The most represented explanation is: "The arrow does not fall off that easily from the shelf". This seems to be obvious (and may be true) but it is not the intrinsic reason for the tilting. Another presumtion is, that the tilting moves the upper limb out of the line of sight, so that the target can be seen. Olympic archers do not tilt the bow at all - and believe me - they see there target too.
Most intuitive archers experiment with their shooting position and end up with a little tilt, because it feels comfortable and makes them shoot better results. The reason for it lies in the way that our eyes and our brain work, to make stereopsis and the perception of distances possible. For stereopsis you need both of your eyes open and focused on an object. When you point with your finger at something, it works best, when the finger is positioned in the line in the middle between bot eyes.
Make a test:
- Point with your finger at some object
- You will find, that your finger is just naturally positioned exactly in the middle between your both eyes.
- Now move your finger to the left (or right) and keep it pointed to the object
- With a rising distance of your finger to the middle line, your uncertainty rises too. At some point you can't be sure, that you are still pointing exactly to the object.
When you hold your bow perpendicular - the way that olympic archers shoot - one of your eyes (hopefully your dominant one) is right behind your string. You look at the tip of the arrow, to bring it in a defined position to the target. You have to know the distance to the target before you shoot! Your second eye is absolutely useless. The distance calculation can not be made by the brain, because the informations that are delivered from your eyes are almost useless. The situation gets even worse if you have a cross dominance. That means, that your dominant hand is on the other side then your dominant eye.
The right eye is in the same line with the arrow and can not give any information to the brain that is useful to calculate distances. The left eye has a big distance (A) to the arrow (blue dot). But its information is not being used to make the shot. Some olympic archers even wear a eyepatch to eliminate any information from that eye.
As you may comprehend, such kind of shooting has a lot of disadvantages and it is one reason why archers decide to shoot intuitive/instinctively. So let's tilt the bow.
Shoting intuitively/instinctively is the perfect way for archers that had problems with cross dominance in the past. Because both eyes have a equitable role in the shooting. No eyepatches, closing one of the eyes or changing the bow arm is needed.
That's it. Stay curious.