II. Teaching the “Nuts and Bolts”
A. General Tips. Assessing the value of information involves:
1) incorporating new information into the manager’s decision tree, and
2) revising probabilities using joint probability tables or Bayes rule.
We place at least as much emphasis on the first point as on the second. For
instance, it is worth having students practice building one or two decision
trees with all revised probabilities already supplied. Once the logic of the tree
has been laid bare, more complicated decisions can be tackled.
B. Launching a new product. An alternative to using the oil drilling
example in the text is to revisit the example of launching a new product (see
Chapter Twelve of this manual). Version 1 is simpler and should be presented
first.
1. Suppose that the firm can purchase a macro-forecast concerning the
course of the economy, before making its launch decision. The forecast is
one of two kinds: positive (+) or negative (-). In light of a positive
forecast, the probabilities of the different scenarios are:
Pr(Strong|+) = .5, Pr(Moderate|+) = .4, and Pr(Recession|+) = .1.
In light of a negative forecast, the chances of the different scenarios are:
Pr(Strong|-) = .15, Pr(Moderate|+) = .4, and Pr(Recession|+) = .45.
Finally, the chance of a positive forecast is .6 (and a negative forecast .4).
The decision tree below shows that the firm should launch the product in
light of a positive forecast but abandon (or postpone) the launch if the
forecast is negative. The resulting expected profit is $7.08 million – $1.16
million greater than the expected value of launching the product without
the macro-forecast (see Chapter Twelve of this guide).
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2. The situation is as in version 1, but instead of being given the revised
probabilities, the manager must calculate them. Management starts with
the following information about the accuracy of the macro-forecast. In 5
of 6 strong economies, the forecast has been positive, Pr(+|S) = 5/6. In 6
of 10 moderate economies, the forecast has been positive, Pr(+|S) = 6/10.
In 3 of 4 recessions, the forecast has been negative, Pr(-|R) = 3/4. Recall
that the prior probabilities are: Pr(S) = .36, Pr(M) = .4, and Pr(R) = .24.
Combining these facts, we can generate the following joint table:
Strong Moderate Recession Total
+ .30 .24 .06 .60
– .06 .16 .18 .40
Total .36 .40 .24
From this table, we can compute the revised probabilities of version 1 above.
For instance, Pr(S|+) = Pr(S&+)/Pr(+) = .3/.6 = .5, and so on. Then, the
decision tree and decision recommendation are as above.
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.
6
Positive
Forecast
$0
$0
7.08
$20
S
R
11.8
.
5
.
1
-$22
Do Not
11.8
Launch
$20
Success
R
-2.9
.
1
5
.
4
5
-$22
.
4Do Not
0
Launch
Negative
Forecast
M
M
.
4
.
4
$10
$10
Additional variations.
1. Suppose the joint table is:
Strong Moderate Recession Total
+ .216 .24 .144 .60
– .144 .16 .096 .40
Total .36 .40 .24
In this case, the information is worthless. The outcomes + and – are
independent of the future course of the economy. Revised probabilities
are no different than the prior probabilities: Pr(S|+) = .216/.6 = .36, and so
on.
2. Suppose that Pr(+|Strong) = 8/9, Pr(+|Mod) = 1/2, and Pr(-|Recession)
= 1/2. The resulting joint table is
Strong Moderate Recession Total
+ .32 .20 .12 .64
– .04 .20 .12 .36
Total .36 .40 .24
Computing revised probabilities and putting them into a decision tree
shows that this test is also worthless! Regardless of the forecast (even if it
is negative), launching the product is the best course of action.
D. Suggested Problems Problems 3, 5, 7, 8, 9, and 11.
E. Mini-Case The Science of Baseball (see accompanying text).
The Science of Baseball
The national pastime of baseball has been called a “game of inches.” The
umpire calls a pitch a ball instead of a third strike, and the next pitch is hit
for a home run. A ball hit just beyond the short stop’s reach becomes a
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game winner. Baseball is also a game of decisions and statistics. Managers
make dozens of moves and decisions during a ball game. General
managers put together team rosters (drafting players, making trades) by
continually gauging talent, again based on player statistics.
For the last ten years, the Oakland Athletics under General Manager
Billy Beane have been the leading proponents of “money ball” – using
statistical analysis to build the strongest winning team with a limited total
payroll.1 “Old-school thinking judged a prospective ball-player by whether
he had the traditional “tools”: the abilities to hit, field, throw, and run
throw. Scouts believed they could judge these talents simply by watching a
prospect play. This subjective assessment could be backed up by the
traditional hitting statistics (batting average, home run, and runs batted in)
and pitching statistics (win-loss record and earned run average).
Beane was one of the first to realize that these old school methods were
often biased and inaccurate. How good a ballplayer looked on the field was
far less important than how many runs he produced (or for a pitcher how
many opposing runs he prevented). A new breed of baseball analysts were
uncovering much better hitting and pitching statistics to predict winning
performance. Oakland’s record between 1999 and 2004 proved the point.
Oakland was the second winningest team during this span (and in the top
10 each year) despite having one of the lowest payrolls (between 25th and
28th among 30 major league teams). Almost a dozen teams have followed
Oakland’s statistical lead. In building a winning team, today, the right
statistics (and, of course, money) talk.
Statistics and playing the averages also matter on the field, 162 games a
year. Put yourself in the shoes of the manager of the local team. It is the
seventh inning of a 3-to-3 ballgame. The opposing team has runners on
first and third base due to an infield single and an error. There is one out,
and the opposing team’s left-handed “cleanup” hitter is coming to bat.
Should you allow your starting right-handed pitcher to face the batter, or
should you use your ace left-handed relief pitcher?
In pondering this decision, you have no shortage of probabilistic
information. Begin with the opposing hitter’s batting average. Let’s say he
is a .300 hitter (i.e., has averaged three base hits in every ten times at bat).
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This is a fine performance. However, in his last ten games, the player has
hit poorly, averaging only .240. But today he already has hit a double
against the starting pitcher. However, he is slow of foot and frequently hits
into double plays (which your starting pitcher is adept at inducing). Yet, the
relief pitcher may be the better bet. The cleanup hitter averages only .255
against left-handers, and the relief pitcher has allowed opposing hitters
only a .235 batting average. A telling factor, however, is that the hitter has
11 hits in 24 lifetime attempts against your left-hander.
Our purpose in this example is not to establish the manager’s optimal
decision (although second-guessing is fun); rather, it is to make the point
that any decision requires categorizing the past data on the basis of the
most relevant predictive factors. This example is complicated because for
every factor working in one direction, there seems to be another factor
working in the other. Nonetheless, the only way to make the best-informed
decision is to take all relevant factors into account.
To sum up, from a manager’s or general manager’s point of view,
baseball is a game of tendencies and percentages. The difference between a
fine .300 hitter and a poor .200 hitter is one extra hit in every ten times at
bat. Small as it seems, this difference looms large over a 162-game season.
Earl Weaver, the former manager of the Baltimore Orioles, was a vigorous
proponent of baseball by the numbers. In making pitching decisions, he
kept tabs on the batting record of each opposing hitter against each of his
team’s pitchers. Not everyone (especially his pitchers) agreed with this
approach. As Jim Palmer, Baltimore’s Hall-of-Fame pitcher put it, “The
only thing Earl Weaver knows about pitching is that as a player he couldn’t
hit it.”
1 On building a winning ball team using the “new” statistics, see M. Lewis, Money Ball, (New York, N.Y.: W. W.
Norton & Company, 2003). Bill James was the first to apply a modern statistical approach to baseball.
ADDITIONAL MATERIALS
I. Short Readings
J. A. Paulos, “The Advanced Metrics of Attraction,” The New York Times,
July 15, 2014, p. D3. (Here is a novel application of Bayes Theorem.)
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A.Tugeng, “As Data about Drivers Proliferates, Auto Insurers look to Adjust
Rates,” The New York Times, April 19, 2014, p. B4.
J. Eaglesham and R. Barry, “Stockbrokers who Fail Test have Checkered
Records,” The Wall Street Journal, April15, 2014, pp. A1, A2.
S. Wheaton, “Credit Score by Multiple Choice,” The New York Times,
December 31, 2013, pp. B1, B2.
D. Brooks, “Forecasting Fox,” The New York Times, March 22, 2013, p.
A29.
N. Silvers, “The Weatherman is not a Moron,” The New York Times
Magazine, September 9, 2012, pp. 34-39
.
T. Gryta, “Studies Likely to Fuel Cancer Screening Debate,” The Wall Street
Journal, May 16, 2011, p. B2.
L. Landro, “Hidden Heart Disease,” The Wall Street Journal, November 9,
2010, pp. D1, D4.
P. Healy, “Musicals Born on Broadway Cause Jitters,” The New York Times,
October 1, 2010.
J. Markoff, “Burned Once, Intel Prepares New Chip Fortified by Constant
Tests,” The New York Times, November 17, 2008, p. B3.
S. Banjo, “Doing Your Home Work,” The Wall Street Journal, December 11,
2007, p. R6.
J. W. Miller, “Why Miners Look for Buried Treasure in Belgian Museum,”
The Wall Street Journal, March 20, 2007, pp. A1, A13.
J. W. Miller, “Gumshoe’s Intuition: Spotting Counterfeits at Port of Antwerp,”
The Wall Street Journal, December 14, 2006, pp. A1, A18.
J. Nocera, “The Future Divined by the Crowd,” The New York Times, March
11, 2006.
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S. Begley, “Afraid to Fly after 9/11, Some Took a Bigger Risk – in Cars,”
The Wall Street Journal, March 23, 2004, p. B2.
C. Binkley, “Casino Chain Mines Data on its Gamblers, and Strikes Pay
Dirt,” The Wall Street Journal, May 4, 2000, p. A1.
L. Tarkan, “Value of Second Opinions is Underscored in Study of Biopsies,”
The New York Times, April 4, 2000, p. D7.
“How the Tire Problem Turned into a Crisis for Firestone and Ford,” The
Wall Street Journal, August 8, 2000, p. A1.
“Compiling Data and Giving Odds on Jury Awards,” The New York Times,
Jan. 21, 1994, p. B18.
“Behind Monty Hall’s Doors: Puzzle, Debate, and Answer,” The New York
Times, July 21, 1991, p. 1.
II. Longer Readings
J. Seabrook, “Snacks for a Fat Planet,” The New Yorker, May 16, 2011, pp.
54-71. (This article discusses how Pepsi searches for tastes.)
S. Saigal, “Probability Management in Action, Analytics Magazine, Summer
2009, pp. 19-23.
M. Gladwell, “Most Likely to Succeed,” The New Yorker, December 15,
2008, pp. 36-42. (How well can job success be predicted?)
D. N. Sull, “Disciplined Entrepreneurship,” MIT Sloan Management Review,
46, Fall 2004, 71-77.
J. W. Ulvila and J. E. Gaffney, “A Decision Analysis Method for Evaluating
Computer Intrusion Detection Systems, Decision Analysis, March 2004,
35-50.
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E. Urbanovich. et al, “Early Detection of High-Risk Claims at the Workers’
Compensation Board of British Columbia,” Interfaces, July 2003, 15-26.
Watkins, M. D. and M. H. Bazerman, “Predictable Surprises: The Disasters
You Should Have Seen Coming,” Harvard Business Review, March-April
2003, 72-80.
J. E. Smith and R. L. Winkler, “Casey’s Problem: Interpreting and
Evaluating a New Test,” Interfaces, May-June 1999, 63-76.
J. Weisberg, “Keeping the Boom from Busting,” The New York Times
Sunday Magazine, July 19, 1998, p. 24. This article examines the risk
calculations and decision methods of Robert Rubin, Treasury Secretary
in the Clinton administration.
III. Recommended Case
Exercises on the Value of Information, Harvard Business School,
(9-893-006), 1994. Teaching Note (5-396-275)
IV. Quips and Quotes
Grace is given by God, but knowledge is bought in the market.
Risk varies inversely with knowledge. (Irving Fisher)
The race is not always to the swiftest, nor the battle to the strong — but that is
the way to bet (Damon Runyon)
I know the records of the horses, the abilities of the jockies, the condition of
the turf. I probably know more about what horse should win than anybody in
the country. But there’s one thing I don’t know – how the horse was feeling
when he got up in the morning. (Clem McCarthy, horse track sage)
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In gathering information before making an important decision, be prepared to
spend about 1 percent of what is at stake. (Ronald Howard)
Test everything. The most important word in the vocabulary of advertising is
test. Twenty-four out of twenty-five new products never get out of test
markets. Manufacturers who do not test market their products incur the
colossal cost (and disgrace) of having their products fail on a national scale
instead of dying inconspicuous and economical deaths in test markets.
(David Ogilvy, Confessions of an Advertising Man)
Education is the process of moving from cocksure ignorance to thoughtful
uncertainty.
It is an old maxim of mine that when you have excluded the impossible,
whatever remains, however improbable, must be the truth. (A. Conan Doyle)
After his team lost 73-0 in the 1940 NFL championship game, quarterback
Sammy Baugh was asked if things might have been different if his team had
scored first. “Sure, it would have been 73-6.”
Always get a second opinion.
The best way to have a good idea is to have a lot of ideas.
If you can tell the difference between good advice and bad advice, you don’t
need advice.
If three people call you an ass, put on a bridle.
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