Does the DC for the effect of a Beast Master ranger's animal companion's attack ever increase?

Question

A similar question has been asked for Pathfinder, but I could not find any specific rules for 5e.

As an example, we have a Beast Master ranger with a wolf companion. The wolf has an added effect on its Bite attacks.

Bite. Melee Weapon Attack: +4 to hit, reach 5 ft., one target. Hit: 7 (2d4 + 2) piercing damage. If the target is a creature, it must succeed on a DC 11 Strength saving throw or be knocked prone.

For player characters, the DC for this type of effects is calculated as follows (example from the Ranger's Spellcasting feature):

Spell save DC = 8 + your proficiency bonus + your Wisdom modifier

When you select the Beast Master Archetype (PHB, p. 93) at level 3, your companion gains the following benefits of your proficiency:

Add your proficiency bonus to the beast’s AC, attack rolls, and damage rolls, as well as to any saving throws and skills it is proficient in.

Does this mean that the DC 11 Strength saving throw of the wolf's Bite attack increases with the proficiency bonus of the Ranger? Or is the DC of the bite attack for the wolf not actually calculated, but determined as a set value?

Answer 1

No

The text you've quoted pretty much answers your own question.

Add your proficiency bonus to the beast’s AC, attack rolls, and damage rolls, as well as to any saving throws and skills it is proficient in.

A Wolf is proficient in Perception and Stealth, so you add your proficiency bonus to those. You increase the Wolf's AC of 13 by your proficiency, its +4 to attack rolls is increased, and you increase the bite attack's damage by your proficiency as well.

You do not actually increase any of the wolf's raw stats or their own proficiency bonus, so even if the ability was capable of scaling, you didn't actually change any of the properties it'd scale with.

The wolf still has the same ability scores and proficiency bonus as before.

Even if you do increase the Wolf's abilities (through your levelups or a magic item), it won't make any difference:

If the target is a creature, it must succeed on a DC 11 Strength saving throw or be knocked prone.

This is a set DC. Nowhere does it offer any sort of calculation for you to recalculate the creature's DC, so you'd have to homebrew it scaling of a stat if you make your own stronger wolf. I assume it'd scale of strength, working under the assumption that it has a proficiency modifier and a current strength of +1, meaning a DC 11 going by default DC calculations.

Answer 2

YES (most likely)

If using the Revised ranger.

The revised ranger states that the animal uses your proficiency bonus for its own purposes AND is added to AC, skills, saving throws, attack and damage. (the skills part may be a counter argument)

Also, the revised companion gains attributes when you do, so this also raises the question on what happens when you raise its STR by 2 or more.

In general: monster manual entities do not follow a logical point buy build mechanic and they seam to be manually adjusted for their CR. However by comparing the wolf and panther, we can see that their proning* ability is determined by the formula: 8 + STR + Proficiency (2), which is 11 for the Wolf and 12 for the panther respectably.

So, the DC of the proning ability should increase if STR is increased at the very least, and there is also an (perhaps slightly less solid) argument for increasing it for proficiency as well.

But the DM could deny it, because we simply don't know if the DCs are determined by a logical formula or are simply hard set at random (non-random by play testing). The wolf - Panther comparison seams to be in favor of the formula theory.

Likewise, since the animal companion is buffed/scaled in many regards compared to its wild type. There is no reason for a DM not to house rule it to be ok, it would be in good taste. The only concern is if the ability would be to strong with a higher DC and that requires play testing. But this can be compared to a the shove ability, or since it is a bonus ability, more closely to a much weaker shield master feet - and it is not considered overpowered.