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The Scoring For The Decathlon And Heptathlon Favors Running Over Throwing

How do you think the decathlon and heptathlon are scored?

Take a moment. OK, do you have your answer? It’s probably wrong. It also probably makes at least as much sense as — and possibly a good deal more than — the method used by modern track and field.

Decathlon, which at the Olympics is a men’s event, is composed of 10 events: the 100 meters, long jump, shot put, high jump, 400 meters, 110-meter hurdles, discus throw, pole vault, javelin throw and 1,500 meters. Heptathlon, a women’s event at the Olympics, has seven events: the 100-meter hurdles, high jump, shot put, 200 meters, long jump, javelin throw and 800 meters.

To tally these diverse events, which are measured in seconds, meters and centimeters, into a single overall score, the metrics for each event are fed into a series of equations. However, any scoring system for a multidiscipline competition will by definition have value judgments baked into it. In the case of the decathlon and heptathlon, that has resulted in decades of undervaluing throwing while overvaluing short-distance running, which in turn has resulted in top decathletes and heptathletes all converging around a certain kind of skill set and physique. It doesn’t have to be that way.

As it stands, each event’s equation has three unique constants — \(A\), \(B\) and \(C\) 1— to go along with individual performance, \(P\). For running events, in which competitors are aiming for lower times, this equation is: \(A \cdot (B – P)^C\), where \(P\) is measured in seconds. For field events, in which competitors are aiming for greater distances or heights, the formula is flipped in the middle: \(A \cdot (P – B)^C\), where \(P\) is measured in meters for throwing events and centimeters for jumping and pole vault.

\(B\) is effectively a baseline threshold at which an athlete begins scoring positive points. For performances worse than that threshold, an athlete receives zero points. 2

The \(A\), \(B\) and \(C\) constants vary by event and by gender. All events have a \(C\) parameter (the exponent) between 1 and 2, making the scoring system progressive. In track and field, that means that as an athlete performs better, he or she is rewarded increasingly generously. A progressive system thus especially rewards standout performances rather than a consistently good performance across events.

For example, the 100 meters formula for points is \(25.4347 \cdot (18 – time)^{1.81}\). A 0.75-second improvement from 11.50 to 10.75 would yield 165 additional points. However, another 0.75-second improvement from 10.75 to 10.00 seconds would yield 179 additional points.

This scoring philosophy wasn’t always in place. Early systems in the late 19th century merely ranked competitors in each event and summed those ranks. The first points-based system based on magnitude of results rather than relative rank came from the U.S. in 1884, but continued to award points on a linear scale — making a one-second improvement on a slow time as valuable as the same gain on a world record. Next came a Finnish table introduced in 1931 and formally adopted by the International Association of Athletics Federations in 1934, which acknowledged that performance is increasingly difficult to improve at higher levels because of natural limits of the body, and further improvements at those extremes should be rewarded more.

The first IAAF international women’s tables arrived in 1954, for which officials used principles of physics to devise the formulas. Unfortunately, the science was bunk, because it falsely assumed that velocity, rather than kinetic energy — which is proportional to the square of velocity — was the output of human work. This velocity-based system heavily discounted throwing events, which awarded points at a decreasing rate with higher performance. Points effectively stalled out after throwing a certain distance. Those calculations were soon adopted for men and remained in practice until 1984, when mounting pressure about the system’s lack of incentive to further improve throwing performance beyond a certain point pushed through reform.3

The 1984 tables used the principle that the world record performances of each event at the time should have roughly equal scores but haven’t been updated since. Because world records for different events progress at different rates, today these targets for WR performances significantly differ between events. For example, Jürgen Schult’s 1986 discus throw of 74.08 meters would today score the most decathlon points, at 1,384, while Usain Bolt’s 100-meter world record of 9.58 seconds would notch “just” 1,203 points. For women, Natalya Lisovskaya’s 22.63 shot put world record in 1987 would tally the most heptathlon points, at 1,379, while Jarmila Kratochvílová’s 1983 WR in the 800 meters still anchors the lowest WR points, at 1,224.

The 1984 change also made all parameters progressive, and targets of 8,500 and 6,500 were set for top overall scores for the men and women respectively.4

After decades of tumultuous modification in decathlon and heptathlon scoring, the tables set in 1984 are still in place. However, standout performances still earn more in certain events than they do in others:

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These charts unambiguously show where an athlete gets the best point return on performance, short-distance running, and it’s clear they’re investing their training accordingly.

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The system has a clear bias toward short-distance running events. This is in large part due to these running events having C (exponent) parameters all north of 1.8, significantly higher than throwing ones, which are between 1.0 and 1.1.

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It’s no surprise, then, that those who excel at decathlon/heptathlon specialize in sprinting, and their performances in those events closely mirror those of the specialists competing in the same individual events detached from the decathlon.

The average top 10 decathlete/heptathlete generalist in running events performs at something around 90 percent of the average medal-winning specialists. However, in throwing events, the generalists’ distances are only roughly 70 percent of the average medal-winning specialists’.

One might assume from these charts that top decathlete/heptathletes are uniformly tall, lean speed machines rather than brawny powerhouses that can hurl an object far distances, but the data suggests otherwise.

The correlation between BMI (body mass index) and overall points for men and women is indeed negative, but only -0.060 and -0.109, respectively.

Anecdotal evidence also doesn’t align with the notion that there’s a tradeoff between throwing strength and skill in other events: The winner of the competition has often been the best shot-putter in the field. But athletes are well aware of the minutiae and incentives of the scoring system before competing and train their bodies in such a way as to maximize points according to that system long before they hit the track. Thus, it’s likely that some stronger, heavier athletes simply decided before the competition either to slim down or not to compete.

There are strong positive correlations between better performance in each of the short-distance running events and long jump5 (all of which heavily rely on flat-out sprinting speed). There’s also positive correlation between the shot put and discus throw (though the other throwing event, javelin, has little correlation with those two). All other events have only small correlations between them.

Comparing which events correlate best to overall points, the men are highly correlated with long jump (0.74), while shot put, pole vault, discus throw and 1,500 meters each have correlations less than 0.50. For women, long jump (0.72) also correlates best with overall points, while javelin throw only correlates at 0.30. These findings corroborate research that shows that in the heptathlon, performance in speed events is overwhelmingly the biggest determinant in predicting overall success, dwarfing the importance of the strength and endurance events.

After 30-plus years of scoring table peace, is there still room for reform?

We don’t lack for options. John Barrow, a professor of mathematical sciences in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge, has proposed a physics-based system akin to the flawed 1954 model, but this time getting the science correct by using proportions based on kinetic energy. Another method, proposed by Wim Westera, a professor of digital media at the Open University of the Netherlands with a background in physics and math, attempts to construct a points model based on the frequency of performances. Also, researchers at Saarland University and the University of Kaiserslautern suggest a system based on standard deviations.

Perhaps another way to tweak the system would be to award outlier performances even more generously. Such a system might diversify competitor body types by creating different “paths” one could take to decathlon/heptathlon glory. As of now, most competitors earn roughly 700-1,000 points per event across the board. But a highly progressive system would create larger disparities in where an athlete derives his or her points. Faster athletes would focus on the running cluster of events and rack up the majority of their points there, while stronger athletes could aim to take the throwing path to gold.

Of course, none of these alternative scoring systems tackle the largest factor determining scores: the events themselves. The fact that the sprinting events and long jump so well correlate with each other puts a large premium on athletes who can reach top speeds.

Another way of adjusting for this imbalance is possibly removing a speed-based event from the decathlon to make the enneathlon. Or adding another strength-focused event (e.g., hammer throw) to form the hendecathlon. Women could go down to the hexathlon or up to the octathlon.

Footnotes

  1. Here are tables showing those constants for each event in the decathlon and heptathlon. (Opens PDF.)

  2. Strictly adhering to the formulas, athletes who don’t meet the threshold technically score a set of complex numbers with an imaginary component.

  3. In addition, a new high jump form and better technology in vaulting poles threw off many of the table’s underlying premises.

  4. At the 1984 Olympics, still contested under the old scoring system, the U.K.’s Daley Thompson missed breaking the decathlon world record by a single point. After the IAAF’s formal adoption of the new rules, though, his score increased enough to retroactively break the world record, breaking his tie with West German Jürgen Hingsen, a tie Thompson had also retroactively earned after an IAAF investigation revealed Thompson had been mistimed in the 110-meter hurdles as one one-hundredth of a second slower than his actual time.

  5. The correlations between the long jump and running events are technically negative, but running events aim for lower numbers– as in times — so in this sense, I’m calling them “positive.”

Jim Pagels is an economic researcher in Washington, D.C., and regular contributor to Forbes.

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