Piece Ratings

So this is more a thought exercise than anything practical, but I'm curious to know how much people think a piece is worth in terms of rating. Imagine, for example, that black starts the game without its queen, or if you'd like a game example, that something like this happens:

I know this isn't really feasible, but my question for everyone is, what rating difference does there need to be for black to consistently win this game? How does it change if it's a knight that's thrown away, or a bishop, rook, etc. Curious to hear what people think.

PS- I know in the example game, there might be positional considerations too, but my question is just about pieces, so if you'd rather imagine that one side just begins the game missing a queen that might be more appropriate.

Maybe I'm wrong, but I think I could stand a chance against top GMs being a queen up right from the beginning.