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This is even Better! An even bigger can of worms! (And before anyone says, it wasn't me that emailed Him!)
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Subject: RE: Bayes theorem _ applied to refereeing decisions
J***,
Thank you for your very interesting e mail applying Bayes theorem to refereeing outcomes.
I have to confess to not knowing too much about it but I have had your claims investigated by Dr Bill Gerrard, a Statistics expert from Leeds University. He heads a company, Strategic Sports Management that specialise in looking at statistics in sport and he has been doing some work on consistency in awarding penalties in the Super League and its effects on the competition. I also asked him if a random selection of referees each week (referees drawn weekly to referee the games) would benefit the competition.
His response is “pasted” below:
“I think the key finding is that overall the competition is not affected by the inevitable differences between individual referees because any such differences are balanced by your allocation of referees particularly ensuring that the three referees with the highest propensity to award penalties do not in total officiate at more than half the games of any team.
As regards the suggestion of allocating the referees randomly, personally I would argue against this unless you are successful in ensuring rough equality between individual referees in their propensity to award of penalties. Your ability to allocate referees allows you to offset differences between individual referees and as my report shows you've done this very effectively. Random allocation is just that, random, and will inevitably lead to some teams, for example, being refereed more frequently by the referees with a higher propensity to award penalties. The choice as I see it is between every team having the same likelihood of being allocated any referee (and, by implication, expecting to concede the same number of penalties over the season) i.e. random allocation which equalises likelihoods against the alternative of a managed allocation by you which seeks to equalise outcomes i.e. the actual numbers of penalties awarded against teams. It seems to me that fans are more interested in outcomes than pre-match likelihoods.
The last point leads on to the email that you forwarded regarding Wigan, Leeds and Phil Bentham . No need to be put off by J*** W***** invoking Bayes Theorem (which relates to the calculation of conditional probabilities) since the point she makes doesn't need to be dressed up with any sophisticated statistical jargon. [u
The probability that an individual referee would officiate at four games of a winning team and these would be their only defeats is highly unlikely on the basis of purely random variation. We are talking a probability of around 1 in a 1000 for teams with a win percentage over 75%. Highly unlikely but not impossible. My approach in such circumstances is to say that the balance of probabilities raise a "cause for concern" requiring further investigation. The [/uevidence I have available is the award of penalties and this indicates that at least in the Super League games Bentham has awarded slightly fewer penalties against Wigan (6.000 per game) than he has averaged against all teams (6.767) so absolutely no evidence of any inconsistency in this respect.
The converse point that Bentham has favoured Leeds is somewhat self-contradictory since just as it is highly unlikely that you will officiate at a sequence of defeats of a winning team then it is highly likely you will officiate at a sequence of wins for such teams. There is a probability of around 2 in 5 of officiating at a sequence of four wins and a probability of 4 in 5 of officiating at either three or four wins out of four games for teams with win percentages over 75%. Bentham has officiated at three Leeds home games in Super League 2010 with two wins and a draw - not unusual for one of the strongest teams in Super League in recent years. As with Wigan, Leeds have tended to be penalised slightly less frequently (5.667 per game) by Bentham than his overall average (6.767) but well within the expected range due to random variation. So again no evidence at all of any inconsistency.”
Investigation of referee performance takes place every week in the form of a thorough review and individual decisions are scrutinised. Where a statistical bias shows up we will then compare the data with the actual penalties awarded or not awarded. Very often player error is responsible for the awarding of the penalties. I would also question your inclusion of the pre season friendly between Leigh and Wigan as the Wigan team was a joint Under 20 and Academy team with only Liam Farrell and Shaun Ainscough having any first team experience.
I hope this answers some of your concerns but please feel free to get in touch again should you wish to.
Regards,
Stuart
Stuart Cummings
Match Officials Director
Match Officials Department
RFL
Room 113, First Floor, Cavendish Hall, Headingley Campus, Leeds Metropolitan University, Leeds. LS6 3QS
Phone - 0113 274 6505
stuart.cummings@rfl.uk.com
www.therfl.co.uk
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Again, just to confirm, Nowt to do with me!
