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They originate from the player toward the direction the bfg was fired at. As in absolute bearing. And only goes off the moment the blob explode by hitting something. Basically, you could shoot toward a wall, move sideways into a corridor and it would blast everything in the corridor.
Also dubbed the stealth bfg trick.
I allways think the BFG divide all the dmg to every enemy he hit...but not. I find this in the doom wiki :
To determine the damage of a BFG tracer, a random number between 1 and 8 is generated and repeated 16 times. This makes the total damage varies from 16 to 128 (due to the "bell curve" phenomenon, the value is weighted towards the middle of the range). However, due to the Pseudorandom number generator of Doom, this never happens in real gameplay, and the damage is limited to 49-87.
Looks pretty cool.
Basically, the shoot you see is somehow "fake" in terms of damage. It´s still not toally irrelevant. It goes somehow like this.
When you shoot the BFG, the "green bubble" goes ahead, until it collides with anything and explodes. The trick is, the green bubble itself don´t do any damage. Instead, when the green bubble (the bfg shoot) touch something and explodes, its when IN REALITY your BFG shoots more than a dozen straight invisible rays, fanned out, and each individual ray do damage individualy.
So, if when the green bubble explodes when you are very close to an enemy, most likely it will take most of those "rays" suffering heavy damage. But if you are too far, just one or a few rays may hit him.
You can even shoot the green bubble on any direction, lets say "south", then turn quickly and aim at an enemy at "north". When the bubble reach a target and explodes on the south, it will be the enemy you are aiming at the north the one wich will be hit by the invisible rays the BFG REALLY shoots, just when the green bubble explodes.
So think of it as a shotgun with a huge horizontal spread, wich doesn´t really shoots when you "shoot" the green bubble, but instead shoot a lot of horizontally spread rays when the green bubble touches anything solid and explodes.
The bubble itself actually hits hard; but the damage is inconsistent, like most of the random values distribution in vanilla. It does 100 * d8 (8-sides dice, a discrete 1-8 number). Sometimes the bubble would kill 700hp Archvile. Sometimes it whizzles at 100, less than pinky's health pool. Tracers each use multiple random rolls, which averages output values in Gaussian ("normal") distribution.
The most non-intuitive part is that bubble can only hit single target; it doesn't provide any splash damage. Like a fat-looking Mario bullet that is consumed individually.
There is a catch - there is a delay. Rays emitter activates ~0.5 second later, not the moment bubble hits. It makes it even more dangerous to point-blank dance with a Cyber. But it allows to stay behind a cover for a full bubble cycle, without exposing oneself to the crowd, if timed correctly: hide behind a corner, shoot the wall, then look out 0.4 seconds later to spread the tracers goodness.