On Thursday 28th 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.
This is the second in a series of articles putting on record the details behind the data.
Next up, The Yorkshire Whistler and the power of expert and independent review – aka we don’t mark our own homework.
The “Yorkshire Whistler”
I engaged a referee from the area I live in South Yorkshire. He is an active, professional Football Association qualified referee. He has limited knowledge or interest in Scottish football and is a Sheffield Wednesday season ticket holder.
Based on the big calls for that week’s game as established by red card calls, contentious goal awards, goals disallowed, and penalties awarded and denied, he reviews video evidence as provided by the BBC or SPFL and provides a detailed explanation of whether he thinks the decision arrived at is correct or not.
Matches considered involve Celtic and The Rangers. In the dates under review from 2020-21 onwards, the 3rd placed team in the SPFL Premiership has been 14, 28, 35, and currently 15 points behind the 2nd placed side.
What constitutes a big call is to some extent subjective based on the issues the media highlights (Sky Sports, BBC Scotland for example) but also the decision-based talking points gaining traction on social media amongst fans of either Celtic or The Rangers. Any penalty or red card awarded is automatically reviewed.
If the decision is deemed correct there is no impact on the match outcome. If a decision is deemed incorrect then an expected points impact is calculated.
Penalty Expected Points
Expected points (xPts) are calculated where penalties are awarded.
The expected points model is based on analysis done by the American Soccer Analysis site.
Based on game state (time in match and score at that time), it calculates how many “points” a goal is worth in getting a team towards three points (awarded for a win in league football).
A goal scored in the 90th minute when the score in 0-0 is worth 1.7 expected points to the home team. Whereas a goal to make the score 5-0 in the 90th minute is not worth any expected points.
For penalties, the expected points are multiplied by 0.77 which is the historical probability of scoring a penalty (note Opta calculates this as 0.79).
Therefore, a penalty awarded in the 90th minute when the score is 0-0 would generate an expected points value of 1.7 x 0.77 = 1.31.
Red Card Expected Points
The impact of a red card in football is less than that of a penalty.
I analysed 172 red cards awarded in the SPFL Premiership between 2020-21 and the current season.
The impact in terms of average points dropped compared to the game state (score and match time) at the time of the red card being awarded conformed simplistically to the following model:

A red card awarded any time up to the 55th minute resulted in an average of 0.51 points being dropped. Thereafter the impact lessens as the match moves towards the 90th minute.
This model does not consider which side was home or away nor the specific match score at the time of the red card. Nor is there a Celtic/The Rangers adjustment to acknowledge their relative dominance over the rest of the league. This will serve to understate the overall impact for the purposes of this study.
Independent Expert Assessment of Big Calls
The Yorkshire Whistler has been operational over the periods of The Rangers run without conceding a penalty.
Based on his expert and neutral judgement, Rangers should have conceded six penalties since the start of the 2021-22 season.
They were:

Ironically, the Yorkshire Whistler deemed the penalty Rangers DID get awarded on January 18th, 2022, as being incorrect for a foul by Alfredo Morelos. However, referee Kevin Clancy failed to award a penalty to Aberdeen for a foul by goalkeeper Allan McGregor on Ryan Hedges.
In addition to the six penalties that should have been awarded against Rangers in this period, The Yorkshire Whistler opines that a further five were incorrectly awarded TO Rangers but also four should have been awarded TO Rangers but were not.
Overall, the Yorkshire Whistler has reviewed all the big calls from matches involving Celtic and Rangers over two completed and two-thirds seasons.
Based on the expected points won or lost through either benefitting or being penalised by a wrong call, the overall summary is (correct up to 29th March, 2024):

Overall Celtic have been penalised by an estimated 7.04 expected points over this period whilst Rangers have benefitted from erroneous calls by 3.93 expected points.
That is a swing of 10.96 expected points Celtic have potentially been penalised for relative to their main rivals because of incorrect decisions. The last two league titles have been won by only four and seven points respectively.
Does this indicate a pattern of assistance, or is this just the result of honest mistakes that are due to incompetence and will therefore likely even themselves out over a while?
Next up – how likely are teams to be awarded penalties?