In this article, we will attempt to understand what expected goals are, use xGs to predict football matches and, finally, analyse the model created by the duo Mark Dixon and Stuart Coles from the University of Lancaster in the North West of England.

Sports betting, at least for those aspiring to treat it as more than a recreational hobby, has long been familiar with the concept of expectation, and specifically the idea of expected value.

Bets win and lose, but much of what happens is just a consequence of luck.

Over the longer term, however, knowing one’s expected value allows a bettor to estimate what they can expect to win over a larger sample of bets. ‘Expected’ is just another word for ‘arithmetic mean’ or ‘average’.

More recently, the concept of expectation has found its way into soccer via the notion of expected goals, or xG. Expected goals is used as a performance metric to evaluate soccer team and player performance by assigning a probability to a scoring opportunity that may result in a goal.

This is calculated by using historical data for equivalent opportunities and the goal conversion rate. Thus, the xG for one scoring opportunity will lie between 1 and 0.

Furthermore, summing the xG in a game with a number of goal scoring opportunities will give the xG for the game itself, or more commonly, the xG for each team in a game.

In theory, xG provides a truer representation of the quality of play of teams in a game, and the superiority of one team over another, than the actual goals do.

Goals are scored with a fair degree of luck (what statisticians call ‘noise’), and using an actual scoreline to predict what a team might do in their next game might be less reliable than using their xG.

In a sense, goals are like wins and losses in betting, whilst expected goals are like expected value. If this is the case, can we use xG instead of goals to predict the outcome of soccer matches for a betting profit?

Goals versus xG

The mathematician and author of Soccermatics: Mathematical Adventures in the Beautiful Game David Sumpter has provided some guidance on the relative usefulness of goals versus xG when attempting to forecast the outcome of future games. Sumpter illustrates the difficulty of finding a forecasting signal from goals data succinctly.

“From a statistical point of view the result of a soccer match is almost as much noise as it is signal. A mathematical explanation of this can be found directly from the Poisson distribution. Goals in soccer are Poisson distributed and teams score about 1.4 goals on average. The variance and the mean are equal in the Poisson distribution. So, the standard deviation is the square root of 1.4, which is 1.18. Thus, the noise (1.18) is only slightly smaller than the signal (1.4).”

xG, by contrast, is a measure of chances created, and thus offers a better measure of the quality of a team during a single match than goals.

It typically contains less noise and more signal. For both goals and xG, the amount of noise in match results decreases as the number of games being studied is increased. However, the rate of decrease is initially steeper for xG than it is for goals.

Sumpter uses this information to recommend what sort of data we should focus on when attempting to make forecasts of future games. For one or two matches, it’s the match report itself that provides the most useful information.

On the other hand, for samples of over 15 games, or the better part of half a season, goals data will potentially be as reliable as xG.

The noise will still be a little bigger, but the difference is small. Furthermore, goals represent reality – what happened – whereas xG is a probabilistic model of scoring chances. If it’s inaccurate, it may indeed prove less reliable than the goals data.

In between these extremes lies an exciting area from the perspective of utilising xG as a forecasting tool. Sumpter argues that the xG report will be most useful between three and six games, whilst seven to 15 games might be better served by a comparison between goals and xG.

For this article, I built an xG prediction model that used the most recent six games played by a team to assess whether it could be used to deliver a betting profit.

Dixon-Coles Model

The most well documented approach to forecasting soccer matches was published by Mark Dixon and Stuart Coles (of Lancaster University) in the Journal of Applied Statistics in 1997.

Unsurprisingly known as the Dixon-Coles model, it develops the concept of attack and defence strength, by comparing individual teams’ goal scoring and conceding to the league averages over a specified number of previous games.

These are then used to estimate the expected number of goals each team will score in their next game.

Finally, the Poisson distribution is used to calculate the probabilities of individual goal tallies, where the expected number of goals is the distribution’s mean. Pinnacle has a previous article describing the methodology.

Here, I have adapted the model to use xG instead of goals, calculating the attack and defence strengths using the six most recent home or away games. My data set included games played in the English, French, German, Italian, and Spanish Premier divisions during the 2015/16 to 2019/20 seasons.

Forecast probabilities for home, draw, and away result outcomes were converted to implied fair betting odds, and then compared to Pinnacle’s closing prices.

Where the latter were longer, this represented the prediction model’s theoretical value. Value bets were then compared against results.

The chart below shows the profit time series from the 7,795 value bet opportunities identified by the model, from a possible total of 18,006. The flat stakes profit over turnover was -5.0%. This compares to a loss of -4.3%, had every 18,006 result been bet blindly to a single unit stake. Given that the average expected value for this sample was 38.9%, to say this is an underachievement would be a huge understatement.

Potential Model Invalidity

Perhaps the first clue in the failure of this model lies in the figure of the average expected value itself.

With average odds of 4.69, a figure of nearly 40% for the average expected value from bets that make up over a third of all possible opportunities would strongly suggest a huge variance in the implied fair betting odds when compared to Pinnacle’s actual prices.

A correlation plot between the model’s forecast xG values and the actual xG values recorded for the forecast game confirms the point.

There is a lot of noise; the modelled xG does not do a particularly great job at accurately predicting a team’s actual match xG.

The source of the model’s failure may be harder to unpick, as there are potentially at least four problems with it. Firstly, using a Dixon-Coles model to forecast soccer scores may be inherently flawed. The Poisson distribution at the heart of it assumes that the scoring of goals is independent; that is to say, one goal does not cause another to be scored.

However, this ignores the influence of player and team psychology. Teams which fall behind may become more motivated than they previously were to redress the balance, whilst teams that draw level might be more motivated to push on.

What is good ROI in sports betting ?

If that is the case, the idea that goals just go in at random must surely be questioned.

Dixon and Coles themselves reported that their original forecast model under-reported low score results (0-0, 1-0, 0-1 and 1-1). To confirm this finding, I have separately reordered both my model-predicted xG, and actual game xG data from lowest to highest, and plotted them as an artificial correlation below (solid line).

It is clear that there are fewer actual low-xG scores than my model is predicting, whilst there are more high-xG scores than there should be (the dashed line).

What Dixon and Coles found for goals also seems to apply for xG, a finding not wholly unsurprising given that match goals and match xG do correlate well over large data samples.

A second possible source of error will be the xG model itself. For my data sample, the total xG was 97.8% of the actual goals scored in the games. Whilst that seems like a good match, it is hard to know whether this difference might be enough to affect the validity of an xG prediction model.

What can bettors learn from preseason matches ?

A third source of error may be in my choice of the number of recent games used to calculate the Dixon-Coles attack and defence strengths.

For the reasons I set out earlier in the article, I chose six games. Perhaps a different figure, higher or lower, would have worked better.

Such a change would be relatively easy to implement, although it would need a complete re-run of the model and that is not something I will do here.

Furthermore, all six games have received equal weighting. Dixon and Coles recognised that more recent games should perhaps receive more weight when calculating average strengths, and introduced such weighting in later versions of their model.

Again, it’s a feature I could model myself, but given the time-consuming nature of the process, I have opted not to.

There is one final, and possibly more existential problem with my model in attempting to make a profit from forecasting soccer matches.

All the other possible sources of error aside, even a good xG model, one far better than mine obviously is, may not be able to deliver a non-random profit because it is not as good as the model the bookmaker is using to compile their odds.

Given that Dixon-Coles is a well-documented model, and xG now a widely used metric, it’s possible that all the information such a forecasting approach brings is already incorporated into the bookmakers’ odds.

A Relative-Skills Contest

Sports betting is much like the competitive sports on which it is based. It involves a relative skills contest between two or more sides, competing to see who is best at predicting the future.

The better the forecaster, the more reliable and valid their assessment of true outcome probabilities (and hence betting odds) will be. Mistakes are punished with financial penalties.

Pinnacle, arguably the best data analysis bookmaker in the business, will have exceptionally reliable prediction models, far better than mine. We know that Pinnacle has customers who can make non-random profits, but I’ve discussed previously how rare these may be.

If Pinnacle represent the Aston Villa of prediction models, these sharp customers are more like Liverpool and Manchester City.

Sure, you might have a good model, maybe a Reading or a Derby, good enough to make decent predictions, but not consistently good enough to beat the best models. My model here probably wouldn’t even qualify for the Isthmian League.

With regard to whether xG can be effectively utilised to make money from a soccer betting market, the issue is this. The odds a prediction model provides are a reflection of the quality of the information that goes into it.

xG might indeed offer a useful data resource to build a prediction model, but if Pinnacle are already incorporating that information within their own model, as well as other useful information I don’t possess, my prediction model is not going outperform theirs.

Any information that my xG data brings to the table is already incorporated into their odds. It’s Canvey Island F.C. versus Aston Villa.

If Pinnacle (and indeed other bookmakers) are already utilising xG within their prediction and odds-setting models, which is likely given the length of time the data has now been widely available, it’s questionable whether my use of such data will improve on what they are already doing.

So can xG data allow me to find a profit from soccer betting? As with every other form of data analysis for betting purposes, the answer will depend on how you use it. And how you use it will have to be better than the way the bookmakers currently do.