One of the first things gamers learn about dice is that the average roll on 2d6 is 7; however,
2d6-7 is not 0.

The simplest explanation is that 2d6-7 isn't zero because 2d6-12 is 0.
2d6-7 is actually approximately 1, which means that your Mangler getting shot at by those Winter Guard Infantry is actually going to take an average of 1 damage per hit, and is probably going to lose a big chunk of its health.

Arm min pow

So what's going on here?
In Warmachine, there's no such thing as negative damage. If you roll a 6, and subtract 7 because of ARM, the rules treat that result as 0 damage, not +1 health to the jack. This is why Dice-12 is 0, and not -5.
If your warjack suffers 36 attacks, it will take (on average):
5 attacks for 1 points of damage (rolled a 8)
4 attacks for 2 points of damage (rolled a 9)
3 attacks for 3 points of damage (rolled a 10)
2 attacks for 4 points of damage (rolled a 11)
1 attacks for 5 points of damage (rolled a 12)
Add all that together and you get:
And 35 damage over the course of 36 attacks works out to just about one damage per attack roll.
Ok, fine, but what if the example were an ARM 20 Juggernaut instead of an ARM 19 Mangler? Or an ARM 18 Nomad? That graph up there shows a nice curve, but it's kinda hard to read. What are the average damages for ARM-POW?

Dice Minus Expected Result
0 7
1 6
2 5
3 4.03
4 3.11
5 2.28
6 1.56
7 0.97
8 0.55
9 0.27
10 0.11
11 0.03
12 0

You'll notice that the actual averages start diverging from what you might expect at "dice - 3". That's the first instance of the "zero damage floor" coming into play. If you roll snake-eyes, the rules turn that 'negative one' result into a zero. This continues as you go further down the chart. It's actually fairly easy to memorize, if you round things a little bit.

"Bonus Damage" kicks in at Dice Minus Five, and proceeds from there. Even if you just remember that Dice Minus Seven is 1, you're in much better shape than you would be otherwise.