On the 1st of December, 2020, the numbers 5, 6, 7, 8, 9 and 10 were drawn out in the South African National Lottery. There were 20 winners sharing the jackpot. In fifty years of lotteries across multiple countries, a consecutive set of numbers like this had never been drawn and the chances of its happening were 42,375,200 to 1. It was a such a statistical anomaly that it drew an incredible amount of news in South Africa, and a state investigation was immediately called.
Of course, to assess if something really is a statistical anomaly, you need context. Whilst 5, 6, 7, 8, 9 & 10 seems an incredible run of results for a lottery ball machine to draw, the odds of this happening are identical to the odds of any sequence of numbers. The odds of any sequence of numbers being drawn (including consecutive numbers) in any lottery draw are the same and whilst the odds of five to 10 being drawn were over 42 million to one, so were the odds of any random set of numbers. But of course, something that’s peculiar and doesn’t feel and look right should draw attention and should merit further inquiry. It should not be dismissed as crazy conspiracy theories, particularly when there may be grounds for such concern.
South Africa is a country which has unfortunately had its fair share of large scale corruptions right up to Presidential level, therefore something that felt peculiar merited investigation – the reader will know where I’m leading with this.
The recent VAR non-penalties against Rangers have encouraged people to look to the record books and investigate how many and how few penalties Rangers get. To the Celtic fan, there is a gut feel that Rangers benefit and the statistics seem to bear this out.
There is a huge statistical anomaly in Scottish football where the differential in penalties (i.e. the difference between penalties conceded and penalties received) is plus 33 for Rangers over the past 5 seasons. You would expect it to be positive for successful teams, but it is only +8 for Celtic over the same five season window. Of course, there may be nothing in the statistical anomaly of the range of penalties, but to dismiss the Celtic fans as tinfoil hat conspiracy theorists ignores the last 30 years’ experience of Celtic fans, where the SFA colluded to prevent a star Portuguese international striker signing for us at a key point in the season, when referees went on strike because Celtic discovered that one had lied in relation to the decision against the club, or the fact that our (at the time) biggest rivals used taxpayers’ money to fund a team and yet miraculously Scottish Football found they had received no competitive advantage in spending money they didn’t have to get better players. Even in the last week, we have seen that a sheriff, a leading lawmaker in the country) allegedly forged documents to try and have the law act in favour of his club. Like in South Africa, where experience has demonstrated that it is right to investigate statistical anomalies, in Scotland experience of the last 30 years at least, have shown that it is right to question the statistical anomaly around refereeing decisions.
So what of the South African lottery investigation? Well, it showed that whilst drawing the numbers 5 to 10 felt peculiar, there was nothing suspicious in it, and it was the random luck of 42 million to one. They did, however, find that there was considerable corruption within the South African Lottery setup in terms of grants, funding and other things and so, whilst the number distribution was not a setup, it generated investigation which found corruption. Whether you find that 42m-1 was just a chance happening, or greater corruption, looking into statistical anomalies is always the right thing.