Math A-lympiad: Final 1993-1994

Decathlon and heptathlon

In this exercise the participants can use the book ‘IAAF. Scoring tables for men’s and women’s combined events competitions’. (This book will be referred to as “yellow booklet”).

Introduction

In important athletic competitions such as world championships and the Olympic Games, many people wonder how the scoring is done in the decathlon for men and the heptathlon for women (see appendix 1). Most questions relate to the way in which performances in the various components of such a combined event (see appendix 1) are converted into points. There is therefore a need for an article to describe this clearly. In addition, such an article would provide a good opportunity to examine further a number of aspects of combined events and to examine possible variations. Such an article must satisfy a number of conditions.

General preconditions

• The article must be easy to follow for an interested layman.
• In order to increase the attractiveness of the article it must consist of more than just text. Charts can thus contribute here.
• In addition to the article, appendices, charts or text may also be given to give more detailed information to people who have more detailed questions.

Specific preconditions

1. Facts
   - A part of the article must deal with the history of the scoring, in particular the premises of Ulbricht (see appendix 2) and progressive and regressive performance tables/graphs (see yellow booklet, page 6).
   - There must be explanation on the tables that are currently used (see yellow booklet).
2. Considerations with regard to the facts
   - The tables currently used must be held up to the light in a critical way. The results of the 1992 Olympic Games can be used as an example for the arguments and reasoning (see appendix 3).
   - The all-round nature and/or extent of the decathlon must be considered. The world records in the individual events can be used in this respect (see appendix 4). Examine the all-round nature of the heptathlon in the same way. Are the winners real all-rounders or rather specialists in a certain section?
   - The difference between the decathlon and the heptathlon, or the difference between the performances of men and women must be considered.
   - The modern decathlon mainly consists of explosive events. Exceptions are the 400 metres (a kind of extended sprint) and the 1500 metres in particular. Do these events occupy a separate place with regard to performance? How does this point relate to the heptathlon?
3. A few questions which lend themselves to examination, the results of which can also be included in the article
   - The best decathlete at this moment, the American Dan O’Brien, missed the last Olympic Games, because he failed at his starting height in the pole vault in the American selection competitions. (The athletes themselves specify their starting heights. If you start too low then you have to jump more often and that costs energy.) With sports such as sailing the worst performance can be left out of consideration. This would have saved O’Brien. Is this a reasonable proposal that must be studied further, or would this spoil the beauty of the combined event? Would the results of the last Olympic Games change radically here or not at all? The disadvantage is that in their training the decathletes could just forget about a certain event that they find difficult. The risk of that would be that a lower performance in another event would have to stand. The condition for being able to drop an event is that all events “pay” the same.
   - Suppose that you are considering setting up a decathlon for pairs or threes. Different versions can be considered here: every sportsman does all events and the best result counts, or the events are divided equally (5-5 or 4-3-3). Put a team together (from the participants of the last Olympic Games) that would score the maximum. Can the Netherlands find a male duo or trio (see appendix 5) that would get more points than Robert de Wit on his own (Robert de Wit may not of course be in this team)?
   - A possibility more or less related to this is to consider starting an international combined event competition. A national team would then consist of two male athletes and two female athletes. The article must formulate ideas about the possible sporting content of such a combined event (which events and why) and about a possible way in which the teams could be compared with one another (points or otherwise, how to weight the performances of men and women).

Exercise
Write the article on the decathlon and the heptathlon that satisfies the general preconditions given above and the conditions given under points 1 and 2. Furthermore the article must deal with at least one of the questions given under point 3. A choice can be made here depending on the available time.

Appendix 1

The male decathlon consists of ten athletic events completed over two days.

The female heptathlon consists of seven events held over two days.

Appendix 2

Page 10 of the yellow booklet (last two paragraphs) contains a passage on the premises of Ulbricht. This is freely reproduced here: With track events two performances are chosen on the basis of statistical data. 0 points are given to the lowest performance and 1000 points to the highest. The performances are converted from time into speed and then there a linear distribution of points is made between the lowest and highest speed. The speeds are then converted into times to produce a table in which the times are linked to points. This yields a progressive table (graph). With field events Ulbricht takes the starting speed of the movement as the most important factor. This starting speed is converted into a jump or a throw. Ulbricht assumes that the distance covered is proportional to the square of the starting speed. A lowest and highest performance is selected in the same way as above to which 0 and 1000 points are awarded respectively. After that, the square root of the distance is taken and points are distributed linearly. After that the square roots are converted into distances to yield a table in which distances are linked to points. This yields a regressive table (graph).

Appendix 3

The results of the decathlon and heptathlon from the 1992 Olympic Games are given below.

Appendix 4

The world records (up to 1992 inclusive) in the various events are given below. These world records are (generally) not achieved by decathletes and heptathletes but by specialists in such events.

Appendix 5

Below are the best of season performances for 5 Dutch decathletes in 1992.