I archived this. Trinfinity Sivir is the build I support now. This build isn't horrible, but I think Trinfinity is a bit better in almost every aspect.

I know Manamune is nigh-ubiquitous on Sivir builds, but I wanted to try something else.

A while back, I was looking at forums, and everyone hated Tiamat. It may have been buffed since then - it's 50 damage, and I saw the figure 42 somewhere once.

In any case, I think it's a good early item, if you plan around it. Here's what I've been thinking:
1) While it's true that Sivir farms well enough without it, Tiamat elevates her farming from overpowered to *absurd*. In any case, the attack damage is enough to jump start your Ricochet farming.
2) It does an adequate job of health/mana regen. I put Clarity in my build to pick up some slack, but it's not really necessary. Teleport is better for quick returns to your lane after shopping trips.
3) If you get it early, it's more damage than Manamune early on ( Manamune is stronger later).
4) Perhaps the most minor point: you get a little bit of splash damage for the rest of the game. You'll like this later when 500 things are on the screen all the time. True, Ricochet alone is more than good enough, but Jesus, do minions poof into piles of gold now!
5) It's cheap. You get some early attack damage, and somewhat adequate health/mana recovery, all for 2070. As long as you don't get anything redundant and pointless when it comes to recovery, it should be an acceptable way of getting regen out of the way early.

If you want Boomerang Blade to do the work for you, though, this build has worked for me on that front.

I've tried roughly the same build on Caitlyn. It's adequate. Haven't tried Ashe yet, but same deal. Either of these two would benefit more from Tiamat, since their farm skills cost more.

EDIT: Ashe, now that I've played her, apparently doesn't need mana regen, so I wouldn't recommend giving her Tiamat. I think Caitlyn's ultimate can Tiamat-splash, so that could be amusing.

Your unique passive only works if you're moving. You don't want to take chances with melee characters anyway. Look for just the right time to stand in place and plink away; hopefully, you have allies with some CC.

In this section, convert all percentages to decimals, e.g., 42% means .42.

Several things *multiply* by each other, contributing to your "right click" DPS. They are:

1) Attack damage
2) [1 + (Chance to crit)*(crit damage multiplier - 1)]
3) Attack speed; proportional to (1 + attack speed bonus).
4) Damage reduction multiplier (armor, special skills, whatever). 30% reduction would make this a .7.

All of these should be increased together to get more damage per second on average.

Caution: You won't do too well with this unless you can actually get a few hits in at a time. Also, only (1) and (4) apply for Boomerang Blade, so you won't be as strong at long distance as you would be if you'd just piled on the Bloodthirsters.

There's a little randomness with the crit chance, but the average over a game's worth of attacks will turn out more or less like the above, with crits happening some times more than others.

: Already discussed.
I like to get this early. It's really good for the cost, and I always want more movement speed. It affects (2) and (3). Note that the chance to crit will help out your...
(1) and (2) get a huge boost. This leaves (4)...
If they have much armor, you need this sooner rather than later. (1) gets a bump here, too.
It helps everything. Mana, health, damage, movement, crit rate. The Phage bonus keeps things from running away from you or toward you, whichever is worse.
Everything else is pretty good now, so let's put some more damage in there. (1) is slightly more important overall because of Boomerang Blade. Postponed to the end because Tiamat does a decent job of keeping you healthy.

Boots: Tough choice. Mercury's Treads can save you, so can the Ninja Tabi. Ionian Greaves of Lucidity can help (your ult is fabulous). Berserker's Greaves aren't too bad either, but you can afford to skip them if you use your ult at just the right times.

Note that damage gets boosted a fair amount early in this build, so you can still count on the Boomerang Blade for most of the game. It might fall a bit later on in effectiveness.

Like having another Spell Shield. 2v1 is way too dangerous without one. Health and mana are useful, too. Can replace Last Whisper or Bloodthirster, depending on what the enemy is up to armor-wise. Mercury's Treads would be redundant if you get Banshee's Veil, but Ninja Tabi wouldn't be.

If for some reason you fall way behind early, you still have a great support ultimate, and Boomerang Blade/ Ricochet are still good for harassing and clearcutting. If you're just having such a bad game that you won't be able to scratch anything for the rest of the game, then get this and just try not to die too much. Also, Soul Shroud is a nice support item, too, and you'll get you use your ultimate more often.

Fortify for the early farming boost. Clarity also helps you farm. Between items and your ultimate, you shouldn't need Ghost, but it's one of my favorites in any case. Teleport is always an option. Exhaust is nice for DPS builds, and you could pair that with Ignite. Heal is a nice throwaway. I don't know, I waffle on this a lot.

Updated because people seem to like this build

For the moment, I'm leaving it as Exhaust and Teleport. Teleport lets you go back for health/mana and return quickly, and has other uses on top of that.

Redid these.

No more CDR because it's not super-important in auto-attack builds.

Went 21/9/0 for the evasion bonuses, and added some evasion runes.

MRes/level runes to balance defenses out

ASpd runes to make up for the build being light on ASpd (the ult picks up a lot of slack here and you can somewhat get away with that, though)

Up to you. Hard to say. Early levels of BB might help you dominate more early, but you'll get less bang out of it later. Still, anything that gets you early money is a nice long-term point investment.

Ricochet level 1 or 2 is nice, but there are diminishing returns.

Spell shield lets you get a Boomerang Blade throw in with impunity.

You should always put a point in your ultimate whenever possible with every character. (Maybe there are exceptions, but they're exotic and I haven't heard of them.)

Pros:
single-target DPS
Early-to-mid-game Boomerang Blade damage
Move speed
Support abilities
Mad farming skillz
Great turret-hugger harassment skill (especially early-mid game)
Loves 2v1 ganking

Cons:
Squishy
Boomerang Blade gets weak later
Ricochet doesn't hurt champions as much
Not good when outnumbered ( Banshee's Veil can help, though)
Relies on allies for CC (and she needs it from them badly to function)