficient. (They don’t appear to vary much with month, year, or direction.)
[EDITED to add:] Hmm, but buying off the merpeople might be risky? It would mean more attacks by other things that might turn out to be potentially ship-sinking. In particular, more demon whales, and our best demon whale countermeasure isn’t very good. I’m not terribly sure that paying the merpeople is actually wise.
Looks like you’ve put in more work than I did below and come up with very similar answers, the one diff I see is that you tried
foam swords as a speculative guess that water elementals are non-linear and explain the extra sinkings/a way to reduce non-sinking-related damage
whereas I just went for
a third cannon for a bit of marginal equity against Nessie