Let's Use Math to Predict the End-of-Season Table

After today's loss, Fulham sit at a uneasy 32 points in the Football League Championship. The team hasn’t been exactly exciting to watch (Jokanovic felt like he owed an apology to the fans) and as a result the team is only 6 points off the relegation zone. Seems like we have a pretty good chance to get relegated right? Wrong. According to statistics, Fulham will be sitting comfortable come the end of the season. Granted, the math says that the team will still be in 19^th place, but point-wise far from relegation. But where does that math come from? I’m glad you asked.

The short version is that I used Fulham’s total points after each game to create time-series data that allows for a simple linear model to be established. From that model we can look at expected total points before each future game, and more importantly, develop an expected amount of total points at the end of the season and a confidence interval for that expected amount.

But now you’re probably saying, ‘But Bryan, I love over-complicating a beautifully simple game and turning it into a problem out of a math book. Please tell me more.’ Well, do I have some data for you.

In order to predict where Fulham are going to be at the end of the season, we need to look at not only Fulham’s total points over the past 31 games, but also the total points of the other teams as well. Using the linear model described above, here is what Fulham’s season is shaping up to be:

Each game number is on the x-axis, and the total points is on the y-axis. The red line is Fulham’s true points up until the most recent game, and the blue line is the expected number of total points from the start until the end of the season. We are really interested in that number and the green line, which is the 90% confidence interval for the remaining 15 games of the season. For my fellow data geeks, here is the graph in number form:

I couldn’t squeeze the labels into the screenshot, so here they are: The 1^st column is game number, 2^nd is actual total points, 3^rd is expected points, 4^th is standard error, and 5^th and 6^th columns give you the 90% confidence interval. Now take this and run the same regression for the other bottom 9 teams in the Championship and your league tables end up looking like this:

The most comforting thing about this for Fulham supporters is the 49.12 expected end of season points. Which itself isn’t a pretty number, but given that is 7 points above Bristol City and 9 points above MK Dons brings a mild amount of good feels. Bristol’s 90% upper bound doesn’t even break into Fulham’s 90% lower bound. Also, most of the confidence intervals are fairly large and do a fair amount of overlapping, so there will most likely be more movement up and down than what the table shows.

So this is all great, but what does this mean in the real world and for the next 15 games?  Can we really rely on this data to accurately predict the end-of-season table?  The honest answer is not really… kind of… ish. This model only uses one variable to predict the outcome for each team and let us not forget, Football is a human game, which means that teams make mistakes, fall in and out of form, get injured, etc. Really crazy things happen. Cough *LEICESTER CITY* cough-cough. We may look back on this article at the conclusion of the season and laugh, but that doesn’t mean that this table isn’t a good place to start. Let’s do our best to enjoy the final 15 games of the Championship, because things are about to get weird.

Acknowledgement: Thank you to Dr. Erica Johnson (Gonzaga University) for her help and feedback.