And I disagree with you! Or at least am talking about something significantly different. Your scenario ignores the many variables that affect a football match - the keeper having a mare/stormer, City being crap/stunning that day, injuries ...
I was talking about Pawson's set of matches not being big enough to extrapolate from, or not without introducing a significant chance of error. Extrapolating up from a set of 5 is far worse than extrapolating up from a set of 15 - any variation is exaggerated when using a set of 5.
The thing is that set can be skewed hugely by including one match in that period, the cup semifinal, either as a draw or a loss. Win %age goes from 80% to 66% in one match. That's just bad statistic interpretation, which is why I wouldn't use them as an argument scaled up a lot. (e.g. from Aug 2016 to date, our PL record is 4-0-1 with Pawson. Nothing wrong with that recent record. 29-30 wins in a season will do nicely yet he's a bad ref for City?)
If I had to pick one thing about Pawson, it's that I think he's a bit green still at the top level. Last year was only his 3rd regular top level season (20+ matches in the PL) and he's given a semifinal. In his 4th, he's got a final. Both seem very fast to me. Strangely, Sunday appears to be his first league cup match this season.
Mason? I just think he's a crap ref. For everyone.
And I ignored Taylor. He's so ludicrous that there is no point.
Again, to draw a line in the sand at 5 and say ‘you can’t extrapolate from that’ is just wrong. Sure, the smaller the database the greater the margin of error if you extrapolate from that alone. And I agree that the smaller the data pool, the greater the chance that conclusions drawn from statistics alone are inherently more risky. But it is one thing to proceed with caution from a limited evidential basis, quite another to disregard that body of evidence altogether, especially when basic empirical evidence is aligned with more subjective analysis.
You are right that there are many factors that might explain the outcome of a game. The performance of the referee is one of the important variables, but no amount of statistical analysis can result in an accurate prediction of when a full back is going to ping in a world from thirty yards for the one time in his career. But what statistics can tell you is that, even allowing for a small datapool, and acknowledging that there may be an entirely innocent explanation, nonetheless there are anomalies that are worth investigating. Sometimes that investigation will reveal nothing untoward, sometimes not.
So with Pawson, you start out with a limited datapool, which suggests we are significantly disadvantaged by having him as the referee especially in tight games. Is that just ‘one of those things’ or is it suspicious? Thats exactly the problem - so that’s when you start to look at individual instances with some care and in some detail rather than relying solely on raw data analysis. And you look at decisions like the yellow cards he showed Kane and Alli when it was still 1-0 and you think ‘how was that not a red?’ And you look at his performance (which for some reason you seem to ignore) in the FA cup semi final, and the way Arsenal were allowed to kick Silva off the park, and the emerging patterns seem to get a bit more solid.
There are other issues that might be illuminating if they were to be investigated- eg the number of cards he issues against City players compared with the opposition, the ratio of fouls committed to cards given, the number of penalties awarded/not awarded and so on. With Mason in 2012 there were a lot of worrying trends before the Wolves game - one I remember was that we were ten times more likely to concede a penalty with him in charge than any other referee.
Going back to Pawson, I’d agree that drawing firm conclusions from a limited datapool about the number of games won/lost and nothing more is unsafe. But it begs a number of questions. When you look at his failure to show red cards on two separate occasions against a top 6 rival when the score was 1-0 that begs yet further questions. When you add his inept display in the semi final last year the questions mount up.
Pawson stinks. The only question is ‘what of’.
