Why winning bursts are entirely random
The soccer boffin's weekly dose of betting wisdom
Human life is everywhere a state in which much is to be endured and little to be enjoyed. So said Imlac, a character in The History of Rasselas, Prince of Abissinia, a book by Samuel Johnson. It was published in 1759.
Imlac was talking about life in general, not anything in particular, but he could have been talking about betting. Profits, if they accrue at all, accrue in bursts.
Between them are long intervals in which wins either just about cancel out losses or else fail to keep up with them.
Fyodor Dostoyevsky understood this. Dostoyevsky was a 19th-century writer. He was also a hopeless gambler, in more than one sense of that phrase.
In Dostoyevsky’s story of The Gambler a young man called Alexei Ivanovich plays roulette. Alexei says: “I drew one conclusion, which I think is correct: in a series of pure chances there really does exist, if not a system, at any rate a sort of sequence – which is, of course, very odd…
“One day, or one morning, it will happen, for example, that red and black alternate, changing every minute almost without any order, so that neither red nor black ever turns up more than two or three times in succession. The next day, or the next evening, red only will come up many times running, twenty or more, for example, and go on doing so unfailingly for a certain time…”
What Dostoyevsky could not accept was that there is no way of telling when one of these sequences will start or when it will end. They are purely random. There seem to be patterns in them but there are not.
Anyone who bets must hope that bursts of profit will be numerous enough and good enough to make up for the drawn out periods of marking time or worse. And they have to try to find a way of coping with those long lulls and slumps.
In 1944, near the end of the second world war, Germany aimed rockets at London. Londoners called them doodlebugs. Dan Gardner tells the story in a book called Future Babble.
“These ‘flying bombs’ were a horrible new weapon, unlike anything seen before. At first, Londoners didn’t know what to make of the threat. All they knew was that, at any moment, with little or no warning, a massive explosion would erupt somewhere in the city. But gradually people began to realise that the rocket strikes were clustered in certain parts of the city, while others were spared.
“Rumours spread. Nazi spies were directing the missiles, some said. The spies must live in the parts of the city that weren’t being hit… It was a compelling explanation and yet it was wrong. As terrifying as the rockets were, they lacked precision guidance equipment and the best the Germans could do was point them at London and let them explode where they may.”
RD Clarke worked for the Prudential Assurance Company. He studied where the doodlebugs had fallen. In 1946 he published a paper in the Journal of the Institute of Actuaries called An Application of the Poisson Distribution.
Clarke divided a large area of London into 250 metre squares and counted the number of squares with no bombs, one bomb, two bombs and so on.
Then he used the Poisson distribution to answer this question: if bombs had fallen randomly, in how many squares should he have expected no bombs, one bomb and so on? The two sets of numbers corresponded almost exactly.
Clusters occur naturally in all sorts of things, from the deadly to the trivial.
A life of Gunners and greyhounds
On the Racing Post we try to write about people who do a hard job without sounding as though we think we could do it better. One of our predecessors, however, did become Arsenal manager. And he was successful too.
George Allison managed Arsenal for six seasons in the 1930s and 1940s. He won the League twice and FA Cup once. Before the first world war he wrote for the Sporting Life, which was later incorporated into the Racing Post.
Allison is usually described as a greyhound correspondent. In his autobiography – I have a copy – he said he wrote “special articles” and “a different sort of sports story, something away from the style of the ordinary racing paper”. He also said: “After football, racing was dearest to my heart, with an added virile interest in greyhound coursing.”
Allison became Arsenal’s programme editor and after the first world war he joined the board of directors.
Herbert Chapman, the team manager, died in January 1934. He would have won a third League title and had already won the FA Cup once. Allison became team manager after season 1933-34.
According to players, Allison was a successful manager because he recognised his limitations. Centre-back Bernard Joy said Allison “lacked the professional’s deep knowledge of the game.” Tom Whittaker, who had been Chapman’s assistant and would become Allison’s successor, took training.
It was an example of what in another field Charlie Munger has called knowing your circle of competence. Munger, the partner of stock-market investor Warren Buffett, said: “You have to stick within your circle of competence. You have to know what you understand and what you don’t understand. It’s not terribly important how big the circle is. But it is terribly important that you know where the perimeter is.”
Allison, paradoxically, was a successful manager because he realised that he did not know how to be a successful manager.
Criticism of referees overlooks fans’ faith
Seventy-seven per cent said good, 12 per cent said bad and 11 per cent said neither or do not know.
You would never have guessed that so many people think referees are good from the voices we hear.
Sky Sports also reported evidence that referees and assistants get 98 per cent of their calls right. You would never have guessed that from the complaints about them.
Encouragingly there seem to be a large number of people who quietly appreciate that the standard of refereeing in the Premier League is high.