Patterns of Assistance: Not All Penalties Are Equal

On Thursday 28^th March the following podcast was recorded on the A Celtic State of Mind platform. You can view it here or listen wherever you consume your pods.

For the fourth piece as a follow-up, I consider what the timing is around when penalties are awarded, and how impactful they are.

I have established whether awards were correct or not and shown how penalty awards relate to a team’s ability to get into the opposition box.

Impact of Penalties

As regards the penalties awarded, I would expect the impact in terms of expected points (xPts) given the time of the penalty and the score at that time to be broadly similar between Celtic and Rangers given their dominance over the rest of the league.

I analysed the 275 penalties awarded in the 2020-21 to 2023-24 season to date. Note that Hamilton Academical and Dundee are excluded from the summaries due to only being in the league for a single full season. All teams who have been in the league for three of the four seasons under review are included in the results.

Based on the time the penalty was awarded and the score at the time, The Rangers had the highest positive expected points (xPts) from penalty awards with 18.57 from their 39 penalties. Celtic were next on 13.56.

The Rangers also had the least expected impact from penalties conceded with 3.27 expected points being estimated to be lost. St Johnstone were second with 7.61 and Celtic 4^th with 8.38.

In terms of the overall differentials in expected points between those awarded and conceded:

The Rangers benefit from over 15 xPts from penalty awards overall. This is 2.95 times higher than that of second-placed Celtic despite the Hoops winning two of the three titles in the seasons completed.

Indeed, the Z-Score of -2.61 indicates that The Rangers' score is outside the 95^th percentile and is statistically significant, the only score in this analysis to be so.

The penalties Rangers get in their favour are significantly more impactful (beneficial) than those awarded to the rest of the league.

Timing of Penalty Awards

I would expect that in terms of when penalties are awarded, there would be little difference between Celtic and The Rangers as regards the average minute of the game of each award for and against.

Here is a comparison of the average time in the match Celtic and The Rangers are awarded and concede penalties:

On average. Celtic get awarded a penalty in the 59^th minute yet The Rangers’ average is the 48^th minute – 11 minutes earlier. The league average is the 53^rd minute.

On average Celtics opponents get awarded a penalty in the 45^th minute but The Rangers don’t get penalised until the 67^th minute – 22 minutes later.

An earlier penalty award means the potential benefit of a 0.77 expected goals (xG) shot arrives sooner. Football is a low-scoring sport and neither Celtic nor The Rangers lose many games from winning positions. In the period under review, Celtic have drawn 10 matches from winning positions and lost just two (out of 136 matches). The Rangers have drawn 10 also and lost just one (out of 134 matches). Therefore, the earlier the goal for, the better.

The differential between when teams are awarded and concede a penalty on average is:

The Rangers, on average, receive a penalty 25 minutes earlier than they concede. Whereas Celtic, equally dominant in the league, receive a penalty 10 minutes later than they concede one, on average.

The Z-Score for Rangers is -2.31 so beyond two standard deviations from the mean and highly statistically significant. It is the only  teams' score to be so.

Plotting the average time of penalties received and conceded:

Rangers are the clear outlier, with Celtic having the least favourable profile. Given the extent both sides dominate the rest of the league, the disparity appears even more significant.

One significant pattern may be coincidence and two may be bad luck, but three?

We are starting to see clear evidence forming of a pattern of assistance for one club. But heh, the “Penalty to Rangers!” meme must be indulged.

Next up: do red card trends buck the pattern?

Note: data correct up to 3^rd January 2024.