strafe jumping explained

Strafe Jumping explained and how to do it
In this video I'm going to try to explain to the best of my knowlegde how strafe jumping works in games like Quake 3, Quake Live and Quake Champions.
There are already many strafe jumping tutorials on youtube but I believe an understanding of what strafe jumping actually is will help a lot in learning and developing your strafe jumping skills.
In the video will explain
How and why strafe jumping works
How to circle jump (circle jump)
How strafe jumping is done in a practical way in-game (practical strafe jumping)
How strafe jumping works in different games (strafe jumping in different games)
and in the case of Quake Champions, how it's different for different champions.
First, some basic physics.

PHYSICS

A vector is a geometrical object that has a size or length and a direction. They can be drawn as arrows. (arrow to the left) 5, here we have a vector, (arrow pointing up) 7, here's another one.
A force, a speed or an acceleration all consist of a size and a direction, they can therefore be described as vectors. For example, 5 km/h. This is a speed in that direction (draws arrow in some direction).
Or 7 m/s/s, an acceleration in that direction.
A vector can be split into parts and described that way instead. Like this, this diagonal vector(draws diagonal vector) can be described as a force upwards and a force to the left, combined.
To show you exactly what this means I have an example from my physics book from high school.

Here we have a top view of a river going horizontally, and a rowing boat. The person in the rowing boat is rowing it towards the other side of the river with a speed of 2 meters per second.  At the same time the river is running to the right and the water is moving the boat with a speed of 1.5 meters per second.
Now how will the boat move? It won't go straight over, right? The resulting vector from these two vectors will be diagonal. This is how the boat will move. But how fast will the boat move diagonally?  The resulting speed will be faster than both of it's components and it can be calculated with some simple trigonometry.
If we just move this vector to the right we can see that it's a right sided triangle, meaning one of it's angles is 90 degrees. That means we can use the Pythagoras theorem to very easily calculate the missing side.
a^2+b^2=c^2
This is pythagoras theorem. c is the side opposite to the 90 degree angle.
So, this can be a, and b, and c.
2^2+1.5^2=c^2
That will be:
4+2.25=c^2
So
6.25=c^2
Then
c=2.5
The boat will be moving diagonally with a speed of 2.5 m/s.
A velocity to the side and a velocity forward resulted in a larger velocity diagonally.

Straferunning

In doom we could exploit this very thing because of how physics in the game worked, the max speed walking forward and the max speed walking to the side are the same. But in Doom there is no real diagonal movement like if you pressed forward or backward and a strafe key in a more modern game. Moving forward while strafing will simply calculate a diagonal movement from the forward vector and the strafing vector.  The diagonal vector would then just like with the boat be bigger than it's two components. So walking diagonally in Doom is faster than walking straight! Add the run button and you can go pretty damn fast in the game, when you are straferunning.

Fast forward to Quake 3 and game developers have figured out how to do proper diagonal movement.
Here, the diagonal running speed gained by pressing forward and a strafe key is not calculated from the forward/backward and strafing velocities but is set at the same max speed as moving forward/backward/left and right. It is it's own direction.
All of the eight possible directions that you can move in with the keyboard are treated the same, running in any of them will max you out at 320 ups.
In the Quake 3 engine you can only accelerate up to 320 ups in any direction.
If we try to make our own diagonal movement like in Doom by running forward, letting go of W and then hitting strafe, the ground friction will stop our forward movement, the same thing will happen if we run forward and then press strafe without releasing forward, the forward movement will be completely replaced by the diagonal movement.
We will need something else to propel ourselves beyond 320 ups. Strafe running isn't really working, what we need to do is something called strafe jumping.
Strafe Jumping

Now if I just run forward here and let go off the forward key the friction between the player model and the ground will slow me down until I stand still.

But if I continually jump while going forward and time my jump presses so that I jump as soon as I land, no ground friction is ever applied. I can then let go of the forward key and still keep moving forward while keeping all of my momentum.
This is what I would call bunnyhopping.
Since I'm not applying any acceleration force with my movement keys, I can look in any direction without affecting my speed and direction of movement.
This is the first thing you need to learn.
Hold forward and start jumping, release the forward button and try to keep your speed at 320 ups.  If you jump too late, ground friction will be applied and you will lose speed. (show losing speed)
In a game like Counter-Strike you have to time your jump button press really well to bunnyhop. In Quake 3 there is some leniance, if you press jump a bit before you land the game will buffer your jump action and execute it when you actually land. So it doesn't matter                                        if you press jump a little bit early. This makes it way easier to bunnyhop without losing speed in Quake than it is in Counter Strike and therefore no scroll wheel jumping is needed either. Space is the default jump key but many Quake players, I would say the majority, jump with the right mouse button instead, mouse2, one of the reasons is that there's alot of jumping in Quake and it takes less physical effort to press mouse2 over and over again than pressing space with your left thumb. This is of course a preference thing, there are several pro players who jump with Space.
Practice bunnyhopping like this until it feels natural and you are never failing by jumping too late and losing speed.

Now because we can keep our 320 ups momentum in one direction by bunnyhopping without it being affected by friction, we can start applying acceleration in another direction, and if we apply it in the right direction our resulting velocity vector will be higher than 320 ups, just like with the boat and Doom.
Here I'm hopping forward in 320 ups without holding W, I turn my mouse and when I now press W I will accelerate in the direction I'm looking up to the max speed of 320 ups. When I reach 320 ups in the direction I'm facing I'm going to stop accelerating because the game won't allow me to accelerate past that. But as you see, even though I've only accelerated up to 320 ups in two directions, the resulting speed is more than 320 ups.
I will draw it for you.
Here is our character from the top. We are moving 320 ups forward. This circle just represents all the directions we can move or turn in, in the game on a 2 dimensional plane. If we set forward as 0 degrees on this circle, than this is 90 degrees to the right, this is 90 degrees to the left, and backwards is 180 degrees. I draw a perpendicular line to the direction of movement.
If we are going 320 ups forward and accelerate up to 320 ups in another direction on the upper half of this circle, the resulting velocity will change direction and end up between these two and it will be larger than 320 ups.
Any acceleration in any direction on the upper half of this circle(fill in circle) will increase our speed because they add a speed forward. If we accelerate in this direction(draws arrow), we get a forward force if we split the vector(draws components). If we apply acceleration to a direction that is more than 90 degrees away from our direction (draws arrow) of movement we are going to brake our forward momentum (draws backward component).

Back to Quake 3, now what I'm playing here is actually a mod for Quake 3 called Defrag and not vanilla Quake 3. Defrag has a special Hud built into it called gazhud that's gonna help us here and it's a very good tool for learning how to strafe jump.
First we enable it in the defrag settings.
Now I will explain what all of this is.
The bottom part is just a compass that splits up the directions in 4 parts, like north, west, east and south. Except I don't really know which of these colors that is north. The large arrow is the direction we are moving in.
These red bars show acceleration and deceleration. The one to the right of the crosshair is acceleration and the one to the left is deceleration.
What we are interested is this green bar here. It will show the angles we need to look in while applying acceleration with our movement keys to increase our speed in the direction of our velocity. If we apply acceleration in a direction where there is green on this circle(mark circle), we will accelerate. As you can see, it looks just like my drawing. It is only green up to 90 degrees in each direction. If we apply acceleration in any direction on this forward facing half of the circle, our resulting speed will increase.
Now I try the same thing I did before, I jump forward with a speed of 320 ups, let go of W, turn, press W and as you see my resulting speed is faster than 320.
What you also can see is that the green bars, the acceleration zones,  have shrunk and moved away from the direction of my movement. What is going on here?
As I said before the max speed which I can accelerate up to in any direction is 320 ups. This is also true while I'm in the air.
If I go more than 320 ups in the direction of my movement and accelerate up to 320 ups in this other vector that is not a braking force on my first vector, all the vectors between these two will be more than 320 ups.
As you can also see the acceleration zone has shrunk an equal amount on the other side.
This is because if I break down my velocity vector into components, there must be an equal vector on the other side or else we wouldn't be moving in this direction.
I can no longer apply acceleration in any of these directions, since the max speed the game allows me to accelerate up to in one direction is 320 ups and all these vectors are larger than 320.
The acceleration zones will continue to shrink with increased speed towards the 90 degree mark on both sides.
Here's how it looks. I'm holding down W and turn my mouse. (show W strafing towards one side only).
Now if I keep turning, I will continue to accelerate, but I will also eventually hit a wall or fall down a pit.
Instead I can alternate between the sides to keep me on course and move somewhat in a straight line.
As you can see the acceleration zones get smaller and smaller because the faster we go the less directions there will be that we are not already moving equal to or faster than 320 ups.
What I'm doing now is strafe jumping using only W.
Now as you see the faster I go the more I need to turn my mouse when I alternate between the sides to catch acceleration. This method of strafe jumping doesn't really seem very practical to use in game, if I have to swing my mouse like this while trying to shoot enemies and navigate through the map....I'm gonna have a bad time.
As I said before all eight directions you can move in with WASD work exactly the same. Instead of moving forward with W, I can move in the same direction using W+D. The only difference is the direction I need to look in to move in the same direction. As you can see the big arrow that indicates the direction of my momentum is pointing towards the door, just as when I walk forward, I just apply the acceleration in a 45 degree angle from my crosshair.  If I'm turned sideways and move with a strafe key I'm applying acceleration in a 90 degree angle.
Now if I move towards the door with WD and start strafe jumping by turning to the right I will do exactly the same thing as I did when I strafe jumped with only W. I'm applying acceleration in the exact same directions as I did with only W, the only difference is the way I need to look to do so because of the 45 degree tilt.
(back to drawing)
When I strafe jump with W the acceleration zones on my hud will be placed at the same place as the directions I'm applying acceleration in. But if I strafe jump with WD the acceleration zones on my hud will shift 45 degrees to show me which ways I need to look in. (show on drawing)
So even if I'm looking here when I'm pressing WD I'm actually applying acceleration in this very same direction as I did before with only W, on the upper or frontal half of the circle.
Now only using W + D when strafe jumping is almost as unpractical as using only W cause look how far back I need to turn to catch my left acceleration zone. Note that even though I'm looking backwards when I catch this one I'm applying acceleration in this direction because of the 45 degree tilt when moving with W+D.
What I want is acceleration zones close to the direction of my momentum so I don't have to turn so much. One of these zones is a good one, the right one, because it's close to the crosshair.
What I can do then is to simply switch movement keys during my strafe jump from W+D to W+A, now I'm using the right acceleration zone from when I'm accelerating with W+D and the left acceleration zone from W+A.
Now this is effective. This is the regular strafe jump that most players use. It is the easiest and probably also the most effective way of strafe jumping gameplay wise.
This is what you need to learn, practice and perfect.
I press W+D while bunnyhopping, I catch the acceleration zone and slowly keep turning to the right because the zone gets smaller while simultanously moving to the right, the zone moves to the right because the velocity vector is moving to the right. When I need to correct the direction of my movement I switch sides and do the same thing with W+A.
Note that the switch is done quickly because you won't get any acceleration when the crosshair is between the acceleration zones, and when you reach the acceleration zone you keep turning in the same direction, only much slower.
Now you can alternate between each jump, every second jump or mix it up as much as you want. The fastest way to go from point A to B is switching sides every jump because you will move in a straighter line but it is also much harder to do since the risk is you will miss these acceleration zones.
Oh right, that's another thing. In-game, you won't see the acceleration zones so you will have to learn them by feel. I'll turn the gazhud off just for a second to show you some strafing without it. It's just something that you learn by practicing.
If your game has a speedometer like Quake Live you can use that one to see that your strafing is working. Ideally your ups should constantly be increasing at a high pace. If it's standing still you are not hitting your acceleration zones so you need to correct your angle with your mouse until the numbers move again.
So this is the regular strafe jumping method but you can strafe jump using any of the 8 movement directions possible by WASD or whatever movement keys you are using. And just like you can combine W+A strafing with W+D strafing you can also combine these eight in any way you like, some are easier done and more effective in game but they are all equally fast, because remember, the only thing you are doing is applying acceleration in the upper half of that circle, in the directions you are still not moving 320 ups in.
Here are some examples.
W+D/S+D - normal strafe jumping but sideways
W/S
W/D
A/D
The role of the mouse in strafe jumping is simply to make small adjustments to the angle you are accelerating in with your movement keys because of the limitations in only being able to move in 8 directions with the keyboard.
This brings me to the fun fact that I've heard many people question how you would be able to strafe jump with a controller.
Strafe Jumping with a controller is theoretically more effective because it doesn't matter at all which way you are looking in. You don't even have to touch the looking stick and you can still strafe jump perfectly. Because an analog stick is not limited by 8 directions so you can continue to apply acceleration in the acceleration zones while they shrink(animation with analog stick and acceleration circle/zone) without having to look in certain directions for fine adjustments.
Theoretically the optimal way to play Quake could be with an analog stick for movement and a mouse for aiming because your movement could be completely separate from where you are aiming if you are skilled enough with the movement stick.
In reality though, the same precision that makes the mouse good for aiming also makes it good for hitting strafe angles, and the tiny analog stick on my xbox controller is far less precise. Maybe it could compare if it was way longer. Here is some strafe jumping in Quake Live using only the movement stick on my xbox controller.

Anyway, back to regular strafing. Have you learned it yet?

Now this looks pretty good but there's something missing, my starts are kind of slow.
What is missing is the circle jump.

Circle jump
You can actually go over 320 ups without leaving the ground. If you add enough acceleration in other vectors than your velocity vector you will beat the ground friction. The amount of turning control on the ground is much higher than your air control though so your velocity vector will keep changing position much faster if you turn around on the ground. To accelerate your ground speed past 320 ups you will therefore have to do a very quick turn and keep turning.
The interesting thing with this is that you accelerate much faster on ground than in the air, the highest possible speed you can accelerate up to on ground is much lower though.
This is why people use something called a circle jump to start their strafe jumping.
Now you can do a circle jump using any directional buttons just like when strafe jumping but the most useful one is using W+D or W+A because then you will be turned the right way when it's time to do the regular W+A or W+D strafe jumping.
This is how you do a circle jump. You start by running forward. Ideally you will first just move forward until you hit 320 ups because going in a straight line is the fastest way of going from 0-320. When hitting 320 you press a strafe button while still holding in forward and quickly turn the mouse to accelerate, then you jump and because the acceleration in air is much slower than on the ground your mouse turn should slow down as soon as you jump. The max ground speed when turning in Quake 3 is 410 ups. A good circle jump will land you on 500+ ups.
This takes some practice to get it right.
A good way to practice is by just trying to land circle jumps of 500+ ups or by trying to clear gaps in Quake 3 or Quake Live that can't be jumped over normally. For example:
T7
Aerowalk
T4
Then you need to incorporate your circle jumps into your strafe jumping.
You always start strafe jumping by doing a circle jump since ground acceleration is faster than air acceleration. After a while it will feel natural. It's good to practice both from the right and from the left although just being able to do them on one side is good enough and won't hinder you much in gameplay.
Circle jumps are not only good for starting a strafe jump faster or clearing gaps, they are good any time you need to accelerate quickly in one direction.
(infected footage)
(ffa footage)

Practical strafe jumping
We've already established that circle jumps should be done at the beginning of a strafe and that the normal way of strafe jumping with W+A alternated with W+D is probably also the most effective way.
This is also how 99% of players strafe jump exclusively. Maybe even more than that.
But in my opinion there are two other ways of strafe jumping that are practical and complement the regular strafe jump.
The first one is the most important one to learn and it's called half-beat strafing or half-beating. It is something I believe every Quake player should learn. It is that useful.

If I strafe jump using only A and D the acceleration zones will shrink towards 90 degrees away from my A and D directions and that brings the right zone from A and the left zone from D to each side of the direction of my movement. These zones should be very useful since they are so close to where I'm going, if I strafe using them I can still look very much forward. The problem is that the mouse movement needed is more difficult than regular strafing so in itself it isn't effective, I might as well use regular strafe jumping.
What is effective however is combining it with regular strafe jumping.
If I instead of alternating between W+A and W+D alternate between W+A and D or W+D and A the acceleration zones will end up very close to each other. At 700 ups I barely have to move the mouse to strafe jump.
This is half-beating. It is very useful to have in your skillset because sometimes you want to keep looking in one direction while still accelerating and half-beating allows that. If I only used normal strafe jumping I would have to switch sides after a while to not get a too big turn and run into a wall. With half beating I can look in one direction and still go in a straight line.
This is useful in many different occasions like when you expect or suspect an enemy to be at a certain position and want to keep looking in that direction to maybe be able to do a flick rail if you spot him. In game modes where you have to move fast, like CTF, half-beating helps your gameplay a lot.
If you can do the regular strafe jumping well, learn the half-beat. It is very easy as you can see and it's very useful.

The second alternative method of strafing is not as important and can't be used in as many situations but I believe it can be useful.
It is the first method of strafing that I showed you, strafing with only W.
This is useful for the same reasons as half-beating, when you want to look in a certain direction while strafing. With W you can keep accelerating while looking even more to the right or to the left because of where the acceleration zone is placed. This even allows you to circle strafe an opponent, keeping your crosshair on him or near him while accelerating around him in a circle.

If you combine these three you can move in more patterns than if you only use regular strafe jumping. Your movement will be more free from your aiming.

Strafing in different games

Now the strafe jumping I have talked about only applies to a 100% to Quake 3 but parts of it applies to other games as well.
In Quake Champions all heroes except

And that's basically it for this long ass video.
Now this video was purely focused on strafe jumping so it isn't really a good movement guide to Quake. There are lots of other movement skills that can be learned like, wall clipping, ledge grabbing, telejumping, delayed strafe jumping, double jumping and when adding weapons to the mix: rocket jumping, grenade jumping, plasma jumping and plasma climbing. But that is for another video.

Take care, hope you learned something.

mapamapa