The review of the big calls affecting the top two in the SPFL by the Yorkshire Whistler throws up a 20 percent error rate currently.
I then model the impact of that based on the expected points outcomes.
Current Models
As regards goals from open play given, not given, the model used is taken from an American website American Soccer Analysis and therefore is modelled on Major League Soccer matches. I point this out for transparency but the point remains that so long as the SAME model is used to evaluate both clubs’ impacts’ it is not particularly important what the model is as regards source league.
It hopefully goes without saying that these are MODELS and therefore we are not aiming to achieve PRECISION but a fair comparison through reasonable accuracy.
Essentially the time of the goal and the game state is accounted for equally for both teams in all cases.
For the impact of sendings off, the public data is sparse, and I used an article from no less than the Royal Statistical Society. This provided a broad-brush impact of expected points for home and away teams. It did not account for the time of card or game state.
It was applied equally to both clubs, but the problem is that such events are rare and therefore the impact of e.g. “scoring” an impact for a sending off in the 1st minute versus the 90th minute could have a disproportionate impact on the overall picture.
New Model for Red Card Impact
To resolve this, I looked at sendings off across the SPFL from 2020-21 to the current day.
To date, there have been 126 orderings off in that time.
I looked at when the card was awarded and the score before and after, and accounted for whether the team affected was home or away.
Long story short, it didn’t much matter whether you lost a player between the 1st and the 55th minute, on average sides impacted lost an average of 0.51 points whether home or away.
That impact regressed the nearer to 90 minutes given there is less time to play shorthanded.
The pattern of impacts looks quite pleasing:

This would result in the impact for the refereeing analysis looking like (based on the time of the red card):
1st half 0-55 -0.51 2nd half 56-65 -0.41 66-75 -0.31 76-85 -0.21 86-90 -0.11
Impact of Red Cards
In the two and three-quarters seasons of Yorkshire Whistler reviews, there have been only 13 red cards in matches involving the top two.
By applying the above new model, the impacts of wrong calls per season and up to 21st February 2024 is:

Over the nearly three seasons, The Rangers have an estimated 4.47 more points due to the impact of wrong calls and Celtic has an estimated 6.4 fewer points.
The new red card banding will be applied from now on.
The latest report is here.