Battle Authority
In an online world the server resolves the turn and the client draws it.
That sentence is easy to write and hard to mean. Most "authoritative" battle systems are authoritative about the outcome and vague about everything on the way there — and the way there is what the player actually watches. If the server decides the damage but the client decides whether the hit was super effective, then two players watching the same battle can see different fights.
So the server does not send a result. It sends what happened, fact by fact, and the client's job is to animate exactly that.

Nothing in that screenshot is drawn from a local decision. The wild Caterpie was
chosen by the server, its level came with it, and the four actions on the right are
the only ones the client is allowed to offer — each one becomes a request, not an
outcome. The badge at the bottom (32ms · Server: US-East) and the channel strip at
the top are the same session: this is one connection, not a battle bolted onto a
lobby.