Decathlon scoring tables

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The scoring tables for the decathlon have undergone continual evolution since their inception about a century ago, with several changes to both the character of the equations and the indices on which the equations are based.

Decathlon athletic track and field competition

The decathlon is a combined event in athletics consisting of ten track and field events. The word "decathlon" was formed, in analogy to the word "pentathlon", from Greek δέκα and ἄθλος. Events are held over two consecutive days and the winners are determined by the combined performance in all. Performance is judged on a points system in each event, not by the position achieved. The decathlon is contested mainly by male athletes, while female athletes typically compete in the heptathlon.

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Early decathlon tables

All of the earliest attempts at formalizing decathlon scoring, from the first formal submission (prepared by the U.S. in 1884) until 1915, involved linear scoring equations. [1] The American model was based on world records, but models concurrently used by several Nordic countries were based on their respective national records. [2]

United States Federal republic in North America

The United States of America (USA), commonly known as the United States or America, is a country comprising 50 states, a federal district, five major self-governing territories, and various possessions. At 3.8 million square miles, the United States is the world's third or fourth largest country by total area and is slightly smaller than the entire continent of Europe. With a population of over 327 million people, the U.S. is the third most populous country. The capital is Washington, D.C., and the most populous city is New York City. Most of the country is located contiguously in North America between Canada and Mexico.

In mathematics, the term linear function refers to two distinct but related notions:

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences and engineering disciplines, as well as in the social sciences.

The decathlon was first included in the Olympic Games in 1912, requiring a uniform standard. The first Olympic tables adopted were also linear functions; they were based not on world or national records, but, rather, on the 1908 Olympic records for each of the individual events. The tables were soon updated with the 1912 Olympic records – and the universally disliked extension of event scores to three decimal places was discarded in favor of integer scores – and the tables were used thus in the next four Olympiads. [1]

Olympic Games Major international sport event

The modern Olympic Games or Olympics are leading international sporting events featuring summer and winter sports competitions in which thousands of athletes from around the world participate in a variety of competitions. The Olympic Games are considered the world's foremost sports competition with more than 200 nations participating. The Olympic Games are held every four years, with the Summer and Winter Games alternating by occurring every four years but two years apart.

The rapid evolution of the scoring tables caused results to vary widely. For instance, Akilles Järvinen, the silver medalist in the decathlon in both the 1928 and 1932 Olympics, would have won gold in both years rather handily under most later years' scoring tables. [3]

Akilles Järvinen Finnish athlete and decathlete

Akilles "Aki" Eero Johannes Järvinen was a Finnish decathlete. He competed at the 1928, 1932 and 1936 Olympics and won two silver medals, in 1928 and 1932; he served as the Finnish flag bearer at all three games. He also won a European silver medal in the 400 m hurdles in 1934.

Silver medal medal awarded in sports and other competitions for achieving 2nd place

A silver medal in sports and other similar areas involving competition is a medal made of, or plated with, silver awarded to the second-place finisher, or runner-up, of contests or competitions such as the Olympic Games, Commonwealth Games, etc. The outright winner receives a gold medal and the third place a bronze medal. More generally, silver is traditionally a metal sometimes used for all types of high-quality medals, including artistic ones.

Tests for legitimacy

Beginning in 1920, the IAAF considered, at least, the following criteria for a legitimate decathlon scoring table: [4] (1) The table should reflect the fact that, at higher levels of performance, a unit gain (such as a decrement of 0.01 second in sprint times) is more significant than at lower levels of performance, because of the physiological limitations of the human body. (2) The scores for different events should be comparable, in a manner such that equal skill levels in different events (however difficult it is to define such a concept) are rewarded with equal point levels.

1934 scoring tables

In 1934, the IAAF adopted a new set of scoring tables, proposed by Suomen Urheiluliitto (the Finnish athletics federation), that had already been used for a few years in national competitions in Finland. This scoring system implemented vast changes, with the following features: [3] (1) All of the individual events were scored with exponential functions, rather than the linear functions that had characterized all decathlon scoring tables to date. For field events, this was a straightforward statistical procedure; for track events, the reciprocal of the athlete's time, representing speed, was used as the independent variable. (2) The tables ranged from 0 to 1150 points per event. Zero points corresponded to the performances of untrained schoolchildren, and 1000-point performances corresponded closely to world records.

Finland Republic in Northern Europe

Finland, officially the Republic of Finland, is a Nordic country in Northern Europe bordering the Baltic Sea, Gulf of Bothnia, and Gulf of Finland, between Norway to the north, Sweden to the northwest, and Russia to the east. The capital and largest city is Helsinki. Other major cities are Espoo, Vantaa, Tampere, Oulu and Turku.

Exponential function A class of mathematical functions

In mathematics, an exponential function is a function of the form

Multiplicative inverse of a number x, 1 divided by x

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth, and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse.

1950 scoring tables

After World War II, the Finnish and Swedish athletics federations joined forces to draft scoring tables appropriate for Olympic athletes' improved postwar performances. All of the tables remained progressive in nature; in fact, the progressive character of every one of the ten tables increased. [3]

1962 scoring tables

In the years following the implementation of the 1950 tables, controversy arose, in regard to the highly progressive character of the tables. Specifically, the tables conferred a distinct advantage on decathletes who were specialists in individual events, with passing, but not stellar, performances in the other events, while putting well-rounded athletes at a relative disadvantage. To remedy this problem, Axel Jörbeck, of the Swedish athletic federation, devised new tables that were actually regressive in throwing events, while retaining their progressive character in track events. [3] The rationale behind the changes was the proportion between kinetic energy imparted to a throwing implement and the square of its initial velocity – and therefore distance travelled – so that a progressive or even linear table caused unfairly large increments in the score for throwing events.

1984 scoring tables

By the early 1980s, more problems had been pointed out with the then-current scoring tables. [5] Specifically, the regressive nature of Jörbeck's tables for the field events seemed to obviate the importance of elite performances in those events; decathletes' field-event performances had improved to the point where further score increments were practically negligible. Moreover, besides sapping decathletes' motivation to improve in field events, the tables also gave an unfair advantage to competitors in the track events – both because those tables were still progressive and because decathletes' performances in those events were much closer to the world records.

The IAAF working committee therefore met in 1983 in Prague to develop improved tables, putting forth the following nine principles, which still stand today: [4]

  1. The decathlon scoring tables should differ from those used for individual event scoring.
  2. The scores for different events should be comparable, in a manner such that equal skill levels in different events (however difficult it is to define such a concept) are rewarded with equal point levels.
  3. The new tables should be one of the following:
    1. modified versions of the existing ones,
    2. linear in all events, or
    3. slightly progressive in all events.
  4. The tables should be applicable to all levels of performance, from youth to elite.
  5. Men and women should have different tables.
  6. Specialists' performances should be the basis for the scores in the tables.
  7. The new tables should be applicable now and in the future.
  8. The total scores using the new tables for the top world-class athletes should remain approximately the same (about 8500 points).
  9. As much as possible, the new tables should ensure that a specialist in one event cannot overcome top performances in the other events.

The 1984 tables are still in use today, with a slight update in 1998 (adding entries for the long throws for odd numbers of centimeters, which were rounded to the next-lower multiples of 2 cm until 1997).

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Bryan Clay athletics competitor

Bryan Ezra Tsumoru Clay is an American decathlete who was the 2008 Summer Olympic champion for the decathlon and was also World champion in 2005.

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Damian Warner is a Canadian track and field athlete specializing in decathlon, and was the winner of the bronze medal at the 2016 Summer Olympics. Warner previously won silver at the 2015 World Championships and was a bronze medalist at the 2013 World Championships. He also was the Commonwealth champion from the Glasgow games and the two-time and reigning Pan American champion from the 2015 and 2019 Games. Warner also holds the title to the Pan Am Games record and the Canadian record for the decathlon. Notable for his sprinting, Warner holds decathlon bests in the 100 m and 110 m hurdles, running a 10.12 and 13.44 respectively.

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References

  1. 1 2 Viktor Trkal. "The development of combined event scoring tables and implications for the training of decathletes". Archived from the original on 28 September 2007.
  2. ↑ "IAAF Scoring Table for Combined Events". IAAF Athletics. Retrieved 26 October 2017.
  3. 1 2 3 4 "The Decathlon in Olympic History". The Decathlon Association. Archived from the original on 13 January 2008.
  4. 1 2 "IAAF Scoring Tables for Combined Events" (PDF). International Association of Athletics Federations. 2004. Archived from the original (PDF) on 3 December 2007.
  5. ↑ "Official Handbook 2002–2003" (PDF). International Association of Athletics Federations. 2002. Archived from the original (PDF) on 11 July 2013.
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