Also, why does he build this way?
He gets 
(sometimes)+ 
Finishes 
Grabs 
+
Next is 
last items are 
+ 
and 
End build: 
Always builds:
Sometimes buys, after archangel: 
or 
or 
but he sells it later for void & proceeds to End build.
I've seen The Shy mentioned a few times on the League subreddit, but I've never watched him or really know anything about him. However, my assumption is that he's either a highly skilled player overall or very experienced with her and a few other champions.
So in that case, it looks like he builds as a full AP Carry here; RoA is a good item (well... certainly was, it gives a little less health now) for jumping into fights, but the other build path, Tear of the Goddess, means a substantially larger mana pool and AP boost, at the expense of RoA's health while also taking a long time to stack and get a return on your invested gold.
(Because the Tear/RoA combo like on the main AP carries of the game such as Karthus doesn't seem to work in the jungle; gold income is just way too low and you're delaying any powerspikes for too long)
I can't really speak for how good his build is; my take is that it's a risky build with not a whole lot of reward going for it. By endgame, it would be very difficult for you to get any picks off of the enemy team in spite of your high damage because of how fragile you are. That said, I imagine it's extremely dangerous and effective in the hands of seasoned players that know how to position and play assassins in the endgame.
For items:
-He probably builds Ranger's as he has no need for Blue Smite and he doesn't build (and I assume play) like a duelist leaving no need for Red Smite. So he just goes with the item that gives you the healthiest clearing ability. -Runeglaive works well enough on its own for a single damage item if he's buying it early enough -Tear is next as you want to start getting it stacked right away; Ionian Boots give him a quick 25% CDR off items, with presumably 5% from Masteries for a total of 30%. -Now, he buys Archangel's Staff because of the powerspike completing it gives; after the AP item changes, it gives more base AP than it originally did. Added to that, AAS builds Mana Charges twice as fast as Tear does. (I... think. I'm assuming that didn't change.) -Rabadon's isn't a rush item on her, and the 5% bonus AP buff it received means a lot more AP in your full build. Zhonya's is just good all-around for people that know how to make the most of it.
I don't know under what circumstances he's building Abyssal Scepter. It's not the absolute best item for her, mainly because it has no interaction with human Q at range. But it does give her MR and the enemy team an MR debuff when she jumps in. Are you sure he's never built RoA with Abyssal?
I personally haven't had the best experience with Luden's Echo after the AP changes, but it's probably still fine on her for waveclear and extra poke damage for sieges.
Building Haunting Guise has been a tactic for a while; for a reasonably cheap price, you get a pretty strong mid-game powerspike on AP champs: Health, AP, and +15 Magic penetration. Shy wouldn't be completing Liandry's as she doesn't benefit from it like other DPS mages. Obviously, he sells it for Void Staff once VS's percent penetration becomes more effective than Haunting's flat pen.
(This wound up being a little more long-winded than I thought... sorry.)
Thanks for thoroughly clearing up my question c:
its good, pretty standard .
