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From the description in the Monster Manual, one can clearly see the Saber-Toothed Tiger has a Proficiency Bonus of +2.

She has +3 in Perception which is 2 + her Wis modifier (+1).

She has +6 for Stealth, that means she has expertise, so double her proficiency (2 × 2 = 4) + her Dex modifier (+2).

She has a +6 to hit with both her Bite and Claw attack, that is 2 + her Str modifier (+4).

And then she has a static bonus of +5 to her damage rolls which, subtracting her Str modifier of +4, leaves us with a 1.

So I was trying to figure out what might be the case, and there's only 2 options I could think of: she either adds half her proficiency, or half her Dex modifier, per the effects of a hidden feature I can't for the love of me find.

Anyone care to help me find the consistency?

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Monsters in 5E are not built using the rules for player characters. From the DMG's section on creating monsters:

Raise or lower the monster’s Armor Class, hit points, attack bonus, damage output per round, and save DC as you see fit, based on whatever concept you have in mind for the monster. For example, if you need a well-armored monster, increase its Armor Class.

It can be as simple as that: the concept for the tiger at the target CR called for more damage. For CR 2, that's 15-20 points per round. Playtesting may have shown that in order to make the Saber Tooth tiger fit that CR, it needed a slight damage boost. See the section later in the chapter from the DMG link above which discusses offensive and defensive CR. Notably, like most beasts, the saber-toothed tiger has a relatively low AC and is short on hit points. This implies that the offensive capabilities should be stronger to compensate. (And dropping it to CR 1 isn't an option since there's already the regular tiger filling that slot.) Additionally:

Creating a monster isn’t just a number-crunching exercise. The guidelines in this chapter can help you create monsters, but the only way to know whether a monster is fun is to playtest it. After seeing your monster in action, you might want to adjust the challenge rating up or down based on your experiences.

... which again emphasizes that the creature builds aren't just about the numbers; there's some design/development work involved as well.

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