That is a good question.
Affirmations or self-affirmations work provided you do not consider them magic pills. The sub-conscious cannot make the difference between what is real and what is not, it is the reason why hypnosis works, or self-affirmations for that matter.
It is why a hypnotist will tell someone while they are "under" that they are being burned with a cigarette, and everyone can see he is touching the subject's skin with his finger, yet the skin reacts as if it had actually been burned. That is how powerful the sub subconscious is.
So the first major ingredient to self-affirmations that work is understanding how the sub conscious operates.
The second major ingredient for self-affirmations to work is belief. If a subject does not actually believe the self-affirmation, the sub conscious will react accordingly: with non belief.
The third major ingredient for self-affirmations to work is specificity. If a self-affirmation is too general, it has no effect. A good example of that is in your question. "I am the best at everything I do" is too vague.
What does it mean to be "the best"? There is no reference to anything here, so it cannot work.
A self-affirmation like: "I am the best knife thrower in the world" is also not specific enough.
On the other hand, if you state: "When I throw a knife, it always reaches the mark I choose exactly the way I intend it" has more chance of working. Provided you make your intent clear before you throw the knife and you allow yourself a decent amount of practice, the self-affirmation will work in your favor. After a while, you will not miss your mark very often.
I also presume from your question that this has a relation to self confidence building. In this case, self-affirmations can be great helpers. In order for your self confidence building self-affirmations to actually work, they will need to make an ally of the sub conscious, they will need to be very specific, and you will have to believe the self-affirmations are absolutely true.
An example of this could be someone who sees his self confidence go down the drain because he stutters. The cause of his stuttering is an event from the past when a parent shouted at him for something he had not done. After having recognized this, the parent acknowledges this mistake and forgiveness is reached.
His affirmations could be something like this: "I do not stutter", "I have no reason to stutter anymore", "My the cause of my stuttering is gone, therefore I don't stutter", "When someone shouts at me, It does not cause me to stutter".
In conclusion, yes, self-affirmations do work, if done right. Good luck with your self-affirmations.