Question: In terms of win probability for one game, how much of a bearing does one superstar hitter have on his team?
Well, a lot of this has to do with who this superstar hitter is being replaced with. Any easy and somewhat crude method to figuring this out is to find the difference in true talent in terms of WAR/150 of the superstar player and his replacement. You want to make sure you get as accurately as possible an estimate on the true talent WAR/150 of these two players. It will be somewhat subjective, but not too difficult.
Let's take someone like Carlos Gonzalez and for arguments sake, let's call him a 5.0 WAR/150 player. Let's pretend the Rockies are going to sit Gonzalez and in his place start Ryan Spilborghs and let's call Spilborghs a 1.5 WAR/150 player. Keep in mind we are not doing any adjustments for the handedness of the pitcher being faced in this example, and in the next iteration you would definitely need to make this additional adjustment.
So we have a 5.0 minus 1.5 equals 3.5 WAR/150 difference. Since we are attempting to determine how this changes the Rockies win probability for one single game, we need to change units from per 150 games to a single game. We need to then divide 3.5 by 150 which gets us 0.02333 which is how much win probability the Rockies would lose by starting Spilborghs over Carlos Gonzalez, with the one above mentioned caveat. Let's say the Rockies were originally favored to win this game with a win probability of 60.00%. You could now safely adjust this number down to 57.67%. As far as what this would look like on a Vegas money line the adjustment would go from -150 favorites to -136.
This is a quick, dirty and easy method to use when you need to make a quick calculation on how much the win probability should change when a hitter is removed/added to the lineup. The same thing can be done when multiple players are involved, you will just need to add up all the WAR/150 of all the players taken out of the game and offset it against all the WAR/150 of all the players used to replace them.
