Soccer Analytics: Home and Away “Luck”

Will this improbable shot succeed?

As I mentioned in my first post, the game of soccer, due to it’s many degrees of freedom in play, is very non-deterministic. What does this phrase mean? There’s a philosophical meaning for the word “deterministic” which essentially says that all events, including human action, are ultimately determined by causes understood to be external to the will. There’s also an engineering meaning to the word where a deterministic system is repeatable with very high precision because it is a function of the inputs and the initial conditions. For instance, anti-lock brake systems are designed to be deterministic. We don’t want any surprises there!

The opposite of deterministic systems would be a “stochastic” system which has one or more aspects that could be considered randomly sampled and thus can be analyzed statistically but not precisely predicted. So a “non-deterministic” game like soccer can also said to be “stochastic”, because there are many variables in the game which all have their own probability distributions. Whew! All of this so I can talk about luck!


Wikipedia’s definition of luck is a pretty good one, “Luck is the phenomenon and belief that defines the experience of improbable events, especially improbably positive or negative ones.” Over the last two block articles about soccer analytics, I’ve described how sometimes unpredictable events result in scoring goals or failing to score goals. These events could be anything from officiating decisions, a player being surprisingly out of position right when the opponents pass comes to him, a gust of wind that causes a ball to just barely tick up off the crossbar, etc. Since goals in soccer are a much more rare event than points (runs, 3 point shots, field goals, touchdowns, hockey goals) scored in other popular sports, when they are impacted by improbable “luck” it is much more noticeable. If a touchdown is scored after a missed pass interference call and the scoring team goes up 35-14, that is just 7 out of 35 points. If a soccer official calls a questionable foul in the box and the offended team scores their penalty kick (70% chance of scoring), that might win the game 1-0. The luck of having the official see the play as a foul essentially won the game for one team and lost it for another.

Measuring Luck in Soccer

Note that it is impossible to measure the factors that caused the official above to call the contact in the box as a foul (perhaps he ate to many burritos before the game? Maybe his attention was distracted by a low-flying seagull? Perhaps he just hates the color green?). What we hope to do is find a proxy for the measurement of luck that “mostly” captures events when teams are expected to score a certain number of goals but either fail to achieve that number or exceed that number. So in this case, actual goals scored minus the number of expected goals could be seen as outperformance of the expectations for whatever reason. I’ll just call that overperformance “luck”. I also see the opposite where an opponent’s expected goals minus the number of actual goals scored could be viewed as your team’s defensive luck. Averaging the offensive luck and defensive luck will constitute overall luck.

Charts (of course)

In the charts below, I’m measuring the overall luck for teams when they are playing at home vs. when they are playing away. This luck is averaged across all games in the season. I’ve overlaid these two new lines (the yellow and the green) on top of the blue annual salary bars and the orange “no penalty expected Goals” ratio. These home and away luck lines augment the orange xG ratio by bringing in the disparity between xG and actual goals (which, as I’m suggesting, can be seen as luck)

MLS 2022 Season xG, Salary, Home Luck, Away Luck
English Premier League 2022 Season xG, Salary, Home Luck, Away Luck


So what new information does the two luck features add to these charts? We have already noticed that:

  1. The Premier League clearly has a different financial structure than MLS (more on this in a later article)
  2. Therefore, a team’s annual salary is more indicative of success in the Premier League than in the MLS.
  3. xG ratio is predictive of success in both leagues, but more so in the Premier League
  4. Total points during the season is also highly correlated with overall success.

Now we look at the two luck lines to see what they add. What do we see?

  1. Having either Home Luck or Away Luck being smaller than zero is bad for the team’s performance. This is pretty obvious when you think about it, because it shows that the team is failing to convert on opportunities that are expected, whether on offense or defense or both. Why are they failing? Probably for unmeasurable reasons (the team is not getting along, the refs hate the coach, no fans are showing up at home, the team is practicing too hard and is tired during the game, etc.). The teams above the half-way point in the standings all have either a Home or an Away luck average higher than zero. The very top teams tend to have both Home and Away Luck averages above zero.
  2. It seems that a big divergence in Home and Away Luck, especially when one is in negative territory, indicates poorer performance. Note the last 6 teams in the Premier League chart. They all have a fairly large gap. The very worst teams see this gap at Home, and the next worst teams (Southampton and Everton) see the worst luck Away. But all have a pretty large gap between the home and the away. We see similar things in the MLS, where the very worst team by points (DC United) has the worst Home Luck in the league. Orlando City has the next worst Home Luck, but they make up for it through having one of the very highest Away Luck numbers (might be interesting to look into this club).
  3. What do you see? Weigh in on this in the comments? I answer them all to the very best of my ability.

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