Can the Kraken drag a ship?

I instinctively think "yes". Right? I mean... it's the Kraken! It's gargantuan. It's got a 30 strength. It's the undisputed master of the oceans. Right? So of course it should be able to drag your sailing ship through the water like a kid pulling a toboggan through the snow. Right? 

But the RAW math doesn't seem to agree. Granted, I'm definitely a Rule of Cool > RAW kinda guy. But it's late and I'm all hopped up on the Dr. Pepper, so this is bothering me.

Drag weight is Strength score x 30. The Kraken has a strength of 30, so 30 x 30 is 900. But that's for a medium creature. So throw in a x2, and another x2, and another x2 because the Kraken is gargantuan. We're still only at 7,200 pounds. (That's 3,266 kg for the other 192 silly goose countries in the world). A sailing ship in D&D weighs 300,000 pounds. So we're a bit short.

But it just FEELS right that it should be able to do it. So can somebody please offer up some D&D math that'll iron out this conundrum? I must be missing something here.   Thanks in advance! 

Remember, that’s just for what you’re able to carry consistently. If you’re unable to say, lift a large boulder as a barbarian purely by weight, the dm may allow you to make a strength check to lift it for a moment. Also the rules are there for the players and are extremely general. Mythologically, Rocs are famous for being able to lift entire elephants up into the air, but elephants can weigh up to 14,000 pounds, but Rocs can only lift up to 6,720 pounds, this is where you ignore the rules completely for the sake of making the game more fun.

Mostly, the carrying rules were written for normal-sized humanoids. I expect they get equally weird when scaled in the other direction, too.

The size categories are similarly written for normal scales. Gargantuan and tiny are the catch-all categories of "really quite big/small". Any mechanic that scales on size is going to break down when it includes both brontosauruses and krakens.

You could use the grapple rules and just kind of ignore the weight. Both are gargantuan, so one can grapple the other and move at 1/2 speed.

The dragging weight limit is also for dragging across land, while pulling something buoyant across water is easier.  A person can push or pull a floating object across water, that they wouldn't be able to push/drag across dry ground due to it being too heavy.  D&D has no rules to account for this that I'm aware of, though.

If you want the math, you will probably not find it.  So  Rule of Cool > RAW is your method to justifying it to work.

This is one of those situations where, because only the GM is going to ever be the one trying to do it, they can absolutely go ahead and let it happen even if it's not technically accurate to the rules because it's cinematic.

I actually found something for this, in Ghosts of Saltmarsh, Appendix A: Of Ships and the Sea.  There are some supplemental rules, where ships are given Dexterity, Strength, and Constitution stats, and they're basically handled as creatures whose actions are controlled by their crew.  Using those rules, a kraken would grapple and drag the ship as if it were a creature, rather than dragging an object.  The rules for grappling creatures don't factor in weight at all, or relative size, and I kind of feel like they should... but they don't.  As many people have pointed out, this is one of those things that can just happen because you're the DM, but if you still want a rules explanation anyway, maybe that's it.

Boats on water are easy to move.

Its a known technique that when a sailing ship was stuck with no wind they would set out several boats to pull them out of windless areas.

They used to move ships through canals and rivers by pulling them with a couple of donkeys walking them from the shore.

Thats not a game math fact but imagination play should give you the idea that a ship can be moved by something smaller. Not fast but at least moved.

The rules for carrying and dragging are dubious even for medium size creatures (RAW, you can grapple and drag a 2 ton allosaurus, but somehow a 300 lb weight is immovable?) and complete nonsense for larger creatures. I understand why they did away with the lift tables from 3e, those were a pain to work with, but the reality is that you need something similar to represent the range of D&D creatures, as D&D creatures can be absolutely enormous, and ignore the square/cube law. 5e made life even more difficult for itself by compressing the entire range of superhuman strength into the range 21-30. 

For what it's worth, a 3e kraken (Strength 34 Gargantuan) has heavy load 22,400 lb and under normal conditions could drag 5x that, or 10x that under particularly favorable conditions, which is adequate to slowly drag a merchant ship.

I would probably not actually try to work with weights for large things, though, as that will require a significant amount of math, both to figure out the weight limits, and to figure out what things actually weigh. Just figure that in general a creature can drag a similar sized object unless it is exceptionally dense, and can drag a one size larger object if it is particularly light or easy to move.

In real life, a boat with a weight of around 10000lbs needs about 100lbs of horizontal force to get it moving slowly (to overcome it's static intertia). If you apply more force, the boat will accelerate more quickly. 

If you applied that 100:1 ratio for how much force you can pull through water, the Kraken would be able to drag a boat of up to 720,000lbs which is far more weight than any likely sailing vessel (unless you happen to have a massing vessel that is 300+ feet in length). So absolutely, that Kraken can pull the ship around.