The most amazing sporting event of all time?

Today’s news sources are talking about Leicester City’s winning the Premier League as a sort of miracle. The bookies’ initially-offered odds of “5000 to 1” has morphed into a supposedly scientific/mathematical measure of probability — we are being told that Leicester City had “a slim chance of only 1 in 5000” of winning the Premier League. Yet amazingly, they did win it! We are given to believe that “1 in 5000” is a numerical measure of how surprised we should be at the fact that they did in fact win.

That is ridiculous. The Premier League consists of 20 teams, chosen specifically for their ability to beat other teams. Suppose instead of the Premier League on its own, we imagine a much larger competitive free-for-all containing the Premier League, plus the First Division below them, plus the Second Division below them, and so on, till we have 5000 teams altogether playing against each other.

If we knew nothing whatsoever about any given team, in that situation we might assign a “probability of only 1 in 5000” that it would win. In other words, if we picked a team randomly from the 5000, and did so repeatedly, then in the long run we would pick the winning team about once in every 5000 attempts to do so.

But now suppose we are told something about a given team: that it is in the top 20. That should make us raise our numerical assessment of its chances of winning the free-for-all. If we were further told that a team in the top 20 never loses to a team in the bottom 4980, we would very significantly raise our estimate of its chances of winning the free-for-all. It would be something similar to playing the Monty Hall game, except that instead of one out of three available doors being ruled out, 4980 out of 5000 available doors are ruled out.

But that, in effect, is what limiting the free-for-all to only the Premier League does. It means that if we know nothing at all about a team, the repeated act of picking one out randomly in the hope of choosing the winner would be successful much more often than 1 in 5000 times.

To lower the “chances of winning” in the face of further knowledge about a given team is to introduce capricious, subjective factors that cannot be relied on to make statistical judgements of relative frequency. They involve unrepeatable events or events that are not statistically lawlike, and so cannot be reliably extrapolated from. All we can do is guess about credibility here.

Casinos make money reliably because the behaviour of dice, cards, rotating cylinders etc. is statistically lawlike. For example, we know that in the long run about one sixth of rolls of pairs of dice will be doubles. But the behaviour of football teams in the Premier League is not at all lawlike. Bookies have to use numbers in their line of work, but let no one think these numbers correspond to measures of anything real or significant.

I suggest that we should sharply distinguish statistical relative frequency and subjective judgements of credibility. Numbers measure the former, but their presence is a will o’ the wisp when we are dealing with the latter.

Antisemitism is a special sort of personal failing

“Labour left in denial over antisemitism” say the headlines. And it is uncanny how people can be blind to something so glaringly obvious to the rest of us. I think the apparent blindness of political extremists to their own antisemitism is systematic: it exists for philosophical reasons that are worth noting.

Political extremists tend to understand justice as a matter of “groups getting what they deserve”. For example, German Fascists thought “Aryans” deserve their “destiny as the master race” or some such hokum, while of course Jews deserve death. According to this way of thinking, individuals do not matter. What matters is the group an individual belongs to — usually an accident of birth. If one’s forbears mistreated others, one inherits their guilt. If one’s forbears were mistreated, one inherits their entitlement to better things.

Extremists on the left have a much more pleasant way of expressing essentially the same view about collective guilt and the supposed entitlements of groups: they put it in terms of social justice. “We are on the side of the oppressed”, they claim. Of course this also puts them on the side opposed to “the oppressors”. Such side-taking has many forms, but as a rule it is regarded as acceptable to “punch upwards” and unacceptable to “punch downwards”. For example, imitating someone’s accent for satire or pure mirth is considered fair game, as long as the target is “up” — a toff, say, or someone with a pretentious way of speaking. But imitating Ken Livingstone’s “common” accent would be considered completely out of order. It doesn’t matter if the toff is now impoverished or if the “common” man is now a rich and powerful political figure — what matters is birth. Those of working class pedigree are uniquely free of sin, cleansed by their own victimhood at the hands of an “elite”.

These ways of thinking are perfectly suited to antisemites with their standard-issue antisemitic tropes such as that Jews are rich, cunning, bank-controlling, behind-the-scenes international political puppet masters, that Mossad is behind every terrorist outrage including those that benefit Israel’s enemies, and all the ludicrous rest of it.

Antisemites are duly attracted to the extreme left, at least in the UK and Ireland, and their presence there in turn prompts accusations of antisemitism. Yet when the accused sincerely ask themselves whether they are antisemites, their thoughts go like this: “Antisemitism is a form of racism, and ‘racism’ means ‘oppressing people regarded as inferior’; but I entertain no such thoughts, especially towards Jews, so I’m innocent of the charge. I remain a committed anti-racist on the side of the oppressed.”

That train of thought is gruesomely self-congratulatory, but I think we should acknowledge that there is little willingness to do harm or to exploit others in it. Antisemitism is a special sort of racism. It’s more insidious than other forms of racism, because those in its grip find no malice in themselves. That makes antisemitism a special sort of personal failing, one where culpability lies not in malice but in lack of reflection. It’s a philosophical failing, of people who have not taken the obligation to know thyself seriously enough. Western antisemites from the Christian tradition are people who have absorbed much of what is worst about Christianity, yet purged themselves of too little of it. This applies in particular to the doctrine of original sin, which says that blame is inherited. It also applies to ethics in which moral rightness is understood simply as a matter of “meaning well”, of keeping one’s nose clean, of acting out of virtue rather than vice, of avoiding malice.

I think we should treat hatred of Jews among Muslims of the Middle East as something different from Western antisemitism, although the former owes much to the latter. I don’t mean to single out for blame anyone who is historically, scientifically or culturally illiterate, who is unable to think beyond the narrow confines of an inadequate education. But I do mean to blame people who are culturally equipped to reflect on the failings of their own Christian tradition, who are morally obliged to do so, yet who have neglected to do so. In the West, we all must ask ourselves how one of the greatest societies in the world, a politically sophisticated democracy whose people created the greatest art of mankind, somehow managed to create hell on earth.

“If we don’t learn the lessons these pictures teach, night will fall”