Chance News 10

Quotation

The weather man is never wrong. Suppose he says that there's an 80% chance of rain. If it rains, the 80% chance came up; if it doesn't, the 20% chance came up! - Saul Barron .

From: Statistical Quotations

Forsooth

Literary License

"'Four million ... heard it. Ten percent remember it. One percent of those matter. One percent of those do something about it. That's still' - he does the math - 'four people.'" From: _The Betrayal_, by Sabin Willett, NY: Villard (Random House), 1998.

Submitted by Margaret Cibes

Logarithmetic behavior as metaphor

For many years Ed Barbeau has edited a wonderful column in the College Mathematics Journal called Fallacies, Flaws, and Flimflam. In Barbeau's column in the November 2005 issue of the College Math Journal Norton Starr provides a contribution called "Logarithmic behaviour as metaphor". Norton provides examples from a wide variety of writers who say that something is growing logarithmically when they mean it is growing exponentially.

Norton says that he became interested in this when a convocation speaker at his college (Amherst) said:

As opposed to all other appetites which are stimulated by deprivation and satisfied by food, good education stimulates with plenty so that appetite for knowledge and understanding escalate logarithmically to insatiability.

Norton finds examples among faculty, newspapers, television and of course on the web. He writes:

Here are three examples of metaphorical growth from the New York Times, with the third suggesting an improved understanding on the part of this newspaper:

• from a review of Harlow Shapley's autobiography: "if the autobiographer opts for a method he believes will grant him immortality without industry, his risks rise logarithmically."

• from a story about corruption and drugs:"' The drug situation is a horror story, increasing logarithmically.'"

• from a more recent story: "Street crime, fed by an explosion of drug abuse, has risen exponentially."

RRS Coincidence column

Norton Starr, who provides our RSSNews Forsooth items, told us that the RRSNews now has a Coincidence column. He sent us the coincidence story from the Nov 05 RSSNews and suggested some questions relating to this story.

This month's contribution is from Pam Warner of the University of Edinburgh Medical Statistics Unit who relates a story told to her by a colleague named Wilma during a recent morning coffee-break.

Wilma had been waiting in a queue for a check-out (in Edinburgh) and a little boy, accompanying the lady ahead of her in the queue, struck up a conversation with her. He asked her what her name was, and on being told that it was Wilma exclaimed that was the same name as his granny (the lady he was with).

Wilma then returned the compliment, asking him what his name was, and he said Kieran. She in turn commented that that was funny as she had a young grand-daughter (in London) whose name was Kiera.

By this time Kieran's grand-mother (the other Wilma) was involved in the proceedings, and chipped in 'Next thing you will be telling me is that Kiera's Mum's name is Pamela...', to which our Wilma could only reply astounded, 'It is!'

Questions

(1) What's the likelihood of two instances of a grandmother, her daughter (even though in this case it might be daugher-in-law) and her grandson having the same names, say in Britain?

(2) How does the above probability vary with size of population>

(3) How likely is it that such a pair of trios would encounter each other in person?

Pi in the News

“Expressed in digits, pi begins 3.14159…, and it runs on to an infinity of digits that never repeat. Though pi has been known for more than three thousand years, mathematicians have been unable to learn much about it. The digits show no predictable order or pattern. The Chudnovskys were hoping, very faintly, that their supercomputer might see one.” From: “Capturing the Unicorn,” by Richard Preston, in _The New Yorker_, April 11, 2005

Submitted by Margaret Cibes

Question

If you were trying to explain to your Uncle George what it would mean for the digits of pie to be a random sequence, what might you tell him?

Suggested by Laurie Snell.

How stocks share in soccer sorrows

How stocks share in soccer sorrows Phillip Coggan, December 01, 2005, Financial Times
Sports Sentiment and Stock Returns by Alex Edmans, Diego Garcia and Oyvind Norli, Social Science Research Network. www.ssrn.com

Motivated by psychological evidence of a strong link between sporting outcomes and mood, a new study claims a statistically significant link between a nation's soccer team's results and the subsequent day's performance of that country's stock market, attributed to sudden changes in investor mood.

The study analysed about 1,200 football matches played across 39 nations, focusing on the FIFA World Cup or on Continental competitions such as the European Championship. Elimination from those competition is, on average, associated with a stock market performance that is 38 basis points (slightly more than a third of a percentage point) worse than normal.

The Financial Times summarises the results by saying that the magnitude of the loss effect and its concentration in Western European countries with developed stock markets, suggests that investors would have obtained large excess returns by trading on these mood events. The effect seems to be strongest in small stocks, where local investor sentiment is most likely to be dominant. It seems to be unrelated to the potential economic effects - such as loss of merchandising revenue - that defeat might have.

The authors even suggest a profitable trading strategy

One such strategy would be to short futures on both countries’ indices before an important match to exploit the asymmetry of the effect.

They also claim that the loss effect is stronger for more important games, robust to changes in estimation methodology and to the removal of outliers in the data. It seems that there is also a statistically significant stock market loss effect using cricket, rugby, ice hockey, and basketball games in countries where these sports are popular.

However, a similar positive effect was not found when teams won. That may be because sports fans have unrealistic expectations of their team's chances of success. For example, 86 per cent of fans thought England would beat Brazil in the 2002 World Cup quarter-final, even though Brazil were the world's top-ranked team and bookmakers assigned only a 42 per cent probability to an England victory. A loss is more crushing to sentiment than a win is helpful. Furthermore, success in one round still leaves the possibility of elimination in the next.

The Financial Times article goes on to say

The study seems to chime with other surveys which found that increases in heart attacks, murders, suicides and riots are associated with sporting defeat. The mood of the population is adversely affected by a loss, particularly for sports in which a large proportion of the population takes an interest.

Other academic work that suggests investors are not entirely rational and so can be affected by factors like the weather, holidays and even the annual switch to daylight-saving time in the US.

Submitted by John Gavin.