FPL captaincy when you are chasing someone
The captain doubles one player's score. Against a named rival, that is the cheapest way to create or remove variance.
It costs nothing, which is what makes it the best lever
A transfer costs money or a hit. A chip is once a season. Captaincy is free and available every single week, and it is the decision with the largest spread of outcomes.
If your rival captains the same player
Nothing happens. Whatever he scores, you both get double. The gap between you is unchanged, which is fine if you are ahead and useless if you are behind.
The rule
Behind: captain someone they do not. The bigger the gap and the fewer the gameweeks, the more aggressive that choice should be.
Ahead: captain what they captain. Matching removes their chance to gain, which is the entire job when you are defending.
Level: take the highest expected points, because there is nothing to engineer.
State the downside before you commit
The right way to think about a differential captain is not 'how many points could this win me' but 'how many does it cost if he blanks and their pick hauls'. If you cannot say that number out loud, you are gambling rather than deciding.
Overtake states it for you: the probability before, the probability after, and the cost if it goes wrong.
See it for your own league
Paste your league ID. No signup, no FPL password.