I've been working on a set of rules for an AR I'm mulling over. I've asked some questions about various ways to roll (some of which didn't even include rolling!), but I felt like exploring a new possibility. I decided to see how rolling 2d6 would turn out, with the catch being 6,7, and 8 all being "Average" on an unmodified roll. I wound up getting a sample size of 500 rolls, making sure to stop every 50 to get more accurate stats for various lengths of games. While obviously luck will always play a factor, I'm fairly pleased with the results.
The amount of rolls are arranged in order of total - 2/3/4/5/6/7/8/9/10/11/12, and would be categorized as Failure(2), Buggy(3), Poor(4), Below Average(5), Average(6,7,8), Above Average(9), Excellent(10), Superior(11), Unexpected Boon(12).
Next to the individual rolls I total the combined Low, Average, and High rolls, which makes it easier to see how things line up.
50:3/3/6/5/7/10/3/4/4/2/3 Lo:17 Avg:20 Hi:13
100:9/7/9/8/12/21/10/8/7/4/5 Lo:33 Avg:43 Hi:24
150:9/9/14/10/22/35/21/11/8/6/5 Lo:42 Avg:78 Hi:30
200:10/13/18/14/34/41/25/15/10/6/7 Lo:55 Avg:100 Hi:38
250:13/15/20/19/44/48/32/25/15/10/9 Lo:67 Avg:124 Hi:59
300:14/18/23/28/53/54/37/28/22/13/10 Lo:83 Avg:144 Hi:73
350:14/21/26/35/57/61/48/33/26/16/13 Lo:96 Avg:166 Hi:88
400:15/22/31/43/70/70/51/35/28/19/16 Lo:111 Avg:191 Hi:98
450:15/25/31/53/82/79/58/43/36/22/16 Lo:124 Avg:219 Hi:117
500:17/27/35/56/95/87/65/49/37/23/19 Lo:135 Avg:247 Hi:128
In my opinion a near-50% chance to get an Average roll with a 25% chance of going either way isn't bad. I'd like to get some other opinions on the matter, but I think it's worth a spin.