Let's assume an FPS. There are two players armed with miniguns, and only actions they can take are move on the plane (no jumping, no crouching), aim, and shoot. Also they are perfectly aware of each other's position and are in direct LOS. Comparing two situations, a - both players are on a flat plane, and b - one is on the perfectly vertical cliff while the other is beneath him in the canyon, are there any actual advantages of being at higher ground ?

If the players don't already see each other, someone above is more likely to be looking downward and notice the lower player before the lower player bothers to look up, which they rarely do. Further, the upper player shooting on someone below, the person below has moments of confusion before realizing where the shooter is, unless you have a fantastic danger indicator hud better than most modern games have.

My non-scientific opinion: Once actual combat is engaged, then players are already re-oriented on a new plane instead of the default plane of the straight ground - the biggest advantage is that initial time cost of each player creating/aligning that new plane. A higher up player notices the lower player first, fully aligns his plane, then shoots. The lower player, while being shot at, still has to take time to notice the upper player, and then re-orient his plane of combat, giving the upper player more opportunity to do damage before being responded to.

A few other points to consider:

• Higher ground lets you see slightly more behind barricades, which might be enough to shoot the enemy hiding behind it.
  
• Grenades travel farther from above, since (being already elevated) it takes longer for them to reach the ground.
  
• Depending on the nature of the level, the upper player can just back up (pulling himself out of view) to get more cover. The lower player must actually find cover.
  

If the angle between them is very sharp, the person up top might have the edge of the canyon as partial cover, effectively making them a smaller target.

StarCraft I had a 30% miss rate for units firing at a non-flying unit on higher ground - Not a realistic solution, but a workable compensation.

Higher ground lets you see slightly more behind barricades, which might be enough to shoot the enemy hiding behind it.[/quote]
Oh, hadnt thought of that.

Anyway, the reason i'm asking is, i thought about a scenario, from the point of pure offence. If two players are on a flat plane, and cant crouch - if one player shoots a long burst in a semi-circle - he will inevitably hit the other, no matter where the target moves. But if the shooter is at a certain height giving a sharp enough firing angle - target can sidestep in any direction, and will only get hit with a very small chance.

If two players are on a flat plane, and one player shoots a continuous stream of bullets in a circle, the farther away the target is, the greater chance of not being hit, as the bullets will separate as they travel farther from shooter. So it's not 'inevitable', unless the two targets are really close. (The more bullets per second, and the finer the increments of rotation, in conjunction with the distance between targets, would determine whether you get a hit or not)


Your other point is true - if a shooter high up tried to use the same spinning firing pattern, his semi-circle of bullets would end up more-or-less as a straight line ([size=2]Or would it appear as a curved line?) into the ground. However! If I was the shooter on the high ground, I'd instinctively fire in a spiral pattern spraying a large area.
Spraying in a spiral pattern (oriented around your line-of-sight) wouldn't work too well on a flat plane, but would work well from an elevated position. Spraying in a semi-circle oriented around your waist would work on a flat plane, but not from an elevated position. (Both suffer from the bullets spreading farther apart with distance)
I'd use the one most fitting for the circumstance without conscious thought of it.

To help visualize: On the flat plane ([size=2]against a moving target aware of me), I'd fire in a 2D cone, as shown in the image above (though a less-wide cone). On an elevated position ([size=2]against a moving target aware of me) I'd fire in a 3D cone, to cover more ground. On the ground trying to shoot someone at an elevated position, I'd lob a grenade, flee to cover, and try more accurate and much tighter 3D cone to try and 'snipe' the target or at least suppress him giving me enough time to assault the location from a more favorable vantage.

When you fire downhill, your arrow is not 'lost'. You could hit the target's feet, or any other target behind them. When firing uphill, if the arrow misses, its in the sky essentially.
This is why ancient strategies liked it best.
Secondly, the person going uphill risks being blinded by the sun if in the correct orientation (read the roman military handbooks regarding this) which would be impossible when looking downhill.

Also, assuming a parapet, the archer uphill offers his head alone, his lower torso is hidden by the 'floor' upstairs, whereas the downhill target is fully available. This gives roughly 50% more chance for the person higher to hit the lower one.