Let me preface this by saying that I love move speed. I played that other game for about 6 years, in which move speed is hands down the best stat. So I have been using Swift Anklet since I got 2985493703 favor with the beta, and I was of the opinion that it was always the best choice for favor items.
Today I join a 5v5 game and my Swift Anklet is gone. I only have 205 favor. Owned. However, I have a few random favor items... including Amulet of Teleportation. So I say "what the hell" and buy it. I start by teleporting up and capping the first flag, and continue teleporting around capping every flag. I was playing hybrid-spec Torch Bearer.
As the game continues, our opponents become very strong. We are able to hold them off but they get tougher every time. I just continue teleporting everywhere and capping all available flags, taking potshots at the enemy towers in each lane. We are playing Zikurat so I focus on the middle 4 flags. After a while, things are starting to look very bad for us. Their Erebus chases me everywhere, and I can't run away from him because I don't have Swift Anklet. Every member of the enemy team outlevels every member of our team by at least 3.
Then I notice that we are about to hit war rank 10 and the enemies are only at war rank 7. All of my frenetic flag-capping made a difference! My teammates buy Giants and I purchase max rank Armory and Blacksmith. The war is on.
This is when things get really intense. We (TB,Rook,QoT) begin a push in the right side of the enemy base, by the gold mine. As they are working their way in toward the portal flag, I am forced to teleport back to base and to the side flags constantly to stop Erebus who is attempting to capture enough flags that his team can get Giants. By teleporting, I am able to assist my team in pushing the enemy base while protecting mine simultaneously. We successfully cap the enemy portal flag.
This leads to about 15 minutes of me chasing Erebus all over the map in a flag control battle. Meanwhile, my teammates are pushing the enemy base, VERY slowly gaining ground. I am able to prevent him from getting 10 war rank, and we eventually win. I have 26 flag caps. Erebus has 27. Our teammates have about 16 each.
By the end of the game, our opponents were almost all level 20. Our highest level player was 17. They had far more gold than us. And they had Erebus. They "should" have won. And they would have won, if I had had my Swift Anklet.
Using Amulet of Teleportation instead allowed me to turn his game (up-close combat) into my game (map control). This turned a losing game into a winning game, by changing the rules of the game itself. Erebus was beginning to seriously threaten our survival while he was allowed to farm and attack us. By forcing him to move to flag control, I neutralized his threat to our offensive push.
I learned a lesson from this: this game is not that other game. People constantly compare the two, but Demigod has many levels of gameplay that have yet to be explored by the community. I think we will find a complex web of strategies, counters, and counter-counters involving the use of many different gameplay aspects, including favor items. There is no one "best" strategy in this game - only by adapting to your opponents and their playstyle can you win.