After some nice bartering, my character managed to nab a displacer field. With high agility allowing me to reengage enemies via charge, and the house rule that if it goes off in the middle of a lightning or swift attack any attacks after it goes off no longer hit (you're no longer there, of course), I thought this was a great deal.

That was before we got to the space hulk, though. On a flat field, it's easy enough to determine the "random direction" part of the displacer field's dropoff with scatter die or somesuch, but becomes more than a little complicated when you're in an area with safe footing both above and below the character; the system we came up with in a few minutes slightly favoring moving the player up or down. (ended up teleporting two floors above the party... into a nest of genestealers. Infamy was burned.)

So, how does one come up with a fair way to determine the random direction a player travels in, in a three-dimensional space?

I always assumed you got displaced on a horizontal axis. BUT

Roll a d10:

Even means you get displaced on a horizontal axis(along the ground), odd means you get displaced on a vertical axis(up down/side to side).

Then, from there, use the scatter rules.

Or for more detail/options, role scatter twice. Once for horizontal,(backwards forwards side/side) then once again for vertical(up/down/side to side would be neither up nor down).

I misunderstood the first part of your question. Do you roll displacement for each hit on a lightning attack? Just curious.

SilverFayte said:

Roll two scatter dice. One for X/Y, the other for XZ.

Leave it up to GM discretion to decide when the X/Z die kicks in.

I would suggest avoiding the X/Z die as that will be a huge headache for everyone involved

By the book it's one roll for each 'attack' not each 'hit.' My group has decided to house rule it to roll per hit anyway. We haven't had to deal with displacer fields yet, but this sounds like how we would handle it. As for scatter since we use maps on the table for most combats I've pulled out the old scatter die form TT. Then maybe check for vertical with a 1d10-5 meters for height, rounding to the nearest level surface. So, assuming space marines have space to stand, 3m cielings and all the machinery running between levels you would need to roll -3 or less to go down a floor or +3 or more for up one floor. But I'd just ignore the vertical most of the time.

I find referencing old works like the Inquisitor rulebook in GWs Specialist Games section can be helpful.

"Displacer field
Displacer fields work slightly differently from other force fields in that they will either activate and take the character out of harm?s way, or they won?t have any effect at all. The more powerful a hit, the more likely the field is to detect the attack and activate. The field has a basic 50% chance of activating, with a bonus to this chance equal to the damage rolled. If the field activates, the wearer is teleported D10 yards in a random direction and the attack has no effect. If it does not activate, then the field has no effect whatsoever and the injury is resolved as normal. The displacer field will not teleport the wearer to a place it is impossible for them to enter and survive (such as solid cliff face, into empty space or another character?s position) and will stop them 1 yard short if this would be the case. They may however pass through terrain and other characters before materialising again."

Unfortunately in this instance it doesn't got into any more detail than "in a random direction". I did a quick google search to see if i could find any spherical scatter dice (you can get spherical d100s with literally 100 sides) as this would allow for true 3-dimensional scatter from the field's effect. Alas, i couldn't find anything.

I'm considering solving my own problem through writing a short program that rolls the distance, asks the height between floors, and determines the percentage chance you'll end up on each floor based upon the circumference of the resulting floor's cross-section with the sphere of radius equal to the rolled teleport distance, picking a floor randomly based on said probabilities, and then picking a random spot on said cross-sectional circles to place you. I'll post that here if I get it done, in the off chance that anyone else needs it.