This excerpt from Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics
Robert B. Banks brings up some questions to consider when thinking about how to score the Olympics. Read the complete chapter in our new Princeton Puzzlers edition of this book, available in February 2013.
“In response to the sports reporter’s question, the coach replied, “Well, we don’t know for sure, of course, but based on the results of our statistical analysis, there is a 90% probability that the team will set a new Olympics record, perhaps even a new world record.” The sport reporter replied, “well, good luck, coach.”
Key words: for sure, of course, statistical analysis, about, probability, perhaps, luck.
The subjects of probability and statistics are extremely important areas of the broad field of mathematics. In this chapter, and those that follow, we shall look at several topics which show how statistics and probability are used to analyze many kinds of phenomena and events. A complete list of the practical applications of statistics and probability would be endless: everything from the probability that it will rain tomorrow to your likelihood of winning at Las Vegas and from the annual cost of your life insurance to your chances of being kicked in the head by a horse or struck by lightning or attacked by killer bees.
From an almost infinitely long list of applications, we shall consider only a few. We start with an analysis of the medal scores of the 1992 Summer Olympic Games held in Barcelona. In subsequent chapters, we go on to fantastically interesting things like dropping a needle on a table to compute the numerical value of π, determining the probability that two people, within a certain size group of people, have the same birthday, calculating the minimum cost of having all your teeth extracted, counting the number of rice grains on a chessboard, and seeing how well a great many chimpanzees do behind a great many typewriters. But, for now, Jet’s go to the Olympics!
We Need a Better Scorekeeper for the Olympics
In recent years we have observed that the Olympic Games have become increasingly nationalized, politicized, and commercialized. In addition, we have noted that preparation for and participation in the Games has become almost a whole new science. Wind tunnel studies are conducted to attempt to reduce the drag coefficients of bicycle riders and ski jumpers; mathematical models are devised to improve the biomechanics of high jumpers and pole vaulters; high-speed photography is employed to analyze the movements of gymnasts and relay racers; computer analyses are carried out to optimize the performance of kayak rowers and long-distance runners; and so on.
It seems as if everything relating to the Olympic Games is improving except for one thing: the system of final scoring of the participants. After all the incredibly hard work by the athletes and coaches and the countless hours of television viewing by billions of people around the world, all we get at the end is simply a dull column of numbers that tabulates how many medals each country has been awarded. A great many people believe that this denouement-this final outcome-is entirely inadequate.
We also read and hear a lot about the need for “level playing fields” in all kinds of arenas, especially economic and political. In no arena is this need greater than in the matter of determining the final scores of the Olympics. To illustrate this need, the following points and questions are raised:
1. The annual gross domestic products per capita (GDP/cap) of China, Nigeria, and Ghana are nearly identical (about $350). We can say that the three countries are equally “poor”. However, China has a population of 1,180 million, Nigeria 100 million, and Ghana 17 million. Thus, China has 70 times more people than Ghana from wh1ch to draw its athletes.
2. By the same token, the GDP/cap of the United States, Canada, and Norway are about the same ($20,000). So they are equally “rich.” But the population of the U.S. is 260 million, Canada 28 million, and Norway about 4 million. We note that the U.S. has a pool of athletes 65 times larger than Norway’s.
3. Indonesia has a population of 195 million and GOP /cap of $700. Cuba has a population of 11 million and GDP/cap of $1,400. Qatar has a population of 0.50 million and GDP/cap of $17.000. Which country would be expected to receive the most Olympic medals: that country which is the poorest but most populous, that country which is the richest but least populous, or a country in between?