Congratulations Scotland, you have passed Intro to Expected Goals and are now moving onto the advanced class. Most following me know that expected goals are the likelihood that a goal will be scored on a shot. Expected goals is now a term that more and more Scottish football fans are familiar with, understand, and can discuss coherently. Sure, there is the occasional “Yer Da” still yelling about “Goals and Points being the only stat that matters!”, but compared to three years ago, football analytics literacy has grown considerably in Scotland.
However, now that many have the basics down, we need to have a talk about expected goals. On Twitter last week, I noticed there was discussion about the usage of xG and in particular summing xG totals for individual matches and saying things like “(this team) should have scored 2 goals because they had an xG of 2.” Let me first throw myself at the mercy of the metaphorical court, I have created a few different visualizations where a summed xG total for an individual match was present. It is still on the xG maps I publish each week for the SPFL.
I chose to sum xG on the graphics I have posted to try and ease Scottish football fans into xG. With that being said, there are some issues with summing xG for individual matches. Danny Page covers the issues in an article he wrote pretty comprehensively. Danny points out that if you sum the xG, you will miss on on the variance that can occur in a single match. In his article, he says:
Arsenal won 0–3 with a xG scoreline of 0.39–1.49. In these cases, some may say “The right team won” because the xG and real life scorelines match. However, these values are only adding expected goals. But something is missing. Only adding independent probabilities misses half of the story: variance.
A good situation to think of here is a shot with an xG of 0.05. That shot may go in, it has gone in before, but it is not likely. The instances where it does go in is the variance Danny is talking about, but generally it is not a shot that is going to lead to goals often. But let’s say that a team has ten of those 0.05 xG shots, compared to a team that has one 0.50 xG shot. The second team’s shot is much more likely to go in than any of the first team’s shots, but summing the xG in this situation they would both have an xG total of 0.50.
Sometimes those lower xG shots will lead to a win, thus the idea of variance. Typically summing xG over the course of a season variance usually will find the mean. However, anything can happen in one game. Therefore, Danny puts forth that rather than summing xG totals in a single match and making conclusions off that, it would be better to use win percentages based on the xG of each team’s shots and the likelihood of the goal difference for that match based on the xG output, so that is what we are going to do.
To do this, we will take the xG of each shot for a team in a match and run them in a Monte Carlo simulation 1000 times. This is similar to what I do to come up with the numbers for B.U.R.L.E.Y. for the season. With these simulations, we can come up with 1,000 results of matches with the xG results of a particular match and produce how many times each team would typically win and draw, what would be the most common scoreline, and the typical points per game from that xG performance. In addition to seeing the sum of the xG for a match, we will see the team that was most likely to win and what the score would typically be from a match with that xG output.
Using Danny’s xG simulator
and taking all the graphics he came up with as a template, I will now be producing these graphics for every SPFL match. Henceforth, these graphics will accompany the xG maps we have been producing each week and will hopefully give some further insight into expected goals. As this now the “advanced class”, please feel free to let me know if you have questions or comments about this!
This article was written with the aid of StrataData, which is property of Stratagem Technologies. StrataData powers the StrataBet Sports Trading Platform, in addition to StrataBet Premium Recommendations.