I got a PM this morning asking about this, so here's the Final Answer. I used TES

S to figure out how the Dark Brotherhood attacks were calculated.
The chances of getting attacked are based on the PC's level and on how many times you've already been attacked. There are 5 level groups, and each group has a base chance of being attacked that is decreased by 10% for every time you've already been attacked.
Here's the group breakdown and the level percentages:
If you are under level 4, there is a 20% chance of getting attacked.
If you are under level 10, there is a 40% chance of getting attacked.
If you are under level 20, there is a 50% chance of getting attacked.
If you are under level 30, there is a 70% chance of getting attacked.
If you are over level 30, there is a 90% chance of getting attacked.
Note that you will only be attacked if you rest, i.e. use a bed or sleep outside city limits. Also, the number of assassins goes up with the level group.
The sole exception is if you sleep in the Census and Exise Office. That bed will never be attacked.
Now like I said before, the chance of getting attacked drops 10% for each time you've been woken up by the assassins. So after the first attack, a level 1 player would only have a 10% chance of getting attacked, and so forth.
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