If your chance to hit is 1/11, that is, you need to roll 12 to hit, then -1 to hit is a 100% bonus, because it moves it from 1 possibility, 12, to two, 12 and 11.
If your chance to hit is 2/11, that is, you need to roll 12 or 11 to hit, then -1 to hit is a 50% bonus, because it moves it from 2 possibilities, 12 and 11, to three, 12, 11, and 10.
2d6 probability doesn't work that way at all.
There are 36 different dice combinations possible with two 1D6 dice. To visualize this, imagine two dice, each with a different color. (Blue and red) To get, say, an 11, you have 2 options: Blue 6, Red5, or Blue 5, Red 6.
To get a 12, you must get Blue 6, Red 6. Nothing else works.
So, there's 1 combination that gives you a 12, two combinations that give you an 11.
Here's the whole list of possibilities:
2 - 1 Combination
3 - 2 Combinations
4 - 3 Combinations
5 - 4 Combinations
6 - 5 Combinations
7 - 6 Combinations
8 - 5 Combinations
9 - 4 Combinations
10 - 3 Combinations
11 - 2 Combinations
12 - 1 Combination
You'll note that's a curve; that's what's referred to as the bellcurve of rolling 2d6.
This also means that the effect of a -1 bonus changes based on where you are on that curve. Going from a TN of 8 to 7 means you're to hit goes from 41.6% to 58.3% chance to hit.
Going from 12 to 11 is a change from 2.8% to 8.3% chance to hit.
It's quite literally 3 times easier to hit, though the chances of success are still only 1 in 12.
Paul