You cannot possibly quantify something like this as you nave no idea of what could possibly be in the minds of a player X or Y in a given game. And it is subjective to begin with. Let's blow this up to an extreme. What is Wilson's effect on the Caps play? Or what effect on Detroit did the Grind line have? What effect on how the Devils played did the style of Claude Lemieux have?
Haley by himself is not an energizer bunny. But players like him tend to bring the fight to the other team. That in turn, tend to embolden your own team. Or so I believe based on what I watch. Nowhere have said that having him in the lineup is going to get players 5 more goals or 10 more points.
Nor am I going to get into a debate about how to quantify how many games teams will win or loose based upon an intangible asset that cannot be measured. Again, I believe that having players like that can bring a change in attitude to a line up. You can certainly disagree.