Double checked with Umi before I responded, but the 1d8 roll is
generally set up as "If you roll a 1, success, the other 7 fail", so
1d8 is literally a 12.5% chance, and over the long run, progging
once per 8 rounds, on average.

1d12 would be average of every 12 rounds, 1d4 average of every 4 rounds.

You're thinking about the average dice roll of that, given a 1d8 can roll 1, 2, 3, 4, 5, 6, 7, or 8 for a total of 36 out of 8 rolls, which
puts the average roll at 4.5