Random Team Picker
Picking teams by hand always looks rigged — the same strong players end up together and someone feels slighted. Spin instead. Paste the player names, turn on elimination mode, and alternate the winners between Team A and Team B as they come off the wheel: first draw goes to A, second to B, third to A, and so on. Nobody picked the teams, so nobody can complain about them.
For balanced teams: if you know the skill levels, seed the wheel with weights won't balance skill — instead, do a "snake draft": draw the full order with elimination mode, then assign 1st, 4th, 5th… to Team A and 2nd, 3rd, 6th… to Team B. It takes thirty seconds and the draft order itself was random, which is the fairest procedure short of a coin flip per pick. For odd player counts, the last name drawn sits out first and rotates in — the wheel decides that too.