Your power is not considered at all for arena matchmaking. This can create fairness issues due to your initiative being used for arena.

Arena matches are based on rank. For the first 30s, you can only meet someone within 1 rank of you (so 1 rank lower, same rank, or 1 rank higher). At 90s, you can meet someone within 2 ranks of you. 3 rank difference is allowed at 150s, ect ect.

Arena matches have a character level restriction. You cannot meet someone more than 15 levels higher or lower than you in ranked. If you are level 80, you will never meet an opponent of level 96+, or level 64-. At level 90, you can meet anyone from lvl 75 to 100.

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Two players that just faced each other in arena, and neither fought a different person are treated with 2 additional rank differentials (for the specific match only). This means if two players of 1 rank difference just fought, and both immediately que for ranked arena after. They will not be able to meet each other unless both are in the que for over 210s without finding a different opponent. If either of these two players fought someone else, then they can immediately get into a match again.

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For training, its just anyone who is available.