On Friday night as Johnson-Thompson geared up for her final attempt at the high jump, you could see her competitor, Belgium’s Nafissatou Thiam, standing and clapping in time with the spectators. Afterwards both women hugged warmly before running away to prepare for the next event. How Olympian!
The heptathlon is one of a clutch of multi-discipline “combined events" at the Olympics that are, in some ways, the epitome of the entire spectacle. Far more so than marquee events such as the 100m sprint, the heptathlon and decathlon truly showcase the human athlete in all her versatility. In order to win a medal Ennis-Hill, Johnson-Thompson and Thiam will have to compete in three running events (100m hurdles, 200m and 800m), two jumping events (High Jump and Long Jump), and two throwing events (Shot put and Javelin). These events are spread across two days in a particular order culminating in an 800m final. It is an intense, relentless examination of the athlete’s mind and body.
There is just one aspect of the heptathlon, however, that seems utterly incomprehensible. And it is a biggie. I’m referring to the point-scoring system, of course. What the hell is going on there?
At the time of writing this piece, Ennis-Hill is leading the table with 4,057 points after four events. Belgian Thiam is second with 3,985, Barbadian Akela Jones is next with 3,964 and Johnson-Thompson rounds off the top four with 3,957 points.
At first glance this seems unremarkable. Until…you realize that it all seems a bit strange. Is each event marked out of 1,000 points? If so, how come Ennis-Hill has 4,057? Also how do you mark the 100-metre hurdles, the shot put, the high jump and the 200m in such a way that you can add all the scores? How do you even begin to compare scores in such disparate disciplines?
Look at the break-up of Ennis-Hill’s marks and there is little clarity to be found. Why did she get 1,149 points for running the 100m hurdles in 12.84 seconds. While Johnson-Thompson scored 1,053 points for running it in 13.48 seconds.
What in the what in the how???!!!
Welcome, my friends, to the slightly mind-bending world of “combined events" scoring tables.
These tables, first developed over a century ago, help us to convert performances in different disciplines in to scores than can then be added to each other for the purposes of ranking and medals. There was simply no other way to figure out winners of “combined events".
How do you compare someone, for example, who comes first in the sprint, third in the javelin and sixth in the long jump, to someone who comes second in the sprint, sixth in the javelin and first in the long jump?
So the boffins who worry about this kind of things began to make tables, much like logarithmic tables, to convert diverse event scores into points. In one of the definitive papers on the art and science of scoring tables, The development of combined events scoring tables and implications for the training of decathletes, Viktor Trkal, explained that there were “three basic types of combined events points table: linear, progressive, and regressive. In linear tables, the increase in points is even and in line with the improvement in performance, from the lowest score up to the peak. This is expressed as a straight line on a graph. With progressive tables, the growth in points increases with the improvement in performance. Graphically, this is shown as a rising concave curve. With regressive tables, the growth in points falls with improving performance. This is shown as a downward concave curve on a graph."
Confused? Join the club. There are an astonishing number of research papers on the statistics and probabilities of heptathlon scoring, some of them pretty hard for most sports fans to decipher.
For instance, “The general problem in determining the sum of points achieved in the heptathlon is that, on the one hand, the evaluation of the individual performance in a discipline follows normative assumptions about the transformation rules, and on the other hand, linearity between performances measured and points achieved is impossible."
What I’ve been able to gather after many hours of reading and paracetamol-taking is as follows. The points possible in an event range up to 1,000, which is given to a high-standard performance. Anything above 1,000 points requires an exceptional performance in that discipline. Thus, despite performing very poorly in the shot put, Ennis-Hill still has more than 4,000 points from four events, because she was exceptional in the other three, scoring above 1,000 in all.
These points are calculated using one of three equations—originally developed by Dr. Karl Ulbrich in 1952—one each for jumping, running and throwing. The running equation, for instance, is:
P = a*(b-T)^c,
where P is points, T is for seconds and a, b and c are constants, a different set of which exist for each event.
Thus, each performance by each participant in the heptathlon is fed into an equation, which translates this into a score. Which is then accumulated through two days of frantic competition.
It is not a system without complaints. For instance, this analysis finds that the scoring unfavourably rewards those good at throwing.
But overall, I would warn anyone without adequate statistics chops from venturing anywhere close to the mathematics involved. Instead, let us sit back and enjoy the final day of women’s heptathlon. All you need to do is keep in mind that any total above 7,000 is exceptional. This has only happened nine times in history. Six of those totals were by the great Jackie Joyner-Kersee.
Can Jessica Ennis-Hill make it ten?