# Difference between revisions of "Chance News 62"

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From this article we also learn that Martin Gardner recently had his 95th birthday and is still publishing new books. | From this article we also learn that Martin Gardner recently had his 95th birthday and is still publishing new books. | ||

− | (2) | + | (2) [http://freakonomics.blogs.nytimes.com/2009/10/06/do-we-need-a-37-cent-coin Do we need a 37-cent coin?]<br> |

− | [http://freakonomics.blogs.nytimes.com/2009/10/06/do-we-need-a-37-cent-coin | + | by Steven D. Levitt, New York Times, Freakonomics blog, 6 October 2009 |

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Here Norton Writes: | Here Norton Writes: | ||

<blockquote>This article reports on the work of economist Patrick DeJarnette, who developed some unusual results in probabilistic integer arithmetic. We can combine pennies, nickels, dimes and quarters to pay for any item costing below a dollar (freebies included, so (0.99 cents) is the relevant range). With the assumption that each of these 100 prices is equally likely to occur and that a purchaser uses the fewest possible coins, then on average each purchase requires 4.70 coins. DeJarnette asked if some other set of four coins, perhaps including one worth 8 or 61 or 37 cents would yield a lower average. He found that the optimal result uses an average of 4.10 coins per purchase, and is achieved by the sets | <blockquote>This article reports on the work of economist Patrick DeJarnette, who developed some unusual results in probabilistic integer arithmetic. We can combine pennies, nickels, dimes and quarters to pay for any item costing below a dollar (freebies included, so (0.99 cents) is the relevant range). With the assumption that each of these 100 prices is equally likely to occur and that a purchaser uses the fewest possible coins, then on average each purchase requires 4.70 coins. DeJarnette asked if some other set of four coins, perhaps including one worth 8 or 61 or 37 cents would yield a lower average. He found that the optimal result uses an average of 4.10 coins per purchase, and is achieved by the sets | ||

− | (1, 3, 11, 37 | + | (1, 3, 11, 37) or (1, 3, 11, 38). </blockquote> |

− | Norton concludes his discussion | + | Norton concludes his discussion with "there is a lot of play in this curious study." This is verified by looking at the 116 comments at the end of the blog. |

Submitted by Laurie Snell | Submitted by Laurie Snell |

## Revision as of 15:13, 23 March 2010

## Contents

- 1 Quotations
- 2 Forsooth
- 3 Chance moves to CAUSEweb
- 4 Media highlights
- 5 Back of the envelope calculations about Toyota
- 6 Placebos getting stronger?
- 7 Ranking Olympics countries: The first may be last
- 8 Athletes' birthdays
- 9 Stock market bubble-predictor
- 10 Tiger’s average better than average
- 11 Three happiness books
- 12 Flummoxed about flu

## Quotations

"It is a very sad thing that nowadays there is so little useless information."

--Oscar Wilde

Quoted in All too much: Monstrous amounts of data

The Economist, 25 February 2010

"Statisticians are engaged in an exhausting but exhilarating struggle with the biggest challenge that philosophy makes to science: how do we translate information into knowledge? ...

"If you think that statistics has nothing to say about what you do or how you could do it better, then you are either wrong or in need of a more interesting job."

--Stephen Senn,

Dicing With Death

Suggested by Paul Alper

"Of course, there are plenty of veteran basketball decision-makers who don't believe that stats are the only key to success. They'll tell you the difference in winning percentages has less to do with statistical analysis than with statistical freaks. 'If you took LeBron off the Cavaliers, you could give them 10,000 number crunchers, and it wouldn't make a difference,' says [one team executive]."

--David Biderman, “Are Statheads the NBA’s Secret Weapon?”,The Wall Street Journal, March 12, 2010

The article indicates that the 15 NBA teams with data analysts have won 59% of their combined games this season, while the 15 teams without data analysts have won only 41% of their games.

Submitted by Margaret Cibes

“In order for an economy to have an adequate system of financial reporting, it is not enough that companies make disclosures of financial information. …. In addition, it is vital that there be a set of financial intermediaries, who are at least as competent and sophisticated at receiving, processing, and interpreting financial information … as the companies are at delivering it.’”

--Malcolm Gladwell, quoting a Yale law professor, in “Open Secrets”,The New Yorker, January 8, 2007

Submitted by Margaret Cibes

## Forsooth

## Chance moves to CAUSEweb

Chance Project Moves to CAUSEweb

Amstat News, 1 March 2010

This story announces that the Chance materials will be moving to a new home at CAUSEweb, effective March 15. Actually, the Chance News Wiki quietly moved a week earlier--you will see a new URL in your browser! If (by chance) you didn't notice, it was because of the wonderful work by the technical experts at Dartmouth College and CAUSEweb, who enabled a very smooth transition and redirect of links from the Dartmouth site.

Submitted by Bill Peterson

## Media highlights

The College Mathematics Journal has a column called

"Media Highlights". Norton Starr is one of the editors and

his contributions are usually of interest to Chance News

readers. The March issue has two such items.

(1) For decades, puzzling people with mathematics

by John Tierney, New York Times, 19 October 2009

Norton writes:

This article gives an inspiring portrait of Martin Gardner, the

premier exponent of recreational mathematics for over 50 years.

about Martin and ends with a quote from Rohnald Graham:

It invites readers to see mathematics vastly richer and more interesting

than they may recall from their classrooms exercise. Norton says more

Martin has turned thousands of children into mathematicians,

and thousand of mathematicians into children.

From this article we also learn that Martin Gardner recently had his 95th birthday and is still publishing new books.

(2) Do we need a 37-cent coin?

by Steven D. Levitt, New York Times, Freakonomics blog, 6 October 2009

Here Norton Writes:

This article reports on the work of economist Patrick DeJarnette, who developed some unusual results in probabilistic integer arithmetic. We can combine pennies, nickels, dimes and quarters to pay for any item costing below a dollar (freebies included, so (0.99 cents) is the relevant range). With the assumption that each of these 100 prices is equally likely to occur and that a purchaser uses the fewest possible coins, then on average each purchase requires 4.70 coins. DeJarnette asked if some other set of four coins, perhaps including one worth 8 or 61 or 37 cents would yield a lower average. He found that the optimal result uses an average of 4.10 coins per purchase, and is achieved by the sets (1, 3, 11, 37) or (1, 3, 11, 38).

Norton concludes his discussion with "there is a lot of play in this curious study." This is verified by looking at the 116 comments at the end of the blog.

Submitted by Laurie Snell

## Back of the envelope calculations about Toyota

Toyotas Are Safe (Enough). Robert Wright, The New York Times Blog, March 9, 2010.

How worried are you about driving a Toyota? Robert Wright is not that worried.

My back-of-the-envelope calculations (explained in a footnote below) suggest that if you drive one of the Toyotas recalled for acceleration problems and don’t bother to comply with the recall, your chances of being involved in a fatal accident over the next two years because of the unfixed problem are a bit worse than one in a million — 2.8 in a million, to be more exact. Meanwhile, your chances of being killed in a car accident during the next two years just by virtue of being an American are one in 5,244. So driving one of these suspect Toyotas raises your chances of dying in a car crash over the next two years from .01907 percent (that’s 19 one-thousandths of 1 percent, when rounded off) to .01935 percent (also 19 one-thousandths of one percent).

Of course, the type of risk involved is part of the problem.

But lots of Americans seem to disagree with me. Why? I think one reason is that not all deaths are created equal. A fatal brake failure is scary, but not as scary as your car seizing control of itself and taking you on a harrowing death ride. It’s almost as if the car is a living, malicious being.

Robert Wright includes an appendix with all of the computations and assumptions that went into these numbers.

Submitted by Steve Simon

### Questions

1. People seem to make a distinctions between risks that they place upon themselves (e.g., talking on a cell phone while driving) and risks that are imposed upon them by an outsider (e.g., accidents caused by faulty manufacturing). Is this fair?

2. Contrast the absolute change in risk (.01935-.01907=.00028) with the relative change in risk (.01935/.01907=1.0147). Which way seems to better reflect the change in risk?

3. Examine the assumptions that Robert Wright uses. Do these seem reasonable?

## Placebos getting stronger?

The growing power of the sugar pill

by Alix Spiegel, NPR, 8 March 2010

The randomized double-blind placebo-controlled experiment is regarded as the "gold standard" in medical research. This story describes new research indicating that our response to placebo treatments may be getting stronger over time.

To be continued...

Submitted Bill Peterson

## Ranking Olympics countries: The first may be last

Not all countries are rich and snowbound

by David Biderman, *The Wall Street Journal*, February 18, 2010

WSJ staff came up with an alternative system for ranking a country’s success in the Olympics, based on eight factors that they felt could affect a country’s performance. They then analyzed and ranked ten Winter Olympics 2010 countries as of February 16, based on the factors of population, per-capita GDP, average temperature, infant mortality rate, per-capita number of cars bought per month, percent of smokers, per-capita daily protein consumption, and per-capita yearly alcohol consumption.

A chart, “Another Way to Measure Olympic Aptitude”, shows the data for the eight factors, the medal counts, and the WSJ scores for the ten countries.

Italy came out on top, with 3 medals and a WSJ score of 0.942, while Germany came in last with 9 medals and a WSJ score of 0.750.

Submitted by Margaret Cibes

## Athletes' birthdays

Born late year? Choose another sport”

by David Biderman, *The Wall Street Journal*, March 21, 2010

A researcher at Queensland University of Technology compared the distribution of birthdays of the 617 Australian-born Australian Football League 2009 players in particular, to Australian birth statistics in general.

He found the following quarterly data on expected number of birthdays, actual number of birthdays, and percent more/less than expected :

Jan-Mar: 153, 196, +28.1%

Apr-Jun: 155, 162, +4.5%

Oct-Dec: 152, 122, -19.7%

Jul-Sep: 157, 137, -12.7%

He suggested that the decreasing percent changes could be explained by the January 1 cut-off date for youth-sports leagues, which “means players born near or after that date grow up with physical advantages over their competitors, likely influencing them to keep playing.” (Biderman reports that other studies have found similar results in European soccer and Canadian hockey.)

**Questions**

1. If Australian birthdays, in general, were uniformly distributed in any year, how many AFL player birthdays would you have expected in each quarter of a leap year? Of a non-leap year?

2. In what way(s) does the shape of either quarterly distribution in question 1 differ from the researcher’s quarterly distribution of expected AFL player birthdays?

3. How do you think the researcher calculated the expected number of AFL player birthdays in each quarter? What, if anything, might his distribution of expected AFL player birthdays tell you about the distribution of Australian birthdays in general?

4. Would/should this data discourage a young Australian-born person from aiming for an AFL career because he has a late-year birthday? What are some other considerations in making such a career decision?

Submitted by Margaret Cibes

## Stock market bubble-predictor

“The Professor Who Chases Financial Bubbles”

by Eleanor Laise, *The Wall Street Journal*, March 13, 2010

Didier Sornette, director of the six-person Financial Crisis Observatory at the Swiss Federal Institute of Technology in Zurich, last year “launched the bubble experiment by identifying four developing bubbles and forecasting when they'll peak. His predictions are locked away in encrypted files that can't be altered, to be revealed only when the forecasted bubble peaks have passed, on May 1.”

Formerly a geophysics professor at UCLA, Sornette is now a professor of finance, physics and geophysics with a “passion for predicting events in complex systems” such as earthquakes, epileptic seizures, and the popularity of YouTube videos. He applies his work on rocket-tank ruptures to market fluctuations.

While there's lots of complex math behind it, one key pattern is essentially this: periods of unsustainable growth, in which the growth rate is itself accelerating, punctuated by waves of panicky selling. Key elements are the "positive feedback" generated by optimistic investors pushing the price ever higher into bubble territory even as more pessimistic investors produce waves of selling. In the midst of this tug of war, there's an accelerated development of the bubble. …. Only about two-thirds of bubbles end in a crash …. But in his view, as the bubble develops, it becomes increasingly unstable so that any number of small disturbances could cause it to pop. …. So while market-watchers often seek the causes of a crash in the events immediately preceding it, he believes the fundamental origin is in the longer-term build-up of instability.

Nassim Taleb, of “black swan” fame, says that Sornette’s work “is vastly more useful to me than anything else in economics."

Submitted by Margaret Cibes

## Tiger’s average better than average

“Tiger Can Win by Just Playing ‘Average’”

by Austin Kelley, *The Wall Street Journal*, March 20, 2010

Two finance professors at Dartmouth’s Tuck School of Business have “used data from 83,823 rounds of golf on the [PGA] Tour between 2004 and 2008 and created a statistical model that calculate[s] every golfer's skill level” and estimates “each player’s average score for an average round on an average course.”

In that span, they found that [Tiger] Woods could have won 13 of the 72 PGA Tour stroke-play events he entered just by playing his "normal" game (he actually won 24). No other golfer on the tour could have won a single title without a little help from the golf gods. …. [They] estimate that if Mr. Woods can cope with the media maelstrom and put in a few run-of-the-mill days at Augusta National, he has about an 18.1% chance of winning. If Phil Mickelson does the same, he has no shot.

Based on the 2004-2008 data, they estimate Woods’ projected average round on an average course at 68.07, Phil Mickelson’s at 69.19, and Vijay Singh’s at 69.21. According to Kelley, the professors are not sure “how Mr. Woods’s hiatus will affect the statistics, but [guess] that Tiger will return to dominance at some point this year.”

See an abstract of their paper, “Dominance, Intimidation, and ‘Choking’ on the PGA Tour”, in the *Journal of Quantitative Analysis in Sports*, 2009.

Submitted by Margaret Cibes

## Three happiness books

“Everybody Have Fun”

by Elizabeth Kolbert, *The New Yorker*, March 22, 2010

The author describes some 1978 research results indicating that lottery winners were not happier than paraplegic accident victims. The paper, “Lottery winners and accident victims: is happiness relative?”, *Journal of Personality and Social Psychology*, August 1978, is said to be “one of the founding texts of happiness studies, a field that has yielded some surprisingly morose results.”

Then she reviews two 2010 books and one 2007 book about happiness:

(a) By former Harvard president, now Harvard professor Derek Bok: *The Politics of Happiness: What Government Can Learn from the New Research on Well-Being*, Princeton University Press, 2010.

(b) By University of Maryland public policy professor Carol Graham, *Happiness Around the World: The Paradox of Happy Peasants and Miserable Millionaires*, Oxford University Press, 2010.

(c) By Harvard psychology professor Daniel Gilbert, *Stumbling on Happiness*, Vintage, 2007.

Submitted by Margaret Cibes

## Flummoxed about flu

“The Flu Season That Fizzled”

by Betsy McKay, *The Wall Street Journal*, March 2, 2010

Experts cannot explain the unusual “lull” in flu cases at this time of year, compared to the wider incidence of H1N1 swine flu in the summer and fall of 2009.

[C]ases of the new H1N1 swine flu virus have dwindled to a trickle, and run-of-the-mill seasonal flu has barely made an appearance.

The University of Virginia’s student health director stated:

[The] student health center usually sees as many as 130 students a week complaining of flu symptoms this time of year. Recently, no more than three to five students a week have been coming in with fever, cough or other signs of flu ….

It is not clear whether – or how much – vaccination or hand-washing has played a role in the decrease in flu cases. There remains a danger that the H1N1 virus may rear up again, in the same or a mutated form. However, its appearance is also waning in most places around the world at this time.

See “Tracking the Flu” for a time-series chart of the “percentage of all doctors’ visits made by patients with influenza-like symptoms” for seasons 2005-06 through 2008-09.

Submitted by Margaret Cibes