I am a very new DM, and one of my players is a ranger. As I was browsing through posts here and there we decided to use the UA, as everyone is saying the RAW ranger is lackluster. She obtained her wolf in a little side story, and I would like to set up the stats for her companion. I read through the UA, and it states:

> For	each	level	you	gain	after	3rd,	your	animal	
> companion	gains	an	additional	hit	die	and	 increases	its	hit	points
> accordingly.

Now this confuses me a lot, and upon further looking into how HP is calculated, I dont even understand the stats of the simple Wolf enemy. 

So in the Monster Manual the HP of the wolf is 11 (2d8+2).

First question: How is this calculated? The average of 2d8 should be 10. 10+2 is 12. 

Second question: What is the hit die of a wolf? If its 1d8, than in case the wolf is "level 1", its HP should be 10 (max hit die + con modifier). If it is considered to be level 2, its HP should be 17 (Max hit die + avg hit die + con modifier). What am I missing?

Third question: I found a post on a DnD reddit site where someone calculates the stats of a wolf in case the ranger is level 7. It goes like this:

> Wolf
> 
> Medium beast, your alignment
> 
> Armor Class 17
> 
> Hit Points 35 (6d8+6)
> 
> Speed 40 ft.
> 
> STR 12 (+1)
> 
> DEX 17 (+3)
> 
> CON 12 (+1)
> 
> INT 3 (-4)
> 
> WIS 12 (+1)
> 
> CHA 6 (-2)
> 
> Proficiency Bonus +3
> 
> Skills: Perception +4, Stealth +6, Skill of Choice, Skill of Choice
> 
> Saving Throws: Str +4, Dex +6, Con +4, Int -1, Wis +4, Cha +1
> 
> Senses: passive Perception 14
>
> Actions Bite. Melee Weapon Attack: +6 to hit, reach 5 ft., one target. Hit: 11 (2d4 + 6) piercing damage. If the target is a creature, it must succeed on a DC 12 Strength saving throw or be knocked prone.

I think I was able to figure out everything, except the HP.

My first assumption was to start with the given base 11 HP as a level 3 companion. Than at level 4, it gains an additional 7 (5 hit die +con modifier). And the same thing goes on for level 5, 6 and 7, to a total of 11+4*7 totaling 39.

If i start from the 2d8+2, and just add a hit die each time the ranger levels up, I can understand the 6d8 mentioned in the post, but I dont get the +6 modifier. Shouldn't it be +10? +2 base modifier at level 3, and +2 for each 4 levels totaling at +10. And now the problem is that averaging this value leads to 40, not 39, this problem is coming from my first question. 

I am completely lost here.

One last question. The `Bite` attack says +6 to hit. I can explain this as the DEX modifier became +3, and the proficiency bonus also became +3, however I dont understand the reason why DEX modifier is used for the `Bite` attack instead of STR.

Thanks a lot for the answer!