Barbarians should almost always want Great Weapon Master and Polearm Master and use them all the time, even if they think their to-hit roll won't be that good.
As an example, let's say I do 1d12+5 damage and hit 65% of the time because I have a 20 Str at 8th level. My average damage is 11.5*.88(65% with advantage)*2 = 20.2 damage essentially. Now, let's change that to a 16 Str Barbarian with the above 2 feats. So now, my to-hit chance drops to 55%. -5 means it is only 30%. I dropped to a d10 weapon. Yikes. Better look at the numbers though to confirm the suckage, right?
With a 30% to-hit chance, that means my chance of hitting with Advantage is actually 51%. I have roughly a 19% chance of a critical hit with the 1st 2 swings, which would trigger GWM's bonus action attack. So 2.19 d10 attacks and .81 d4(Polearm Master)
So it looks like this:
18.5*.51*2.19+15.5*.51*.81 = 27.1 damage. So even though your base to-hit is only 30%, you end up doing a lot more damage on average.
But it gets better than that - you have a Reaction attack too and 5e allows you to move both before and after your attack - so you move to within 10' of an opponent, swing at them 3 times, and then back away - in order for the opponent to approach you, they'll take a swing from the d10 end of your attack. If you're fighting a melee only opponent, they can be in real trouble at that point.
And if you end up with any bonuses whatsoever, such as 20 Str or magical bonus to hit, the numbers very, very quickly improve because the biggest benefits from Advantage happen when your to-hit chance is near 50%. With a +2 magic weapon and a 20 Str, you should likely hit most opponents 75% of the time without Advantage, 94% with(+19%). With a -5 to hit, those numbers change to 50% and 75%(+25%)...
How these numbers work make Variant Human Barbarian 5s very powerful for that extra feat - they make everything happen by level 4/5 instead of level 8...
