The yeth hound originates in Devonian myth as the local spin on the “black dog” motif prevalent across British and Northern European folklore as a harbinger of doooooom. In fifth-edition D&D, they’re evil fey predators that hunt at night, their howls echoing through the darkness.
To run a yeth hound, you’re going to need to familiarize yourself with the chase rules in chapter 8 of the Dungeon Master’s Guide, because they’re a major component of how this creature hunts, as indicated by the first paragraph of flavor text in Volo’s Guide to Monsters: “Yeth hounds fly in pursuit of their prey, often waiting until it is too exhausted to fight back.”
But first, the usual breakdown. Yeth hounds have a ferocious ability contour: exceptional Strength, very high Dexterity and Constitution, making them both brutes and shock attackers. Their goal is to make the first hit count, but if that’s not enough to slay their prey, they’re tough enough to stick around and finish the job. Their Intelligence is lower than that of an ape, but higher than that of an ordinary dog; they can understand speech but can’t speak. They’re immune to physical damage from nonmagical, nonsilvered weapons, and they can’t be charmed, exhausted or frightened.
Yeth hounds are nocturnal hunters by necessity. They have darkvision, and their Keen Hearing and Smell means they can easily detect prey in total darkness, but beyond this, with their Sunlight Banishment trait, they can’t remain corporeal while sunlight shines on them—it bounces them into the ethereal plane, where they have to stay until after sunset. Therefore, the most dangerous time to have a yeth hound nearby is just past twilight, because this gives it the most time to sniff you out and run you down.
The ideal hunting ground of a yeth hound is difficult terrain, full of natural hazards—slopes, ditches, cliffs, protruding tree roots, ravines, sinkholes and so forth. This kind of terrain makes it difficult and dangerous for its prey to run away, while not inhibiting the yeth hound at all: with its 40 feet of flying speed, it can tear along a couple of feet off the ground. But also, its Baleful Baying feature forces frightened victims to run away from it by “the most direct route, even if hazards lie that way.” (If you want to build a really bonkers encounter, throw in a few opportunistic harpies to terrorize any collateral victims of terrain-related mishaps—or even to try to get to the yeth hound’s prey before it can. When the hound arrives on the scene, maybe the harpies are scared off, or maybe it becomes a three-way fight!)
The range of Baleful Baying is 300 feet, but that’s not the amount of distance a yeth hound can cover in a round. Ideally, it wants its quarry still to be frightened when it strikes, because that more than doubles the expected damage of its Bite. Since the frightened condition lasts until the end of the yeth hound’s next turn, it needs to use Baleful Baying the turn immediately before it strikes. But Baleful Baying is probably also the first indication the player characters will have that there’s a yeth hound somewhere nearby—and the first warning that a chase is about to ensue, and also the factor that determines which of the PCs the hound will chase after. So what triggers it?
Well, since the yeth hound has Keen Hearing and Smell, figure that it can hear a creature trying to be quiet as if it were making a normal amount of noise, and a creature making a normal amount of noise as if it were being very loud. Using the “Audible Distance” table on Wizards of the Coast’s DM Screen Reincarnated (which really should be published in a book!), these correspond to average distances of 70 feet and 350 feet and maximum distances of 120 feet and 600 feet. That’s a long way off! What about smell? The real-world animals with the keenest senses of smell are bears and elephants, and they can pick up scents 10 to 20 miles away! Based on these facts, I think it’s perfectly reasonable to conclude that a yeth hound can hear and smell, or at least smell, any creature within range of Baleful Baying—and therefore it will take this action as soon as it detects them. Then the chase begins.
If you figure that the modal humanoid has a base movement speed of 30 feet and will Dash to try to escape a pursuing yeth hound, that’s 60 feet of movement it can cover in a round—but only 30 feet across difficult terrain. The yeth hound can cover 40 feet in a turn in which it uses its action to bay or Bite, which suggests that it should use Baleful Baying once more upon getting within 10 feet of its quarry.
But now’s where the chase rules come into play. The yeth hound never gets exhausted, so it can Dash as many times as it needs to in order to run its quarry down. But its targets can Dash only a limited number of times before having to make Constitution checks (not saving throws!) against exhaustion. After two failures, a target’s speed is cut in half, reducing the amount of difficult terrain it can cover to 15 feet, which means the yeth hound can use Baleful Baying once it’s closed the distance to 25 feet. This twist is also consistent with the flavor text; it may be that a yeth hound that gets this close to its prey nevertheless waits to bay, and to pounce, until its target already has a couple of levels of exhaustion.
Should it hold off even longer? A third level of exhaustion imposes disadvantage on saving throws, making the target even more likely to fail their save against Baleful Baying. A fourth level halves their hit points, making their doom even more certain. After a fifth level, the target can run no more. At six levels of exhaustion, the target dies, which is no fun for the yeth hound; it wants to kill with its bite. So let’s say the ideal moment for a yeth hound to use Baleful Baying against a target it’s almost caught up to is when they have two to four levels of exhaustion. Before this point, it matches pace with its prey, neither closing the final distance nor letting it get away.
Yeth hounds are creatures of instinct without much ability to adapt, and they aren’t very bright, but one thing they can figure out is whether a potential target isn’t frightened of them. (Figure that Keen Smell includes being able to detect the smell of fear.) As long as there exist creatures nearby that are frightened of a yeth hound, it won’t chase anyone who isn’t. So if plucky little Marigold, the Brave halfling, makes her save against Baleful Baying, stops running, wheels around, plants her feet, scrunches her fists and yells, “I’m not afraid of you!” the yeth hound’s response will quite likely be to run right past her in pursuit of some other victim. The same is true if anyone hits it with a magic or silvered weapon: it stops chasing that target immediately and heads off in another direction. No yeth hound’s got time for that. It will, however, attack a target it’s been chasing who’s made their saving throw if that target has four or five levels of exhaustion, or if they have at least two levels of exhaustion and every other potential target in the vicinity has become immune to its howl.
Other than hitting it with a magic or silvered weapon, the only way to get a yeth hound to break off its attack is to seriously wound it (reduce it to 20 hp or fewer) with nonphysical damage, whereupon it Dashes away.
Traditionally, a yeth hound hunts alone, but the flavor text in Volo’s implies that they’re more often encountered in packs, commanded by an archfey or other influential evil creature. Considering that they have a Challenge Rating of 4, an actual pack of yeth hounds (i.e., four or more together) would be a terrifyingly Deadly encounter for a typical group of mid-level adventurers; PCs would have to be at least level 9 to be able to handle a number of them equal to their own, and level 11 to do so without significant risk.