@p target selector would select the closest player.
So when you run it through an execute command for example:
/execute @a ~ ~ ~ scoreboard player option @p <score> *= @p <score>'
You'd expect everyone to be mutiplying a score for itself.
But what turns out to happen is that if another player stands over the middle of your hitbox and on the negative coordinate side, it will actually target them instead of yourself.
I believe it should make more sense if a player would always, no matter what, see himself as the closest player if preforming an execute command or a command by hand using @p.