On The Rebound.

Expected goals are designed to look at the process of scoring, rather than the singular outcome on the day.

I've previously written about how few big chances aren't equivalent to the same expected goals spread over more shots. The later trades the possibility of scoring a larger number of goals for the greater likelihood that you will score at least once.

Another acknowledged problem when using cumulative expected goals to represent a side's achievements is the treatment of quickfire attempts from rebounding shots.

Often the chances are created well inside the box, sometimes leading to cumulative expected goals totals that exceed 1 for a connected opportunity that could at best only result in a single score.

Choosing cutoff points is always subjective, after all every action in a real match is connected to some degree from the first kick to the last, but in the table below I've charted the percentage of shots for each team in last year's La Liga that came within 10 seconds of their previous attempt.

Over 90% of attempts were made at least 30 seconds after the preceding effort, so the majority of attempts are preceded by a lengthy phase of general play.

The average in 2015/16 for La Liga as a whole was 6%, but Eibar, Espanyol and Real Betis heeded the call to "follow up" with greater regularity.

The problem of over estimating a side's attacking potential by inflating rebounds can be reduced by simulating chances, but limiting such sequences to a maximum of just one actual goal scored.

For example, two sequential chances, in quick succession each having a singular probability of being scored of 0.5 doesn't guarantee a goal, on average, as their cumulative total may suggest. Instead you score with three quarters of such related opportunities.

Real Betis hone their blocking skills against a top Premier League team.

We can demonstrate the difference between the two sets of circumstances by accounting for and then ignoring the connected events in a match simulation.

In 2015/16 Eibar drew a late season fixture with Betis, 1-1.

Visitors, Betis had six shots, one of which was the game's biggest chance, from which they scored, nicely illustrating the value of creating the odd gilt edged opportunity.

Eibar had 21 attempts, 16 of which had a goal probability of less than 10%.

Five Eibar attempts came within 10 seconds of an initial attempt. Four combined low value attempts with more valuable ones, but the final salvo united two attempts that were individually marginally odds on to be scored.

Cumulatively, Eibar's expected goals almost reached three compared to just over one for Real Betis.

Although score effects also played a part, the hosts would appear to have been unlucky to not gain three points.

Simulations based on attempts conform this impression.

A straight simulation of all 27 attempts in the game give Eibar more goals in 83% of the iterations, scoring and conceding an average number of goals per game that equals the cumulative expected goals tallies of each attack.

However, once you treat rebounds as connected events, Eibar's share of victories falls to 77% and the average goals scored does likewise from their average cumulative expected goals of 2.9 to just 2.6.

Expected goals do provide insight into a side's ability or achievement in a single match, but occasionally they over or under rate the teams at the extremes.