It is still within the random chance range but it is an outlier that raises suspicion and doesn't inspire confidence that something fishy is happening.
So, I went and did some maths as well, what I found was, amongst the teams he's reffed the most, what's REALLY interesting is the distribution, because it's SO WEIRD that he doesn't really seem to give Liverpool or City red cards. oh no I've made a table:
It's the distribution of 7 in 54, 0 in 50 and 1 in 56 that has me reaching for my tinfoil hat. It pushes the SSZS beyond what ranomness would explain. Despite the pretty normal numbers for the other teams he's officiated regularly.
If you add in other teams he officiates regularly, the probability of observing something like this falls comfortably within an expected range of randomness. Despite notable deviations for three teams, it's not unusual enough to render the overall distribution statistically significant.
The sum of squared deviations from expected values falls well within the threshold for random variation. This means that while the numbers for Arsenal, Liverpool, and City might seem unusual in isolation, when you factor in all the teams, the overall pattern doesn't indicate anything out of the ordinary. It's just statistical noise.
Yeah, I come to roughly the same unsatisfying conclusion. It looks suspicious but is just on the line of this can still happen randomly and our pattern seeking minds might be making too much of it.
I used the teams overall rate for all games, for games without Oliver, and Oliver’s red card rate. All are pretty close regardless but trying to estimate that is the key assumption and is hard to do.
I love this approach. Curious what patterns emerge if we broaden the sample to current and upcoming opponents of Man City that Oliver has officiated where cards distorted match outcomes. I hope the club is also putting some data science resource to scrutinise Oliver’s highly unusual refereeing behaviour.
Do you have the data for readiness to red card a team's opponent? Thinking of the Kovacic non-card. Do he have form for penalising City's opponents but letting our opponents get away with fewer cards than normal?
I don’t. It would be a lot of manual work to try and do that. It would actually be a great use of AI/Machine learning to estimate the call from previous calls but that’s beyond me
What if you layered on a Bayesian-type analysis that captures the "unusualness" of the decisions? We've got 4 calls (Martinelli's 2 yellows, trosssard's delay of game, this call, the kovacic non call) that come to mind that seem...unusual or atypical. What's the probability that all of those are just random noise given the expected likelihood of such calls?
So, I went and did some maths as well, what I found was, amongst the teams he's reffed the most, what's REALLY interesting is the distribution, because it's SO WEIRD that he doesn't really seem to give Liverpool or City red cards. oh no I've made a table:
https://docs.google.com/spreadsheets/d/e/2PACX-1vSel8zFa1OPYTNqxodZbpxfAdkFupIwfgl4fPlwHgn5h6YDiNP7LadzHbi_AbRq0GJpuR9U_CUnXCRK/pubhtml
It's the distribution of 7 in 54, 0 in 50 and 1 in 56 that has me reaching for my tinfoil hat. It pushes the SSZS beyond what ranomness would explain. Despite the pretty normal numbers for the other teams he's officiated regularly.
I've changed my mind.
If you add in other teams he officiates regularly, the probability of observing something like this falls comfortably within an expected range of randomness. Despite notable deviations for three teams, it's not unusual enough to render the overall distribution statistically significant.
The sum of squared deviations from expected values falls well within the threshold for random variation. This means that while the numbers for Arsenal, Liverpool, and City might seem unusual in isolation, when you factor in all the teams, the overall pattern doesn't indicate anything out of the ordinary. It's just statistical noise.
Which is boring, obviously.
Yeah, I come to roughly the same unsatisfying conclusion. It looks suspicious but is just on the line of this can still happen randomly and our pattern seeking minds might be making too much of it.
What assumption are you making about the true underling distribution of red cards? That impacts the expected standard deviation, no?
I used the teams overall rate for all games, for games without Oliver, and Oliver’s red card rate. All are pretty close regardless but trying to estimate that is the key assumption and is hard to do.
I love this approach. Curious what patterns emerge if we broaden the sample to current and upcoming opponents of Man City that Oliver has officiated where cards distorted match outcomes. I hope the club is also putting some data science resource to scrutinise Oliver’s highly unusual refereeing behaviour.
Now what about him giving City 0…
Yeah that seems unlikely. I might pull that at some point too
Where did you get the data from for the last Arsenal and Manchester City data with red cards for matches and without Michael Oliver?
Do you have the data for readiness to red card a team's opponent? Thinking of the Kovacic non-card. Do he have form for penalising City's opponents but letting our opponents get away with fewer cards than normal?
I don’t. It would be a lot of manual work to try and do that. It would actually be a great use of AI/Machine learning to estimate the call from previous calls but that’s beyond me
What if you layered on a Bayesian-type analysis that captures the "unusualness" of the decisions? We've got 4 calls (Martinelli's 2 yellows, trosssard's delay of game, this call, the kovacic non call) that come to mind that seem...unusual or atypical. What's the probability that all of those are just random noise given the expected likelihood of such calls?
I thought he had given us 8 red cards?
It does look like 8 from 55. Damn out of date data.
The data I saw on referees seems to include this match and the red card and totaled to 7