Earlier in this blog I wrote a post on Win Probability in every possible game situation. I posted the excel files but they aren't as informative as a graph. I made up graphs for home and away and +2, +1, 0, -1, and -2 goal differentials for every minute. I didn't make up graphs for GD's bigger than that because there is basically no point. The fact that a team has a .999% win probability when they are up 4-0 isn't that exciting.
Each graph has the line of best fit and a scatter plot of the data. The equations for those lines are also on the graph along with the r^2 value for correlation. The graphs are below to look at. Some interesting things I noticed:
-Most graphs show a very strong relationship between minute and win probability. The only ones that don't really are when teams are away and are tied, when teams are home and up by 2, and when teams are away and down by 2. Not really sure why these three stick out.
-Some of the graphs have linear relationships, while others are quadratic. Again, not really sure why this is. Why is the win probability when you are at home and tied follow a quadratic curve while the win probability of a team at home and down by 1 is linear? Maybe people have ideas as to why this happens.
-For some of the scenarios (the +2 and -2 GD's for home and away) I didn't start the graph at minute 1 because the data points were a little all over the place. This happens because there are so few data points so the win probabilities are screwed. Example: There aren't many times when a team has a 2-0 lead in the 5th minute.
-I added the graphs of all the goal differentials together for comparison, one for home and one for away. They're interesting to look at.
-Finally, because of this we now have some basic equations to model a team's chance of winning a game. Feel free to use them and check them out.