For full transparency, there is the breakdown of the Two-weapon Fighting Beast Master Ranger 12th level damage.
Round one. Ranger places Hunter’s Mark as a bonus action, both Ranger and Beast Companion close. Ranger takes the Attack Action and gives their first attack to the Beast who attacks twice, getting the 1d6 bonus damage twice, possibly knocking the target prone, and Hunter’s Mark damage once. Ranger then attacks with their shortsword once and their scimitar once.
Round two through three. Ranger commands Beast to attack as a Bonus Action. Beast attacks twice, getting the Hunter’s Mark damage once and uses Exceptional Training to do the Help Action as a Bonus Action. Ranger attacks with shortsword twice and scimitar once.
I am rounding all damage to the nearest tenth of a point, but for fun I am showing the actual result before the rounding. Some of them get rather silly.
Round 1:
Beast Attack 1 (1d8+1d6+6 (14 avg. damage, 8 crit damage), no advantage)
14 x .55 = 7.7
8 x .05 = 0.4
Beast Attack 2 (1d8+1d6+6 (14 avg. damage, 8 crit damage), possible advantage from prone)
14 x .55 x .45 = 3.465 = 3.5
8 x .05 x .45 = 0.18 = 0.2
14 x .7975 x .55 = 6.14075 = 6.1
8 x .0975 x .55 = 0.429 = .4
Beast Hunter’s Mark (1d6 (3.5 avg. damage, 3.5 crit damage), two chances to hit and crit with possible advantage on second chance)
3.5 x 0.857625 = 3.0016875 = 3
Shortsword attack (2d6+5 (12 avg. damage, 7 crit damage), possible advantage from prone)
12 x 0.6 x .2025 = 1.458 = 1.5
7 x 0.05 x .2025 = 0.070875 = 0.1
12 x 0.84 x .7975 = 8.0388 = 8
7 x 0.0975 x .7975 = 0.54429375 = 0.5
Scimitar attack from Nick (2d6+5 (12 avg. damage, 7 crit damage), possible advantage from Vex)
12 x 0.60 x 0.2086 = 1.50192 = 1.5
7 x 0.05 x 0.2086 = 0.07301 = 0.1
12 x 0.84 x 0.7914 = 7.977312 = 8
7 x 0.0975 x 0.7914 = 0.5401305 = 0.5
DPR for Round 1: 41.5
Rounds 2-4:
Beast Attack 1 (1d8+6 (10.5 avg. damage, 4.5 crit damage))
10.5 x .55 = 5.775 = 5.8
4.5 x .05 = 0.225 = 0.2
Beast Attack 2 (1d8+6 (10.5 avg. damage, 4.5 crit damage))
10.5 x .55 = 5.775 = 5.8
4.5 x .05 = 0.225 = 0.2
Beast Hunter’s Mark (1d6 (3.5 avg. damage, 3.5 crit damage), two chances to hit and crit)
3.5 x 0.895 = 3.1325 = 3.1
Shortsword attack 1 (2d6+5 (12 avg. damage, 7 crit damage), advantage from Exceptional Training Help action)
12 x 0.84 = 10.1
7 x 0.0975 = 0.7
Shortsword attack 2 (2d6+5 (12 avg. damage, 7 crit damage), possible advantage from Vex)
12 x 0.60 x 0.16 = 1.152 = 1.2
7 x 0.05 x 0.16 = 0.056 = 0.1
12 x 0.84 x 0.84 = 8.4672 = 8.5
7 x 0.0975 x 0.84 = 0.5733 = 0.6
Scimitar attack 1 (2d6+5 (12 avg. damage, 7 crit damage), possible advantage from Vex)
12 x 0.60 x 0.2 = 1.44 = 1.4
7 x 0.05 x 0.2 = 0.07 = 0.1
12 x 0.84 x 0.8 = 8.064 = 8.1
7 x 0.0975 x 0.8 = 0.546 = 0.5
*Okay, the actual chance to get advantage is 0.8016, not 0.8. But it is close enough!
DPR for Round 2-3: 46.4
Average DPR for four rounds of combat:
(41.5 + 46.4 x 3) / 4 = 45.175 = 45.2
Looking back I said that the Beast Master was doing 44.8 damage at level 12 in my original post, so I was off by 0.4 damage. I think I might have been rounding more the first time around. Or maybe I wasn’t rounding as much? Anyway, here is all the math so you can check it if you want.
Oh and here is the simple math for Conjure Barrage. Looks like I assumed a 55% chance for the target to fail their Dex save, which might be too generous, but it is easy enough to change.
Conjure Barrage (3)
22.5 x .55 = 12.375 = 12.4
22.5 / 2 x .45 = 5.0625 = 5.1
17.5 / target
DPS gain on 3 or more targets