The reason that the cast equipment and runes were chosen were for the ap. Using boomerang can do damage if used right. This build is not for straight in your face damage. Its for hit and run attacks.
The chalice controls the mana at the beginning of the game and end game you have enough mana where you dont really need to worry. If you still worry there is always the golem buff to get.

Sivir has a natural 25% dodge during runs at 18. So when the ninja tabi increases it for another 12% and the dodge runes it gives her the ability to get away and throw the boomerang without much fear of being annihilated when doing it. Wouldn't you rather be able to do a hit and run and sustain little to no damage end game against Champions like Yi or Jax?

I have already tried many other builds. They all have there benefits and weaknesses. This is the one where I found that I can get over 18 kills with 3 deaths. There are also an extreme amount of assists. Also on the items, I have tried many different items and I have found that these work the best. You get the decent amount of mana you need and an appropriate amount of ap to do the needed damage.

Thank you for your thoughts on the subject though. Criticism can always be helpful.

It looks like you just thought of some caster equipment/runes, thought that sivir could use some additional dodge, and called this a build. Sivir is that mana inefficient, especially when your build focuses on her boomerang. There are for better purchases that she can get that would be much more effective(no clue why you'd honestly get ninja's tabi, you're a support, learn your play style). I suggest you try out someone else's Sivir build before you try to make your own. I can guarantee there are at least 10 exactly like yours.