AD&D 1E Redesigned and Rebalanced Assassin for 1e AD&D

[Celebrim]

Incidentally that issue also has a clarification/answer on use of Assassination in combat:

Note that to a large extent this controversy among the sages has to do with whether you treat Gygax's write up of the assassin as primarily focused on the assassin as NPC (hiring one to perform assassinations and spying) or treat the assassin as PC. While the assassin shows up in the PH, I maintain that the original write up is more suitable to an NPC class simulating NPCs interacting with other NPCs - especially when you look at the rules for disguise and assassination and in the light of the clarification of the DMG.

 

[Lanefan]

As James said, 2E is explicit that bonuses are added after multiplying for back stab.

Which at higher levels, when the bonuses can often outweigh the die roll, really hammers the backstriking Thief. The difference between....

roll = 3, x 4 for backstrike, +3 for weapon, +6 for Ogre strength, +1 for Prayer that someone cast = 22, and
roll = 3,+3 for weapon, +6 for Ogre strength, +1 for Prayer that someone cast, x 4 for backstrike = 52

....is rather significant (I'm using the actual numbers for Black Leaf, my currently-in-play 12th-Thief, for this example).

If nothing else, doing it this way for Thieves' backstrike gives them a nice boost.