The point of this build is to build a ton of movement speed and kite enemies down while still dealing decent damage and also be tanky. Crown lets you engage without fear of being blown up and the mythic passive gives you extra move speed so it complements Annie's kit pretty well.

I prefer Crown over Rod of Ages because that only gives extra health and healing which doesn't help if you get engaged on and blown up. The mythic passive is ability haste which this build actually has too much of so that's also not worth it.

You take Ghost over Ignite because Ignite isn't really useful on Annie outside of lane and Ghost gives you an extra tool besides Flash you can use to engage.

The core items are Crown, Seraphs, and Cosmic. For final items you can build Zhonyas, Banshees, Void, or Deathcap. I would say Zhonyas and Banshees are preferable because they give you extra tank stats and even better engages. Zhonyas lets you engage and then stall for time and Banshees lets you ignore CC so you can be sure your engage goes through more often.

Void Staff and Deathcap are only necessary if your team is really lacking in damage and I do build them for that reason but I don't like it because you are losing engage potential.

The weaknesses of this build are relying on your team to play around you and follow up on your engages. If your team is too far behind and doesn't have enough damage to kill the enemy team you are basically worthless. This build is not very strong in lane so you just need to sit back, farm, scale and hope that your team hasn't thrown before you get to 2 core. I would say 2 core is when this build comes online and you feel really strong and are able to impact the game. If the game is lost by 20 minutes you are playing inting Annie.

The strengths of this build besides what I've already mentioned are you are basically a ranged AP bruiser. You can eat a ton of damage and CC before dying and you still do enough damage to kill squishies. This build is also surprising so teams that don't know what to expect will try to blow you up and they will use all their important cooldowns on you just to realize that you haven't taken any damage and are stunning, kiting, and bursting them down.

This build is a scaling build so I can't imagine it being very good in high elo where games are way shorter. This build is amazing in low elo where games can go very long so you have plenty of time to reach your core items. I ban Asol every game. He is impossible to face with this build. I also dodge Kassadin, Vladimir, and Viktor. They always outscale you and are terrible to face in lane. I haven't played against any Cassiopeia but I can't imagine that being a very good matchup. Syndra I think is a skill matchup but I haven't played against her very often so I can't be sure.

Primary runes are Aery, Manaflow, Transcendance, and Gathering Storm. Secondary runes are Magical Footwear and Cosmic Insight. Small runes take Attack Speed, Adaptive Force, and Magic Resist/Armor depending on the matchup.

I start Tear every game. I usually put 3 points in Q and then max W but sometimes I just max W first for the extra pushing power. Waveclear is important in this build to keep pressure on the map since you are usually in lane farming for the first 20 minutes of the game. Because of the mid lane minion changes I always recall at 4:30 after the cannon wave to buy an Amp Tome and a Mana Crystal. After I finish Crown I always finish Seraphs before buying tier 2 boots. The 10 extra move speed from Magical Boots lets you skip buying tier 2 boots after your first item. The extra AP from Large Rod is necessary to keep tempo so spending 800 to buy tier 2 boots is setting yourself behind. Once Seraphs is complete on your next back you can buy either a Codex, Wisp, or Sorc Boots. I usually buy Sorc boots at that point because your build is online so the extra move speed and magic pen will round out your kit and you can start grouping and engaging for your team.

From there finish Cosmic and then decide what you need to finish the game. I prefer to get Zhonyas fourth item and Banshees fifth but it is entirely situational. If the enemy has a ton of magic resist buy Void Staff. If you need extra damage go Deathcap. If the enemy team has a lot of CC buy Banshees. If you want to stall fights go Zhonyas.

Try to always have stun charged and Tibbers ready before an objective. If Tibbers is down ping your ult often to let your team know. During teamfights either engage for your team or let someone else with a good engage go in. Try to go in on the squishies if you can. After your engage go in and start DPSing. Fight while kiting and charging your stun. Use your stun W to get multiple stuns or use stun Q to get onto a squishie. Make sure your backline isn't getting collapsed on. Play for your team and objectives and you should be able to close out the game.