D&D.Sci Pathfinder: Return of the Gray Swan

by aphyer7 min read1st Sep 202122 comments

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Exercises / Problem-SetsD&D.SciFiction
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Edited to add: Consensus is that this scenario is a bit too complicated.  It probably shouldn't be the first D&D.Sci scenario you play - try the original Voyages of the Gray Swan or The Sorcerer's Personal Shopper first, if you haven't played them yet.

Story

You had thought that the Admiralty was done with you after last time.  After their response to your initial suggestions was to assign you to a series of dangerous voyages and hope that killed you, you were quite glad to set foot back ashore and not hear from them again.  You've still been receiving a modest stipend for your past service for the last ten years or so, and that plus occasional odd-jobs for local wizards has left you a fairly comfortable life in the capital of Eastmarch.

So you are perhaps a bit concerned when you receive a summons to attend at once an audience with the Third Lord of the Admiralty.  Your only consolation is that the summons arrives via a courier knocking on your door rather than a squadron of marines kicking it down and dragging you off.

You were not expecting what actually happened, though. When you were called into the Lord Admiral's office, there was only one person it it, and you recognized him.

"Captain O'Neill?"  It's been a while since you saw him.  He's still got the beard and the lively eyes, but he was wearing less braid back then, and a less...fancy...hat...

He chuckles.  "It's Admiral now, actually.  I'm sorry to call you here on such short notice, but a problem has arisen that I could use some help with."

It seems that Captain O'Neill (you absent-mindedly call him 'Captain' rather than 'Admiral' another three times during your conversation, but he doesn't seem offended) has risen through the ranks quite dramatically since you sailed with him on the Gray Swan.  It also seems that he still remembers, and appreciates, your efforts to keep him and his crew alive ten years ago (even if your main motive was to keep yourself alive with them).

He explains that the Admiralty has an extremely important mission.  Sometime later this week, ships need to reach certain locations on this MAP.  He points out two locations. 

You stare at the map in puzzlement.  "Why do you want ships there?  It doesn't look-"

O'Neill sighs.  "Yes, I know.  It is two random places in the middle of the ocean, that do not seem to be of any relevance.  But Mage-Prince Konig is quite insistent that this is a vital objective, of such importance and secrecy that even I cannot be told what it is, and the First and Second Lords of the Admiralty concur with him.  So I need to allocate two ships from those in port today to set sail tomorrow, one to each of those two locations, each carrying an unspecified cargo for unspecified purposes."

That...is odd.  "So, if we stop at Norwatch here-"

The Admiral's teeth are gritted.  "Yes.  I know.  The obvious way to address this is to transport whatever this unspecified cargo is to ports near the target locations using our standard supply routes, switch to a fresh vessel or await repairs, and then make short voyages from those nearby ports to the targets.  However, a majority of the Admiralty Triumvirate-" (his tone of voice makes it very clear who that majority is) "-have decided that, for reasons of operational security, these voyages must launch from Eastmarch, must make their way to their respective destinations without stopping at other ports, and must return directly to Eastmarch afterwards."

You look at the map again.  "That's...rather a long way."

O'Neill nods grimly and lowers his voice.  "My fellow admirals have informed the Prince that the best ships in our Navy should be able to bring the cargo to those destinations without risk of mishap.  I am less confident of this.  And my fellow admirals believe that for the ships to successfully return afterwards is not entirely necessary.  I disagree with this position, but I lack the authority to overrule them.  But I remember what you've done before, and I'm hopeful that with access to the Admiralty archives you might be able to plot as safe a course as possible, and give my men the best chance they can have."  He stands up straighter and looks you in the eye.  "You've saved me and my men before.  Will you do it again?"

Data & Objectives

In the Admiralty Archives, as well as the MAP you saw before, you find a LOG of the past voyages ships have made, and another LOG of the encounters recorded on them.  You note approvingly that someone's been assigning ID numbers to the ships and voyages, so that you don't have to rely entirely on names.

June 1420, Week 1 has just ended.  The next voyages will take place during June 1420, Week 2.  The ships in port today (with you in the capital port of Eastmarch, Hex Q6) are:

The Bloody Diamond, a Barquentine captained by Angus MacDougal. Last voyage was 8 weeks ago.
The Orange Falcon, a Galleon captained by Brandon Buchanan. Last voyage was 7 weeks ago.
The Red Pearl, a Dhow captained by Brandon O'Malley. Last voyage was 6 weeks ago.
The Green Heart, a Dhow captained by Baron Heinrich von Reinhardt. Last voyage was 6 weeks ago.
The Purple Heart, a Dhow captained by Rick O'Neal. Last voyage was 5 weeks ago.
The Saucy Heart, a Barquentine captained by Erin Aubrey. Last voyage was 4 weeks ago.
The Rusty Heart, a Barquentine captained by Sir Gerhart von Zelig. Last voyage was 4 weeks ago.
The Mopey Diamond, a Carrack captained by Conall MacDougal. Last voyage was 3 weeks ago.
The Scurvy Hind, a Dhow captained by Dyllon Keating. Last voyage was 3 weeks ago.
The Mopey Tortoise, a Barquentine captained by Brandon O'Neal. Last voyage was 3 weeks ago.
The Red Duck, a Dhow captained by Conor Callahan. Last voyage was 3 weeks ago.
The Scurvy Swan, a Carrack captained by Seamus Reagan. Last voyage was 2 weeks ago.
The Silver Duck, a Carrack captained by Jack Keating. Last voyage was 2 weeks ago.
The Mopey Hind, a Barquentine captained by Angus MacDougal. Last voyage was 1 week ago.
The White Hind, a Dhow captained by Conor O'Connell. Last voyage was 1 week ago.
The Bloody Bottom, a Carrack captained by Lord Friedrich von Walderdorf. Last voyage was 1 week ago.
The Bloody Swan, a Carrack captained by Count Manfred von Konig. Last voyage was 1 week ago.

You need to choose one of those ships to journey to Hex E8 and one to journey to Hex L13, and assign routes to each of them.  According to Admiral O'Neill, standard Admiralty practice would be to assign the Bloody Diamond and the Orange Falcon to these voyages, but you may assign any ships you see fit.

Most of the Admiralty believes that the most important objective is for both ships to successfully reach their destinations (regardless of whether they make it back afterwards), and that you should maximize that probability at all costs.

Admiral O'Neill would also like you to try to maximize how many of those ships are able to return safely home.

Which ship will you advise the Admiral send to each target?  And what routes will you advise they take?

Bonus Objective: The Admiral's position seems politically tense.  If you can find any useful information in the data, even if it's not strictly relevant to the mission at hand, it might help him improve his position. 

Notes

This is based on abstractapplic's very good 'Dungeons and Data Science' series, and specifically on #4, 'Voyages of the Gray Swan'.  You don't need to have played that one to do this, this one is using a very different ruleset.  EDITED TO ADD: While it should be clear from the data, just to clarify for the particular avoidance of doubt: "Varsuuvius' Law of Random Encounters" as expounded in that scenario DOES NOT HOLD here.

Since the last few D&D.Sci scenarios have been pretty much completely solved, I've tried to give this one a more complex underlying world-model with a lot of different levels of success available.  If you only have a little time to put into it, you should still be able to perform much better than random, but performing optimally is substantially harder - if you have a lot of time, as well as optimizing your success on the main mission there are a variety of secrets scattered in the data for the Bonus Objective.

For the sake of those who wish to work alone, please spoiler your comments if they contain information about the dataset, but you are also free (and encouraged) to work together.

I'll be posting the ruleset and answers in sometime between one and two weeks, depending on whether it looks like people are still working on this.

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Some (late relative to others) initial remarks:

As others have noted, all but one datapoint is consistent with Galleon/Carrack having 30hp, Barquentine/Dhow having 20hp, The one exception being a single case of Carrack taking 5% dmg from Reef. Also as abstractapplic has noted, Barquentines tend to be effected by things similarly to Galleons and Dhow similarly to Carracks. abstractapplic claims that they are the same other than hp, but it would take a massive confounder to account for e.g. the different encounter probabilities (as found by measure, also remarked on below).

Note, per-hex encounter probabilities below don't account for selection effects except that I tended to round up if close call to round up or down. I do count only out-of-port ships that didn't get destroyed in the denominator. Damage numbers don't account for selection effects either.

Encounters:

Reef, Kraken, Iceberg Mefolk and Wyrd Majick Fyre have location dependence as noted by others.

Reef: 

Reef always does at least 1 damage, exponentialish decline with long tail, 3.5-4 average

As noted by abstractapplic, Reefs occur on hexes adjacent to land but not adjacent to ports. I haven't seen anyone mention that for the purpose of this rule, L16 is a land hex. I guess it's a seamount.

The probability of receiving a reef encounter if going through a reef hex is about ~20% for non-Dhow's, and ~4% for Dhows.  Combined with the potentially high damage this makes these a high priority to avoid if not using a Dhow.

Kraken:

Kraken: spiky damage histogram. Spikes decline for higher values (but selection effects?), worse for Carrack/Dhow, and  Carrack/Dhow also seem to lack a low damage component present in the Barquentine/Galleon distribution  . ~3.5 average for Galleon/Barquentine,  ~6.5 for Dhow, ~8 for Carrack.

As others have noted Kraken have "territories". These "territories" actually are just a simple rule as with Reefs:

Kraken territories =  spaces at least a 2 hex gap away from land (where land has the same definition as for Reefs, i.e. L16 is a land hex).

Around 25-30% encounter probability per relevant hex. Combined with the high damage, high priority to avoid for all ships but especially Carrack/Dhow.

You can always avoid Kraken+Reefs by keeping a 1 hex gap between you and land (or L16) when not adjacent to a port. There are minimum length paths that follow this rule between most port combinations except between South Point and either Norwatch and Eastmarch, where a detour is required (a quite significant one for Eastmarch/South Point). 

As noted by others, the target points are in Kraken territory (IMO this is likely a coincidence since that just means they are far at sea). We can avoid going into any additional Kraken territory, but this will require an additional detour (relative to just avoiding reefs) for the western target particularly if avoiding E7 for which we have no data.

Iceberg:

Icebergs: dmg roughly consistent with 1d6 as reported by abstractapplic, so about 3.5 average damage. However, Galleons and Carracks seem to take 1 damage more often and Barquentines and Dhows take 1 damage less often. Maybe coincidence?

Icebergs are found from rows 0-2 in summer (Jun-Aug), in rows 0-6 in spring and fall(Sept-May), and in rows 0-10 in winter (Dec-Feb). (Others have remarked on Iceberg seasonality/northernness more generally).

Icebergs are not particularly high probability (<10%) per hex, but would add up if far enough north. Since this voyage will occur in summer, we don't have to worry about icebergs unless taking a significant detour to the north.

Merfolk:

Merfolk: Do 0 dmg a lot of time, though unlike abstracapplic I am not convinced it is exactly half. Exponentialish? decline if they do do damage, which can go to high values. About ~2.6 average damage for Galleons, ~1.7 for Barquentines, ~6 for Carracks, ~4 for Dhows.

As noted by abstractapplic Merfolk have two zones.

Most Merfolk reports form a giant triangularish donut centered around the northeast corner of J8. The donut looks like it should include F7 and L11, but there are no reports from there, and looks like it should not include O5, but O5 does have one Merfolk report. In the case of F7 this is probably just chance, since it's not visited a lot. All other reports are in another Merfolk zone southwest of Westengard. The giant donut occupies most of the center of the map and is hard to avoid, so should be analyzed further. 

Merfolk have a ~9% probability per hex for Galleons, ~2.7% for Barquentines, and ~1.8% for Carrack/Dhow. 

I have also noticed that relative to the low popularity of these hexes, Merfolk are significantly more likely to be encountered in the southwest region. I have not checked if this is connected with the ship type stats, but I will leave this for now since we don't need to go to that region. 

Wyrd Macjick Fyre:

Wyrd Majick Fyre: high damage, mostly 7 or less, but with tail (exponentialish?) 4-5 average for all except Dhow, which gets ~1.2.

As others have reported, Wyrd Majick Fyre mostly occurs around J8 (almost but not quite aligned with the Merfolk donut hole), with a few random-looking other instances. It is a >10% encounter in these hexes making them important to avoid for non-Dhows even if they did not also have Reefs (which they do).

Pirates:

Pirates: as abstractapplic noted does not do 1 dmg (but does do zero, very often, or 2d3? but with a long tail. ~3.1 average for Galleons/barquentine, ~4.4 for Dhow and ~5.29 for Carrack.

As measure noted, Galleons receive more pirate attacks. Per-hex encounter probability of ~12% for Galleons and ~4% for everything else. Todo: check to see if this depends e.g. on mission type.

Storm:

Storm: usually 0-7dmg. some tail. 2.5-2.6 average damage. Around ~7% chance per hex regardless of ship type.

Sharks:

Sharks: as abbstractapplic noted, dmg is consistent with min(2d4)-1. As with Pirates,  Per-hex encounter probability of ~12% for Galleons and ~4% for everything else. While not as damaging as Pirates, adds a reason to avoid Galleons.

Harpies:

Harpies:  Galleons and Barquentines seem to take 0 dmg 2/3 of the time, and 1-2 damage 1/3 of the time. Carracks and Dhows seem to take 0 dmg 1/3 of the time, and 1-4 dmg 2/3 of the time. So, theoretically 0.5 average for Galleons/Barquentines and 1.7 average for Carracks/Dhows

Per-hex encounter probability is ~9% for Galleons and ~4% for others, but per-hex damage from Harpies is still less for Galleons than for Carracks and Barquentines.

Dragon:

Dragon: long tail in damage; peaks later for Carracks/Dhows; ~3.4 average for Barquentine, ~3.7 Galleon, ~5 for Dhow, ~7.5 for Carracks. 

Per-hex encounter probability is ~2% for Galleons, ~0.06% for barquentines, ~0.3% for Carracks and Dhows. In terms of average damage per hex the extra encounter probability for Galleons more than makes up for them taking less damage per event than Carracks and Dhows.

Route and ship selection (analysis):

Looking at the encounter types that are initally seem location-independent, we have an average per hex movement cost in damage points, by ship type, of:

Ship/encounter| Pirates | Storm | Sharks | Harpies | Dragon | Total

Galleon              | 0.36     | 0.17    | 0.11     | 0.039    | 0.073    |  0.75

Carrack              | 0.19     | 0.18    | 0.34     | 0.069    | 0.021    | 0.50

Barquentine     | 0.11     | 0.18    | 0.034   | 0.021    | 0.019    | 0.37

Dhow                | 0.16     | 0.16    | 0.036   | 0.058    | 0.017    | 0.44

Taking into account ship hp, the Carrack looks the best here, with ~60 hexes of movement.

We are also likely going to go into Merfolk territory though, which adds an additional cost:

Galleon: 0.24

Carrack: 0.11

Barquentine: 0.044

Dhow: 0.072

It's looking a lot more even here between Carrack/Barquentine, but still slightly favouring Carrack. Since not all of the trip will be in Merfolk territory, might as well go for the Carrack?

One other thing - this cost assumes uniformity of Merfolk, though I actually think the southwest merfolk are more aggressive. Should adjust to account for that later.

We also want to minimize chance of sinking, not damage to be repaired in port. If confident average damage will be tolerable, we might want to reduce long tails rather than average damage. This could favour the Barquentine.

Dhow has less chance of hitting Reefs. Going to the east target, we can take a shortcut through Reefs and might want to consider a Dhow for that.

Additional dmg per Reef hex (v. non-Reef):

Galleon: 0.79

Carrack:  0.76

Barquentine: 0.68

Dhow: 0.17

Going to the West target, we might want to take a shortcut through Kraken territory, for which a Barquentine might be more suitable than a Carrack.

Additional damage per Kraken hex (v. non-Kraken):

Galleon: 0.99

Carrack: 2.04

Barquentine: 0.95

Dhow 1.59

We also might want to avoid E7, for which we have no data. There be dragons. I mean ... in-universe hypothetical squared dragons.

Also, early on I noted down some hexes where >1/5 of ships passing through were destroyed. They include some hexes which should not be especially dangerous from the above info, but this could just be that the routes also pass through dangerous hexes. Anyway, something to look at with further analysis, and maybe avoid if not costly to do so.

With all the above in mind, candidate routes and other info messily drawn on the map:

EditL map deleted and moved to imgur since it wasn't being spoiler properly

imgur link

When counting hexes, I don't count the port since these seem safe from the data.

For the west target:

Route A is the obvious choice taking all the above at face value. With a return trip, it will involve 27 hexes, of which 22 are Merfolk hexes and 1 Kraken.

Route B avoids the unknowns of E7. It's the same overall length including Merfolk length as Route A, but has 5 Kraken hexes on the round trip.

Route C also expensively avoids E7. It's 37 hexes, of which 20  are Merfolk hexes and 1 Kraken. No way that's going to be worth it.

I also added route G later which minimizes distance (and avoids E7) at the cost of additional Kraken hexes. 25 hexes, of which 20 Merfolk and  9 Kraken.

All of these routes involve >1/5 destroyed hexes, but I'm not prioritizing avoiding these super hard atm on the theory that these hexes will turn out to just be on paths that go through other dangerous stuff or are long.

For the east target:

Route D avoids reefs,  but is long and goes through Merfolk territory. It also goes through some >1/5 destroyed hexes. 21 hexes round trip, of which 18 Merfolk and 1 Kraken.

Route E takes 2 reefs to shortcut. 19 hexes round trip, or which 4 reefs and 1 Kraken.

Route F takes 3 reefs to shorten the path a bit more. 17 hexes round trip, of which 6 reefs and 1 Kraken. This is the shortest possible path given the constraint that you can't go across land.

So, expected damage for each route :

route/ship type   | Galleon | Carrack | Barquentine | Dhow

Route A (west)    |  26.5      | 17.9       | 11.8               | 15.0

Route B (west)    | 30.5       | 26.0       | 15.6               | 21.3

Route C (west)    | 33.5       | 22.6       | 15.4               | 19.2

Route G (west)   | 32.4       | 33.0       | 18.6               | 26.6

Route D (east)    | 21.1       | 14.4       | 9.5                 | 12.0

Route E (east)    | 18.4       | 14.6       | 10.7               | 10.6

Route F (east)    | 18.4       | 15.1       | 11.3               | 10.0

Route A looks so much better than the other western choices that I am willing to have the sailors brave the squared dragons. Barquentine looking like the best choice even with only 20 hp.

For the eastern target, Route D looks good with either a Barquentine or a Carrack, or Route F with a Dhow. Some considerations: Route D does go through >1/5 destroyed hexes, so I should try to find out if that really is a problem. On the other hand, the Dhow has low chance to hit a Reef but not low damage if it does get hit - high variance is risky. On balance, I pick the Barquentine on D for now.

Current route and ship choice:

So, for now I pick: 

"The Bloody Diamond, a Barquentine captained by Angus MacDougal" on Route A (Q6-P6-O6-N6-M5-L5-K5-J5-I5-H5-G5-F5-F6-E7-E8) and back by the same route.

"The Saucy Heart, a Barquentine captained by Erin Aubrey" on Route D (Q6-P6-O6-N6-M7-M8-L8-K9-K10-K11-L12-L13) and back by the same route.

Comparing to others' selections:

My selected routes A and D are the same ones chosen by abstractapplic, but I use two Barquentines whereas abstractapplic uses a Galleon and a Barquentine.

Yonge selected Route F to go to the east target and for the west first selected something that looks like it should be equivalent to my Route B, in terms of length and types of hexes it goes in, but at the bottom of the comment changes it (why?) to add some additional dilly-dallying in Kraken territory. Yonge chose a Galleon and a Carrack.

measure picked two Dhows (unconventional!), and sent one of them on a route equivalent-seeming to Route E, which looks sensible to me, but the other one is going to the west target starting out at (up to the last hex) the same route (so, super long route), and is a Dhow cutting through Kraken territory, which looks not so sensible.

todo:

Look at Merfolk donut only, check to see if that affects merfolk stats

Look to see if expected damage can reasonably account for observed losses, check where excess losses are occuring (is Jemist right that there are unexpected losses?)

check to see if Captains affect anything

check to see if time docked affects anything

check to see if voyage purpose affects anything

additional remarks:

As Yonge notes, there are 19 encounters not on the planned route I did not see a pattern and attribute this to noise in the data. Note that it is possible that, even if something was displaced by noise, it would still end up on the planned route. I am inclined to attribute the Merfolk event on O5 to such noise, the event probably having really occurred on N5, which was also on the ship's route.

After reading your analysis, I think your strategy has a higher chance of success than mine. On reflection,

I'm still wary of sending any ship that spent <5 weeks in port - that rule's probably there for a reason - but you've convinced me I should have sent the Galleon to L13 and the Barquentine to E8.

Is there a typo in your first specified route?

Yes, thanks; deleted the extraneous N5.

This challenge is very interesting; thank you for making it. I don't think I've found all the answers, but I've gotten as far as I'm going on my own.

Decision:

  • Take The Bloody Diamond to L13, Q6-P6-O6-N6-M7-M8-L8-K9-K10-K11-L12-L13, then (hopefully) back the same way.

(I thought about a detour to avoid whatever's (not?) going on in L12, but decided it's probably fine.)

  • Take The Orange Falcon to E8, Q6-P6-O6-N6-M5-L5-K5-J5-I5-H5-G5-F5-F6-E7-E8, then (hopefully) back the same way.

(I considered alternate routes that punch through F8 and G8 while avoiding icebergs, but decided to gamble that E7 isn't a Kraken hex.)

Location insights:

  • Pirates, Storms, Sharks and Harpies seem to be everywhere; no way to avoid these, save making your journey as short as possible. (ditto Dragons, probably, but they're rare enough that it's hard to say for sure)
  • Reefs are in every sea hex adjacent to land, except for some adjacent to the ports.
  • Icebergs are more common further north.
  • Merfolk have a territory in the centre of the map, and another in the southwest.
  • Kraken have very specific hunting grounds, which my routes go to great lengths to avoid.
  • WMF occurs almost exclusively in hexes adjacent to Q1 and J8. Dragons and/or Wizards on the islands?

Ship insights:

  • Barquentines and Dhows have 20HP; Carracks and Galleons have 30HP. The effects of attacks are denominated in these hitpoints, so it's worth converting percentages to them.
  • Dhows and Carracks handle encounters with living enemies (except Sharks, for some reason) much worse than Barquentines and Galleons.
  • I'm pretty sure that a Galleon is just a 30HP Barquentine, and a Carrack is just a 30HP Dhow.
  • As a general rule, Galleon>Barquentine>Carrack>Dhow. All apparent evidence to the contrary is because the Admirality know Dhows are terrible and keep giving them easy jobs.
  • The Admirality really don't like sending ships out unless they've spent at least five weeks docked; they do this so rarely that I don't have enough data to infer whether the prohibition makes sense.

Encounter insights:

  • This scenario is dice-based, as can be seen from the distributions of some of the simpler encounters: icebergs do 1d6 damage, sharks do min(2d4)-1, harpies do 1d6-2 or 1d6-4 depending on ship type.
  • Merfolk seem to do zero damage exactly half the time. If I had more time I'd investigate what this means.
  • Pirates never do exactly 1HP damage. I suspect that - when they damage ships at all - their damage is calculated from "roll XdY, pick the two lowest".

Secrets(?):

  • Both ships are heading to Kraken territory; I don't think this is a coincidence. I suspect their 'cargo' is either sacrifices or explosives.
  • There's exactly one Carrack that claims to have taken 5% damage, which should be impossible. Did its' captain lie?
  • It's suspicious that L12 is so rarely visited, especially when the Kraken-infested hexes to the south are so popular. My fear that it houses a history-eating monster which causes visiting ships to never have existed is *almost* certainly ill-founded; more likely, it's just the one hex in the Admirality's waters that's not obviously on the way to anywhere.

Some thoughts and insights from my notes that I somehow forgot to write up the first time:

  • Galleons, Barquentines and Carracks have eerily similar average planned route lengths, suggesting the Admiralty treat these three ship types as interchangeable in their planning.
  • This is important because it means that [number of sinkings]/[number of trips taken] is an unusually selection-bias-proof estimator of sinkability for everything but Dhow.
  • This estimator says pretty clearly that Galleons>Barquentines>Carracks.

However

  • The Admiralty keeps recklessly sending ships into hexes at risk of reefs, kraken, icebergs and WMF. Since my chosen routes dodge all of these (though I didn't notice I was icebergproof until other commenters pointed out the seasonality effect), the main questions become how Galleons handle the remaining threats (pretty well), and how frequently they encounter them (. . . whoops!).

And also

  • I have to plot routes which are unusually long: if Galleons handle marathons worse than sprints, that's a problem.

Unrelatedly:

  • Dhows appear to handle a lot of long-tailed encounters (especially WMF) better than Carracks, but I think it's a statistical trick of the light. When faced with an extreme situation, they die and can't report how much damage they took; this skews damage/encounter ratings in their favor.
  • The one place where they genuinely do appear to handle a threat significantly better than Carracks on a by-hitpoint basis is with Merfolk.
  • The ratios of average recorded damage for Merfolk encounters lead me to believe that Merfolk damage is calculated as a percentage of total hull integrity, and not in terms of hitpoints like (all?) other encounters.

Secrets(?):

Somethings more probable than a history eating monster, although not based on me looking at any data:

a) insurance fraud. (Yes, this trip is very risky, but it's very lucrative if we succeed! Oh, no! Well insurance will cover it. Wait, they don't? Uh... what if the ship didn't go there? What if it went somewhere else, where it's not our fault?) Issues: requires data showing that something is a bad idea, or stories.

b) Secrets are hidden by having people not go where they could find them. (May require centralized control, without alternatives; not too unlikely in this scenario, though.)

typo: serious => series in the second sentence

Fixed, thank you.

Excellent to see community D&D.Sci taking place! This looks far more complex than the original series.

I'll be posting my findings in a thread under this comment

Edited as my maths was wrong and I forgot row zero!

First finding: I should stop using excel for these challenges.

Second finding: cell deadliness defined as  where  sums over cells,  sums over journeys,  is whether a journey planned to go through a cell,  is whether a journey resulted in a wreck, and  is the length of a journey

 ABCDEFGHIJKLMNOPQRS
0     1.01%0.71%0.40% 3.46%1.11%1.52%4.04%      
1 0.00%0.61%0.64%0.90%1.25%1.08%1.02%0.94%0.96%0.84%0.86%0.74%0.73%0.78%0.89%1.02%1.42%1.31%
2    0.76%1.12%1.31%1.12%1.19%1.40%0.97%  1.52%0.45%0.28%1.28%1.49%0.69%
3    1.35%1.01%  1.29%1.06%1.23% 0.43%0.39%0.64%0.69%0.91%0.65%0.82%
4    0.00%1.10%0.99%1.32%1.45%1.31%0.94%1.03%1.13%0.98%0.97%0.89%0.65%0.68%0.46%
5    3.46%2.22%1.90%1.59%1.24%1.54%1.16%0.84%1.03%1.27%1.10%1.12%1.05%1.83%4.23%
6     2.55%2.03%1.81%0.72%1.34%1.84%2.12%1.65%1.26%1.35%1.34%1.16% 2.01%
7     3.37%2.05%0.61%0.96%2.14%1.50%1.72%1.53%1.60%1.65%0.97%1.24% 2.88%
8    0.00%0.61%2.19%0.91%0.83% 2.02%1.63%1.32%1.72% 0.56%1.25% 1.62%
9   1.06%1.67%2.14%1.33%0.90%0.98%1.84%1.73%1.75%1.79%1.96% 0.61%1.52%2.25%1.21%
10   1.52%1.10%1.70%1.64%1.24%0.88%1.63%1.42%1.62% 1.62%1.54%0.59%0.89%1.70%1.25%
11  0.00%0.65%1.29%1.55%1.39%1.18%1.92%1.83%1.74%1.66%0.83%1.45%1.03%0.61%0.96%1.17%0.35%
12  0.00%0.00%0.19%0.96%1.47%1.29%1.86%1.79%1.31%0.76%1.56%1.06%1.17%0.96%0.58%1.36%0.46%
13 0.00%0.22%0.15%0.56%0.73%1.08%0.74%0.69%0.79%1.02%1.03%1.07%0.99% 0.84%1.03%0.83%2.02%
14  0.00% 1.48%1.35%1.28% 0.49%0.25%0.12%0.27%0.54%0.67%0.91% 0.96%1.07%1.77%
15  2.42%1.67%1.33%1.27%1.43% 0.56%0.40%0.35%0.33%0.52%0.49%0.68%0.87%1.48%1.76%1.95%
16   2.10%1.63%1.37%1.79%  0.00%0.61% 0.62%0.32%0.36%0.53%4.08%2.38%1.97%

I apologize for not highlighting the cells with some sort of colour but it makes the spoiler tags not work.

Takeaways:

Wreck chance on any given cell is low enough that I probably don't have to take into account high rates of per-square wreck in models

Sharp changes seem to demonstrate that any smearing effect of having ship routes isn't too bad.

Next order of business is to look for things which are common in the deadlier squares. Hopefully this will correspond to things with generally deadlier distributions too.

Further observations having graphed all encounter damage as a histogram:

Dragon: Somtimes does zero, often does a lot of damage, long tail

Harpies: Usually do zero, occasionally do one of a few values up to about 0.2

Iceberg: One of ten-ish values spaced sporadically between 0 and 0.3

Kraken: Exponential-ish distribution with tail going up to 0.9 ish

Merfolk: Usually does zero, flat-ish distribution which goes up to 0.65

Sharks: Often do zero, otherwise one of a few values up to like 0.15, not a big threat

Storm: Exponential-ish with faster dropoff than kraken

WMF: Might be half a gaussian? Also randomy hits high

I suspect due to the frequency of zeros, some captains/ships are immune to certain threats. Will investigate further

Another observation is that lots of the most dangerous squares have no encounters listed. This is spooky and I have a couple of hypotheses:

1: There's an unobserved fatal threat thing going on. For example those are "dragon nests" and if you go there the dragons have some chance to just destroy you. Doesn't seem to be a correlation to other things though so I'm not confident.

2: Some weird selection effects where the useless ships/captains always go via those squares (always include selection effects)

There are two ships in port captained by Angus MacDougal. Am I unable to use both?

Names are not unique identifiers.

The Bloody Diamond and the Mopey Hind are captained by two different Captains named Angus MacDougal. If you have a problem with the MacDougal Clan's traditional naming practices, all eight-thousand members of it would like a word with you.

 Thank you for posting this.
 

My initial observations are as follows:

 

I couldn't find much just by looking at the data.
 
Roughly 90 percent of all type of ship survive their voyage.
Survival rate for different purposes varies between 84 and 92 percent doesn't seem partcularly significant
 
Looking at the survival rates for different combinations of ships and purposes revelas some anomalously low values Carrack carrying redstones only 79%. Dhow and Mythrill 71% are the standouts. Might be a statistical fluctuation, and as we don't know what we're carrying it doesn't help much
 
Ships that sail only one week after their last voyage have a noticeably lower survival rate (74%), otherwise it doesn't appear to have much effect. So provisionally ignore all possible ships that sailed one week ago.
 
Voyages of length 10 or less have approximately the same survival rate of 90 percent, but this falls to 79% and 76% for voyages of length 13 and 14 respectively.

There are 19 encounters that did not take place on the planned route, and one of them occurred on land. This is a small fraction of the total, and they all occurred close to the route suggesting the planned route is reasonably reliable.
 
iceberg encounters are concentrated in the N part of the map, and are more prevelant during the N hemisphere winter.
Kraken encounters seem to be restricted to a small number of tiles which tend to come in clusters, they are slightly more active during the summer. 
Reef encounters seem to be restricted to a small number of tiles which tend to come in clusters. 
Merfolk seem to be restricted to a few moderatly big clusters
Wyrd Majick Fyre is centered on a cluster around J8, with a few random encounters elsewhere. Given the small number there is no reason to think these tiles are any more likely to suffer an encounter from it than any other.

Finding paths which yield the minimum expected damage (defined as all damage done in known encounters on route + 100/hexes on route for all planned routes that went through it but got destroyed yields the following)
Best path to first destination(L13) is:
(1) Q6 P7 P8 P9 P10 O11 N11 N12 M13 L13 
Best path to second destination(E8) is
(2)Q6 P6 O6 N6 M5 L5 K5 K6 J6 I6 H7 H8 G8 F8 E8 
 
Restricting it just to voyages leaving in June leads to::
Best path to first destination(L13) is
(3) Q6 P6 O6 N6 M7 M8 L8 K9 K10 K11 L12 L13 
Best path to second destination(E8) is
(4) Q6 P6 O6 N6 M5 L5 K5 K6 J6 I6 H5 G5 G6 F7 F8 E8
The slightly more northerly route in (4) is possibly because icebergs are less prevalent at that time of year, and they are concentrated in the northern part of the map, however there is no data at the end of the route, and Kraken have been seen in these hexes at other times, and they are more active than normal at this time of year, however the southern route also goes through Kraken infested waters.
  
Assigning double the weight to destroyed ships (and counting all voyages) yielded route Q6 P6 O6 N6 M7 M8 L9 L10 K11 L12 L13 and route (2) again. So this looks reasonably robust against changes to this weighting.
  
  For the captains choosing those that have survived more voyages than any other seemed like a reasonable first guess, however looking at the data suggests that the same name can be given to > one captain e.g Seamus Reagans voyages occur in 2 widely separated groups. So instead we need to look at the ships, which can hopefully be uniquely identified by their ids. Ships are generally commanded by the same captain. The 2 ships that have survived the most voyages are the Orange Falcon followed by the Mopey Diamond.
  
So my provisional answer (Which may be changed if I get time to look into this further) is:
Send The Mopey Diamond, a Carrack captained by Conall MacDougal by route Q6 P6 O6 N6 M5 L5 K5 K6 J6 I6 H7 H8 G9 G10 F10 E9 E8
Send The Orange Falcon, a Galleon captained by Brandon Buchanan by route  Q6 P7 P8 P9 P10 O11 N11 N12 M13 L13

Route Selections:

(Red Duck) Q6-P7-Q8-Q9-Q10-P11-O11-N11-N12-M13-M14-L14-K14-J14-I14-H13-H12-G12-F11-F10-E9-E8 (return same route)
(Scurvy Hind) Q6-P7-Q8-Q9-Q10-P11-O11-N11-N12-M13-L13 (return same route)

Other Notes:

Delay between voyages doesn't seem to affect damage.
Avoid the wizard on J8.
Avoid reefs when possible (adjacent to most land hexes except around ports).
Dhows take less damage per hex (most of this might be from dodging reefs).
Galleons attract Sharks/Pirates/Harpies/Merfolk/Dragons.

If both ships have the same initial moves, will they get the same encounters in those hexes?

You don't know. That might be something you could figure out by looking at the Admiralty logs though.

Nice, though I have been finding LibreOffice Calc rather annoying to work with on this one...

Is the following data point a bug?

voyage 3352 has a storm encounter at P14, which is a land hex

That is definitely what the Admiralty data says.

(Yeah, usually I think freeware Office stuff is pretty much on par with Microsoft Office, but Excel specifically feels genuinely better to me than any of the freeware programs I've found.  Does anyone have recommendations?)

Thanks. I can just switch to Excel then if it's significantly better for this purpose. In my case this is not a problem since I have office 365 access through work - I just normally avoid closed source stuff (other than games) for my personal use. GuySrinivasan mentioned another thing in an earlier thread (comment link), I probably should check that out, though expect a bigger learning curve.

If anyone is still working on this (either current answerers continuing their analysis or latecomers wanting to start), please let me know. In the absence of replies on this, I will publish the answer key tomorrow.