Not really. Why is it $1? Suppose you make a contract with one publisher who will pay you $1 per copy sold and also negotiate with a different publisher who will pay you $2 per copy sold. How much are you deprived then, $1.50? $2? You're assuming that every copy the pirate sold could have been sold by your current publisher(s) but wasn't.
Because I stipulated that the contract was exclusive and time-limited. In other words, the assumption that every copy the pirate sold would have been sold by my current publisher is accurate-- hence the simplicity of the hypothetical.