They did not get slower. Your weapon did not change.
Your position changed what their movement looked like.
The two fights below use the same players, the same range and the same weapons. Blue is you and Red is the enemy, here and everywhere else on this page.
Which one would you rather be tracking?
On the left, Red can dodge in every direction. On the right, several of those dodges run straight into the wall.
Try it. Drag Blue around in each one. Where does Red look easiest to track?
Neither player is doing anything different. The map did the work. Before angles, cover or peeking, that leaves something more basic to work out.
Anything on this page that can be dragged is worth dragging. Every figure can also be flipped to the other player's camera, and most of the value is in doing that.
Imagine an enemy strafing in the middle of an empty room. For the next fraction of a second they can go left, right, forward, back, or somewhere in between. You do not know which they will pick, so your aim has to be ready for all of them.
By the time your shot arrives, the person you aimed at has already moved. That is why the useful thing to picture is not the point they are standing on but the small patch of ground they can get to next.
We will call that patch their reachable space.
It is worth seeing where that patch comes from rather than taking it on trust. The figure below plays the movement at a tenth of speed, from above. Each faint mark is where one run of the window ended. Commit to one key and you finish on the edge, change your mind partway and you finish somewhere inside, and the paths bend because the keys point wherever you are looking while your view tracks someone. Enough runs and the marks are the patch.
How big it is depends on how fast they move and how long you need. We only care about the next moment, not where they could be five seconds from now. A few hundred milliseconds is long enough for a strafe to matter and short enough that neither player has had time to re-plan. The figures use 300 ms because it is a convenient scale. Do not memorise the number. The question it stands for is where can this player get to before I have to react again?
Try it. Before you touch anything, guess what happens to the yellow patch when you push Red back against the wall. Then drag them there and watch.
Some of it disappears. The wall has not slowed Red down at all. It has removed places they were allowed to be, which is a different thing and a more useful one to notice.
You have one too. Everything drawn here for the enemy exists for you, in blue, on every figure on this page. That will matter a great deal later.
Do not aim only at where the enemy is. Read the places they can move into next.
Put an enemy's back against a wall and something changes before either player fires. If they press backward they go nowhere. Some of the diagonals also carry them partly into the wall. Without losing any movement speed at all, they now have fewer useful ways to get out from under your crosshair.
The same idea shows up at a doorway. A player in the middle of a room can dodge almost anywhere. The same player squeezed through a choke has far fewer paths worth taking, even though you can see just as much of them.
Here is the part that surprises people. The enemy is facing you, so their movement keys are oriented by your position. Walk around them and you change which of their inputs still do anything, without them doing anything at all.
Try it. Guess first: as you swing your viewing angle around, does the number of directions still open to Red stay the same, fall smoothly, or jump about? Then drag the angle slowly and watch the count.
It steps rather than slides. At some angles one of Red's blocked keys comes back, because it now runs along the wall instead of into it, and a player who slides along a wall is still moving.
Obstacles do not all work the same way. A wall behind someone stops their feet. A doorway in front of them stops your eyes without restricting their feet at all. A corner can do both at once. Which job a piece of cover is doing turns out to matter more than how big it is.
Where exactly the count steps depends on movement being built from eight fixed inputs, which is how these games work but is not a fact about geometry. It would soften in a game with analogue movement. The angles are not worth memorising.
A useful wall removes movement that would otherwise have mattered to your aim.
Cover can make a target easier to track by taking away their options, not only by hiding their body.
Suppose an enemy moves four metres sideways.
From fifty metres away you barely move your mouse to stay on them. From five metres away that same four-metre strafe can sweep across a huge part of your screen.
The enemy travelled the same distance through the map both times. Your hand did not experience the same movement at all.
That gives us a second thing to care about. The first is how much ground the enemy can physically reach. The second is how large that ground looks from your camera. We will call the second one its screen-space size.
This is not only about range. Hold the distance fixed and walk around someone, and the patch they can reach stays exactly the same size on the map while the amount of your monitor it covers changes enormously.
Try it. Predict first: if you keep the range fixed and only change your angle, do you think the yellow region on your screen changes a little, or a lot? Then walk Blue around Red and watch the two bars. One is measured on the map, the other on Blue's screen.
The map bar never moves. The screen bar collapses by about half. Red has done nothing, and Blue's shot has become substantially easier.
Keeping those two apart is where a lot of positioning talk goes wrong. When an obstacle takes away somewhere the enemy could have stood, their reachable space genuinely got smaller. When you move and the same reachable space simply covers less of your monitor, only its screen-space size got smaller. Both make your shot easier. Only the first one survives them turning to look somewhere else.
Aim cares about movement across your screen, not metres travelled on the map.
Two equally fast strafes can demand completely different mouse movements.
Consider two enemies.
The first is standing in the open. You can see their whole body, and they can strafe anywhere they like.
The second is jammed behind cover with almost nowhere to go, and only their head is showing.
Which one is easier to hit?
There is no universal answer. Every position hands you some mixture of two different things.
Target: how much enemy there is to hit. Room: how much empty space they can move into.
More target is good. Less room is good. Most positions trade one against the other, and that trade is what a position is really made of. On every figure here the target is the body in orange, called the hittable area, and the room is everything yellow around it, the movement room.
Try it. Decide which bar you would rather have large before you start. Then drag Blue around and watch the two trade against each other.
It would be convenient if shrinking someone's movement room always made them easier to kill. It does not, because the same cover that pins a player also hides them. A player wedged behind a crate with only their head visible is extremely predictable and still extremely hard to hit.
So the honest answer is that it depends on what actually costs you shots.
If you lose fights because targets escape your tracking, then taking away their movement room may matter enormously, and you can afford to give up some exposed body to get it. If you lose fights because there was only ever a sliver of head to shoot at, you want the angle that shows more of the enemy even if it hands them a little more room. At very close range, with a weapon that rewards getting as much of the model in front of you as possible, target size tends to dominate outright.
The same position is genuinely better for one player than another, and that is not a failure of the model.
Judge a position by how much target it gives you and how much room it takes away.
Most positions trade one for the other. Take whichever answers the way you actually miss: too little to shoot at, or too much movement to follow.
So far this sounds easy. Find an angle where the enemy has less room to move and more body showing.
There is one problem.
They are looking back at you.
The wall that restricts them may restrict you as well. The angle that makes their strafe look small on your screen may be making your strafe look just as small on theirs. A position is not good because the enemy looks easy to hit. It is good because they look easier to hit than you do from the other side.
Try it. Move Blue off the square line and watch all four bars. Read Red's screen before you decide anything.
Directly in front of the wall, every bar is identical. Red is the one with a wall behind them and it has done Blue no good at all, because the part of Red's movement it removed was never going to appear on Blue's screen from there. It looked like an advantage right up until the second camera was checked.
Do this deliberately until it stops being deliberate.
One more distinction, because it decides what you learn from a fight. What you can hit right now is not the same as how quickly that can change.
A bad position can hand you a very easy shot, because the enemy happens to be standing still and is about to have five good ways out. A strong position can offer nothing at all for a second and then a free kill. If you judge your positions by the shot that was available in the instant you looked, you will keep picking the first over the second.
Three versions of the same wall
Straight in front
Red has a wall at their back and cannot step backwards. But backward movement would barely have crossed your screen from here anyway. The wall has bought you almost nothing.
Off to one side
Now the wall is removing part of Red's sideways movement, which is exactly the movement that was sweeping across your screen. Their dodge gets smaller where it counts.
Too far around
Push further and you end up pressed against cover yourself, with Red getting the same gift you were trying to take. The advantage crosses back over.
Whenever a position looks good, mentally swap the cameras.
A good angle changes their fight more than it changes yours. If it looks equally good from both sides, you have not gained anything.
We can now say what the phrase means, because it is not simply standing diagonally.
Taking an angle means using an obstacle against the enemy's movement without handing that same obstacle equal leverage over yours. It is about creating a difference between the two cameras. That is why both extremes fail. Square to the wall there is no difference to create, and flat against the wall yourself you have created it in the wrong direction.
Since it is zero at both ends and useful in between, there is a best angle somewhere in the middle. Sweeping every angle at a fixed range gives a curve with a shape you can carry around even if you never remember a number from it.
Try it. Guess where on the sweep the advantage peaks before you look. Most people guess further round than it actually is.
The middle is broad and flat on top. There is no single correct angle to memorise, and being a bit off costs you very little.
Under these movement assumptions and this geometry. Change the movement model, the range, or what beats your aim, and the peak moves. The shape does not.
Walk a full circle around someone at a fixed range and keep watching the yellow. It does not stay the same size. In most places there are one or two directions where it looks widest, and those are the worst places to be standing.
Try it. Switch between the four situations and find the widest point in each one before reading on. Watch the shape of the curve rather than its peak.
A flat wall has one worst direction, square to it. A corner has one, along the diagonal. A freestanding pillar has two, one per side. In the open the curve is flat, which is the precise way of saying there is nothing here to angle off and you should stop looking for one.
Those directions are useful because everything else is easiest to describe relative to them. When we need to name one, we will call it a reference direction. It is a measurement and not an instruction: it says where their movement is hardest to cover, and whether moving away from it helps you depends on what the same move does to your own geometry.
Two curves are drawn. The solid one is what you can see. The dashed one is the shape of their reachable space by itself. A wall behind them moves both, because it takes away places they can stand. A doorway in front of them moves only the solid one, because it hides their feet without restricting them. Watch those two come apart and you can see that a piece of cover is doing either job, or both.
An angle is worth taking when it costs the enemy more than it costs you.
Not because it is diagonal, and not because you can see them clearly from it.
Stand right against a corner and one sideways step swings your sight line a long way past it, uncovering a lot of hidden ground at once. Stand well back and the same step barely swings it at all.
So the player further from the corner uncovers the space gradually, and can stop at any point. The player hugging it is committing to whatever is around the other side.
Try it. Before moving anything, guess which player controls the peek: the one close to the corner or the one further away. Then give each of them the same sideways step and compare how much new ground each one reveals.
Whoever stands further from the corner reveals less per step, and therefore chooses how much to show and when. This is being decided while neither player can shoot yet, which is most of a corner standoff. Nobody has anything to hit. What is being contested is control over the reveal, and distance is how you win it.
It is not a universal rule about cover, though. This works when the obstacle sits between the two of you, controlling what you can see of each other. When the obstacle is instead hiding your own body, staying close to it is what keeps you hidden, and backing away simply puts you in the open. Shooting down from behind a raised ledge is the standard example, and the advice there inverts completely.
Ask whose sight line the cover is controlling before deciding whether to back off it.
If it is between the two of you, standing back buys you finer control of the reveal. If it is hiding your body, standing close is what keeps you hidden. The same wall does opposite jobs depending on which side of it you are on.
We can finally go back to the fight at the top of this page. Moving a few metres sideways made the same enemy easier to hit because it changed which of their escapes the wall was taking away, and how much of the rest crossed your screen. Nothing about them changed at all.
Everything above compresses into a short sequence you can run in the moment.
You are not supposed to be calculating any of this while playing. Nobody estimates areas mid-fight, and trying would be worse than useless. The point of looking at it deliberately now is that after enough of it, the questions stop being questions. You see that the wall behind them is doing nothing from where you are standing, in the same way you currently see that someone is reloading.
One check sits in front of all of it. If the fight cannot be won even assuming every single shot lands, then no amount of positioning rescues it, and you should be changing the fight rather than improving your angle.
Almost every position in a shooter is one of a handful of shapes, or two of them stacked. Recognising which one you are in is most of the work.
Each one gives you the situation and asks you to commit to an answer before you look. Then you can change it, see what moved, and take away one sentence that works on a different map. Answer before you touch the figure. Getting one wrong is more useful than reading the explanation first.
Every situation, both cameras, and every setting that has been fixed until now. Drag either player, load any scenario, and put them somewhere the guide never did.
The plain phrasing, and the formal term it corresponds to.
This guide uses the plain phrasing throughout, because it is what you will actually think in. The formal terms are the ones the original framework uses and what anyone else discussing it will say, so they are worth recognising. Each entry ends with the one question that makes it usable while you are playing.
Nothing below this line is needed to use anything above it.
Each of these was introduced by picture earlier. Here is the same thing written down. Ω is solid angle throughout, measured in steradians.
A pinhole camera with unit focal length sends a point on the image plane to the direction . That patch of image sits at distance from the eye, and it is tilted away from the line of sight by . Projecting it onto the unit sphere scales it by , so
The weight is not uniform across the frame, which is the whole reason the solver sums it rather than counting pixels. In a 90 degree view a pixel at the left or right edge carries about 35% of the solid angle of one at the centre, so counting pixels would overstate anything near the edge of the screen by nearly three times.
The solver renders the scene into a framebuffer, tags every pixel as sky, obstacle, model or reachable space, and sums that weight over the pixels carrying each tag. The viewport pictures on this page are that framebuffer, so the picture and the measurement cannot disagree.
Finding one is a one-dimensional optimisation. Sweep the bearing at fixed range and take the maximisers of . The set of maximisers is generally an arc rather than a single ray, which is why the figures draw arcs rather than lines, and the reported direction is the weighted centroid of the arc. When the curve is flat to within a small tolerance every direction qualifies, and no reference direction is reported at all rather than an arbitrary one being picked out of the noise.
Stand a distance from a corner and step sideways by . The sight line past the corner swings by
Sweeping that angle across ground extending a distance beyond the corner uncovers a circular sector of radius and angle , so the newly visible area and its rate are
So the reveal rate falls as one over your distance from the corner. Doubling how far back you stand halves what a single step gives away, which is the whole of the peeking section in one line. The measured curve in the figure earlier is two visibility grids differenced, and it follows that inverse relationship closely enough that the approximation is doing no work the geometry was not already doing.
The geometry above stands on its own and does not depend on any of this. What follows is one way of showing that a larger hittable area and a smaller movement room can pull in the same direction, rather than a claim about how aiming works.
Suppose shots scatter with angular error , and that it grows with the room the target has to move into. For a circular target of solid angle the chance a shot lands is
where the spread itself widens with the room the target has to move into,
rises with and falls with for every positive , so expected damage does the same. That is the sense in which the two halves of the comparison belong together rather than being two unrelated rules of thumb.
The constant is how much of the opponent's available room actually defeats your tracking, and it is what decides which half of the comparison you should weight. Setting it to zero recovers the perfect-aim case, where only the hittable area matters and movement room is irrelevant.
The absolute numbers this produces are not meaningful and are not used anywhere on the player-facing part of the site.
A software rasteriser with a depth buffer and an id buffer, about five hundred lines, no dependencies. Reachable space is stored as a height field over a grid, so obstacles clip it exactly and the same structure serves the map view, the viewport and the sweep.
Every obstacle is a convex polyhedron held both as half-spaces, for containment and ray clipping, and as faces, for rasterising. Boxes and ramps come from the same representation, which is why sloped ground needs no special case anywhere else.
The bearing sweep and the advantage field run in a worker. The field evaluates two full comparisons per map cell, each with its own pair of reachable spaces, and masks any cell where neither player can see the other.
The claims this site makes about the geometry are pinned down by a test suite, so they cannot quietly stop being true:
npm test
Measuring something that was originally argued in prose will occasionally produce a different answer. Sometimes that means the prose was loose. More often the two are defining a term slightly differently, or a simplification that is harmless in a diagram is not harmless in a solver. Each one below is set out the same way so you can judge it yourself.