What sorts of actions would captains take under these circumstances? Rogue waves are so large and powerful--would any action be enough to prevent losing a ship?
Hitting the swell bow first will not necessarily help you.
See https://www.youtube.com/watch?v=A2KqofR05TE for a video of a boat actually hit by a rogue wave. They are riding the swell correctly - but the wave hits from the side.
Note that a swell and a current are known conditions that make rogue waves more likely. And it is not uncommon for rogue waves to be moving in a different direction than the swell.
Still even that may not be enough to save you. The ship that went down in the North Atlantic was hit front on and sunk.
If you go over the wave, half your ship ends up cantilevered over the peak. A ship isn't built to hold half its weight in the air like that. It will break.
If you go through the wave, the upper decks get hit by a wall of water. The windows blow out, the bridge is destroyed, the computers are toast and the ship is swamped.
The wave drag (or wave resistance, to disambiguate from the shock wave drag of supersonic aerodynamics) referenced in sibling comment is the energy contained in the waves created by a surface vessel. The details that you'd have to understand to optimize a hill shape are quite complicated, but for a simple surface vs sub comparison it's enough to know that surface waves exist and that they contain energy that is projected away. A sufficiently submerged vessel does not create those.
Intuitively I would expect rogue waves to be more likely in rougher seas, but it's another thing entirely if the physics of rogue waves requires rough seas locally. I don't disbelieve you, but an explanation of that claim would answer a ton of questions about how rogue waves form (answers missing from the Wikipedia page, which seems more inconclusive) and a page worthy of bookmarking.
EDIT: Your claim seems consonant with the "linear" theory of rogue waves, but as the Quanta article explains that theory is contested by proponents of the "non-linear" theory.
That's a 90 foot wave in a wave tank basically coming from math
Or maybe a herd strength thing where one ship detects and can send out an alert for others to redirect around the path.
Granted, it's usually survivable. Decades ago a friend of mine on a containership experienced a rogue wave with no more harm than being terrified by "either the last thing I was ever going to see or the most majestic thing I'd ever see" but it doesn't always end that way.
Ships used to be built to the largest waves that were conceivable. We underestimated the forces in a rogue wave by a factor of more than 5. Ships today are built stronger, we are careful about seas where rogue waves are more common, and insurance now knows to take rogue waves into account in their policies.
Better predictions as well would be good.
The verbiage in the article is a little too "wanky" for me to tell.
Basically, as explained in the article, many kinds of rare events (like, averages attaining values far from the population mean) can be characterized without knowing a lot of problem-specific details.
For instance, if the typical value for an average of 1000 positive numbers is 10, and you want to know the chance of an outcome greater than 100 (a "large deviation"), you can pretty much just calculate the chance of the outcomes very near 100, without caring about 120 or greater. That is, it turns out that the larger outliers carry very little probability, although that's not obvious.
This phenomenon comes up a lot and goes by several names. It was known to Laplace and there's an approximation used commonly in that area bearing his name. It's also related to the notion in information theory of the "typical set".
Similarly, you can, in some ways, characterize the realizations that cause these extreme values. (As opposed to just computing their probabilities.)
For instance, if I remember right, the typical realization that gives rise to a large average has just a few larger-than-expected values and a vast majority of about-average values, rather than every value being slightly too large. This is a highly general property.