The intelligent use of numbers: What is a goal worth?

The use of data in analysing football allows us to take a more nuanced view of both the events that occur during a match and also to evaluate a side’s ongoing performance to make predictions about their future results.

The two disciplines are closely related.

To make informed opinion about where a team is heading requires the collection of numbers-based descriptive information from their previous matches.

These matches will inevitably contain large amounts of randomness and statistical noise that is unlikely to persist into the future.

If used in an unadulterated form, this can lead to the over fitting of non-sustainable events in the past and a flawed projection of a side’s likely underlying quality.

Going beyond scorelines or results

Football analytics often concentrates on the predictive side of the coin, dismissing the purely descriptive aspect of the discipline as being merely worthy of providing the building blocks for a predictive model.

However, intelligent use of numbers that go beyond mere scorelines or results can add much to a match report and help to illuminate the contribution made in games by players, even if they are unlikely to continue to reproduce such achievements in the future.

Single matches often turn on the actions of less-well-known participants, whose skills have benefitted from the randomness inherent in any natural event to elevate their reputation amongst their fans.

Being in the right place at the right time to score a crucial FA Cup final goal in 1976 certainly cemented the name of the late Bobby Stokes into Southampton’s history and the likes of Roger Osbourne, Lee Martin, Alan Sunderland, Paul Rideout and Ben Watson are more universally remembered because of one decisive goal in May rather than a career of more modest achievement.

History tends to be written in absolutes, but we can capture much more flavour of these ultimately decisive goals from the past by including such variables as the quality of each team on the day, the score previous to the goal and the time remaining in the contest.

Not all goals are equal

Rideout’s score in 1995 against a superior Manchester United left his Everton side with over an hour to defend their one goal advantage, whereas Wigan’s Ben Watson broke the 2013 deadlock as late as the second minute of added time.

Any goal is welcome, particularly an opening goal such as those, but Rideout’s still left much for his team mates overcome, whereas Watson’s virtually guaranteed a Wigan FA Cup Final victory against an also superior, but numerically depleted Manchester City.

The value of Rideout’s 30th minute goal is better measured in terms of how much his individual contribution improved his side’s chances of winning the match and we can use a variety of tools to achieve this.

Many will be familiar with pre-game home win, away win and draw odds for matches.

As a recent example, Arsenal entertained West Ham on Sunday in the first game since Arsene Wenger’s departure become common knowledge.

Here’s the implied probabilities of an Arsenal win, West Ham win or a draw at the beginning of the game from the Infogol app.

It’s a trivial task to work out the expected number of league points Arsenal would win on average from such a contest, using the probabilities of the two outcomes that would secure points for the Gunners.

Taking Infogol’s numbers, there is a 0.71 probability that they will win all three points and a 0.17 probability that they will have to settle for just a single point.

Arsenal’s expected points at kick off is therefore (0.71* 3) + (0.17 * 1) = 2.3 league points.

The initial probabilities for each team are dependent upon the average number of goals we expected Arsenal to score against West Ham at the Emirates Stadium and how many West Ham might score in return.

The probabilities are calculated from a Poisson calculation, which we’ll describe in more detail in future posts.

Those figures were respectively 2.5 and 1.0.

However, once the game begins, another variable becomes a factor. Namely the time remaining.

The initial figures relate to a 90 minute game, plus stoppage time and they will decay as time elapses.

This decline in goal expectation is not constant.

The rate of scoring gradually increases as a game progresses, as teams becomes more adventurous, legs become tired and fresh ones are introduced from the subs bench.

The rate of scoring gradually increases as a game progresses

Around 45% of goals are scored in the first half and the remaining 55% come after the break and we can use these actual figures to model the change in a side’s initial goal expectation at any point in the match.

To take the simplest case, at half time at the Emirates, Arsenal’s 2.5 expected goals would have fallen to 55% of that initial figure or 1.38 compared to 0.55 for West Ham.

The match probabilities would now be 0.57 for the Arsenal win, 0.29 for the draw and 0.14 for a West Ham victory, and the respective expected points would have fallen from 2.3 to 2 for Arsenal and risen from 0.53 to 0.71 for the Hammers.

So immediately we can quantify the cost to Arsenal in terms of expected league points of their failure to break the deadlock, and the expected benefit to the visitors of remaining on level terms against superior opponents.

Time only gradually alters the expectation of each team, but goals cause the largest changes to a side’s prospects, and Arsenal finally opened the scoring in the 51st minute through Nacho Monreal.

Monreal’s goal increases Arsenal’s probability of winning from 0.56 to 0.85. The draw becomes a 0.12 probability, because West Ham now need to “win” the remainder of the game by exactly one goal to achieve this particular final outcome.

And an Arsenal loss or a West Ham win can only happen if the visitors outscore the hosts by two or more goals in the final 39 minutes plus stoppage time.

Goals are the ultimate cause for celebration at football matches

The chances of this happening can also be calculated using a Poisson approach, using the remaining goal expectations for each team. This amounted to just a 3% likelihood of West Ham turning the match completely around after the 51st minute.

More personally to Monreal, his goal improved Arsenal’s expected points from 1.98 to 2.67, a net gain for Arsenal of 0.69 expected points.

So we can easily put a value on Monreal’s goal, although importantly this does not imply that he can be relied upon to always provide such a valuable contribution when the Gunners require a breakthrough.

It is merely descriptive of a Sunday afternoon in late April.

Ultimately, Arsenal won the match 4-1, with Alexandre Lacazette completing the scoring in the 89th minute.

Lacazette’s goal barely moved Arsenal’s expected points. They were projected to win an average of 2.992 points at 3-1 in the 89th minute and this increased by just 0.007 of an expected point at 4-1.

Goals are the ultimate cause for celebration at football matches, but breakthrough goals such as Monreal’s and Ben Watson’s count for more in the context of a single game. They can, if you wish, be quantified and are probably worth celebrating slightly more enthusiastically because of it.


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