How much does it hurt a football (soccer) team to play a man down? What about two men down?

How does that cost shift depending upon whether the team is up or down at the time of the penalty - does playing down a man more heavily impact defense or offense?

Related: Are there ever any scenarios when playing down a man can actually improve a team's odds of winning? (Doubtful, I know, but I've heard of crazier paradoxes.)

Is there research out there on short-handed odds?

(Short-footed is probably the more appropriate term.)