An expected goals model frames quite well what everyone knows to be true: that not all goals are created equal. Goals are created from tap-ins and bicycle kicks and all the shots in between, and expected goals allow analysts and fans to quantify the likelihood a shot will go in the net, and therefore the value of a shot. The next logical step in the discussion of goals is to analyze their value. Goals aren't created equal but neither are goals equal. The goal that makes a two goal lead a three goal league does not nearly have the value as that stoppage time goal that captures all three points.

To measure the value of a goal I looked at game states in MLS from 2011 to 2015 and built a series of functions that estimate the expected points for home and away teams given the score of the game and the minute being played. Each of the functions fit tightly with the actual data and had an R squared greater than 85%. The expected points functions look like this for games with a difference of two or less goals.

Pretty graphs after the jump