#### October 2011

# STATISTICS, SPORTS AND SPIES

By Tom Herzog, Ph.D., Distinguished Scholar; and CIPR Staff
Many former students have struggled through an undergraduate
or graduate university course in statistics. Their only memories are that they
are just thankful that the course was over and that they somehow got a passing
grade.

Nevertheless, statistics has wide application to important
problems in many different disciplines. Since the start of World War II,
Bayesian statistics has enjoyed a renaissance with a wide variety of successful
applications. In this brief article we focus on some analytic work that helped
the Team USA men’s volleyball team win the Olympic gold medal in 2008 in Beijing.
We also briefly discuss a successful application of Bayesian statistics^{[1]} to cryptanalysis during World War II. In contrast, we describe a failure of
classical statistical methods in Merck’s analysis of a clinical trial study
involving its drug Vioxx.

**• Team USA Men’s Volleyball**^{[2]}
The story starts with Carl McGown,
a former Brigham Young University (BYU) volleyball coach and an assistant coach
for the Team USA men’s volleyball team in the Athens 2004 Olympics. After
reading the book *Moneyball*—the
story of how the Oakland Athletics baseball team employed statistical methods
to develop winning teams despite having a lower budget than most other major
league baseball teams—McGown contacted his friend Gil Fellingham, a professor of statistics at BYU who holds
both a doctorate in biostatistics and a master’s degree in physical education.

McGown gave Fellingham reams of data from international volleyball matches. These data covered every
touch in every match of the top teams in the world over a single year. Fellingham and his colleague Shane Reese analyzed these
data using Bayesian statistical procedures. The study, which cost $8,000, recommended
that a larger proportion of scarce practice time be devoted to serving and
suggested specific techniques for doing this. McGown and the U.S. men’s volleyball team followed the suggestions. Although
the team was ranked 14th in the world, it managed to finish fourth in the 2004
Olympics. McGown attributed a lot of this success
to the advice he got from professors Fellingham and
Reece.

In the 2008 Olympics in Beijing, with further help from Fellingham and Reece, the Team USA men’s volleyball squad
made it to the top, winning the gold medal.

Among other projects, Fellingham and Reece have since worked with Philadelphia Eagles coach Andy Reid, a former
BYU football player, to try to help Reid and the Eagles improve their
performance on the football field.

**• Clinical Trial Studies**

The purpose of clinical trial studies typically is to
compare the efficacy of two or more different treatments, or, less typically,
the side effects of such treatments. Both issues lead to statistical inference
questions in which the task is to compare the proportion of successes to failures
of the treatments. Over the years, there have been a number of clinical trial
studies that have generated controversy.

One such study was conducted by Merck in 2000 to compare the
side effects of its non-steroidal anti-inflammatory drug, Vioxx,
to those of naproxen—the generic name of a competing non-steroidal
anti-inflammatory drug produced under a variety of brand names such as Aleve. In
this study, as reported in Ziliak and McCloskey (2008),
eight of the people treated with Vioxx suffered heart
attacks during the study versus only one from the group receiving naproxen. Merck
used classical statistical testing procedures in its analysis. Ziliak and McCloskey (2008) castigated Merck for claiming
that because of “the lack of statistical significance at the 5 percent level,
there was no difference in the *effects* of the two” drugs. Merck would later be sued for such adverse side effects; its
losses were in the billions of dollars.

The question is, what does all of
this have to do with insurance?

**• Applications in Insurance**

It turns out that Bayesian statistics has wide application
to insurance as well as to sports.

I have used Bayesian statistical procedures to model the Federal
Housing Administration’s home equity conversion mortgage (HECM) program.^{[3]}^{} In
fact, my article describing that work won the Actuarial Education and Research
Fund’s 1989 Practitioner’s Award. Along with Professor Fellingham (2005) and his BYU statistics department colleague Dennis Tolley,
I have authored an article on predicting future health claim costs.

Bayesian models can also be employed as part of the NAIC’s
Solvency Modernization Initiative. For example, Glenn Meyers (2008) of ISO has
written a series of articles in which he uses Bayesian models to predict future
claim losses for property/casualty insurance. An advantage of this approach is
that the result is an entire probability distribution, so the results are
already calibrated. Of course, almost no statistical models are exactly correct
and these Bayesian models are no exception. So, even the best models are
unlikely to produce precisely calibrated results.

Going beyond insurance, Kanellos (2003)
describes an application of Bayes’ Theorem to data searches in his article “18^{th} Century Theory is New Force in Computing.” This should provide an idea of the
wide range of problems that are amenable to solution by Bayesian methods.

**• Brief History of Bayesian Statistics**

Before concluding, let us try to sketch the origin of the
Bayesian paradigm of statistics.

Bayes’ Theorem goes back to the Reverend Thomas Bayes, who
was born in London around 1702. According to Stigler (1987), “Bayes was an
ordained Nonconformist minister in Turnbridge Wells
about 35 miles southeast of London.” When Bayes died in 1761, he left £100 and
his scientific papers to his friend, Richard Price. After adding an
introduction and an appendix, Price presented Bayes’ essay “Toward Solving a
Problem in the doctrine of Chance” to the Royal Society.

The famous French astronomer, probabilist and mathematician Pierre Simon Laplace, who
lived from 1749-1827, both championed and extended Bayes’ work. In his
text *Essai** philosophie sur les probabilities (Philosophical Essay on Probabilities), *Laplace (1825) described a mathematical* *framework for conducting statistical inference. This constituted the
essence of Bayesian inference. During the later part
of the 19th century, Bayesian statistics fell out of favor with most
statisticians who, preferred the competing classical
or frequentist paradigm of statistics instead.

However, Bayesian statistics has enjoyed a renaissance over
the last 70 years. Its first major application during this period was its use
by British mathematicians to break the German cipher machine known as “Enigma.”
These mathematicians preferred their own theory based on Bayes’ Theorem to the
competing statistical theory based on relative frequencies championed by their
compatriot R.A. Fisher.^{[4]} While
it is a large stretch to say that Bayes’ Theorem won World War II for the
British, it certainly helped their cause.

__References__

DiVenti, T.R. and T.N. Herzog, “Modeling Home Equity
Conversion Mortgages,” *Transactions of
the Society of Actuaries*, Vol. XLIII (1991), 261-275.

Fellingham, G.W., H.D. Tolley and T.N.
Herzog, “Comparing Credibility Estimates of Health Insurance Claim Costs,” *North American Actuarial Journal*, Vol.
9, No. 1 (2005).

Hodges, A., *Alan Turing: The Enigma*. London:
Vintage, Random House (1992).

Kanellos, M. *18*^{th}-century
theory is new force in computing. CNET News.com, February
18, 2003 (available at
http://news.cnet.com/Old-school-theory-is-a-new-force/2009-1001_3-984695.html).

Laplace, P.S., *Philosophical Essay on Probabilities*,
translated from the fifth French edition of 1825 by Andrew I. Dale. New York:
Springer (1995).

Meyers, G., “Stochastic Loss
Reserving with the Collective Risk Model,” *Casualty *

Actuarial Society E-Forum, Fall, 2008.

Stigler, S.M., *The** History of Statistics: The Measurement of Uncertainty
Before 1900*. Cambridge: Harvard University Press~~,~~ (1986).

Walch, T., “Y. statisticians may help Eagles’ game,” *Deseret News*, January 14, 2005
(available at http://www.deseretnews.com/article/600104761/Y-statisticians-may-help-Eagles-game.html).

Ziliak, S.T. and D.N. McCloskey, *The** Cult of Statistical Significance*. Ann Arbor, Mich.: The University
of Michigan Press (2008).