Last night, after two days of intense competition, the Olympic Heptathlon finally finished. Team GB’s Jess Ennis secured gold despite the scoring system that is weighted against her, as we showed a few weeks ago. In the wake of this, we’re going to have a look at what would have happened using the scoring system that we proposed as an alternative at this Games. Would the results have been the same? Would it have been fairer?
Firstly, the official results for the Heptathlon are here for those who want to view them as we go along. Secondly, I recommend you read the first post before we continue; this post may not make much sense without that background.
Let’s just clarify what our scoring system aims to do. The point of the Heptathlon is to find the best all-round athlete over 7 events. Therefore, we think that all 7 of these events should have equal importance in deciding on a winner. One criticism of our Proposed Scoring System (PSS) is that there are more running and jumping events than throwing events, and thus the throwing events should be given extra weight. However, the way we interpret the IAAF’s Official Scoring Tables is that there is no deliberate weighting towards any one of the 7 events. Scoring for all 7 events was derived using the same means: finding benchmarks for 0, 1000, and 1200 points and finding a curve between them that was sufficiently progressive to encourage athletes to keep improving. As such, we feel that any accidental weighting in the original system should be removed, which is why we constructed the PSS. PSS was designed precisely to make sure that all events are equally weighted, and it is up to the IAAF to decide whether they want to honour the intentions of Karl Ulbrich, the inventor of the current scoring system, or whether to keep his outdated figures for new reasons.
On Friday morning, the Olympic Heptathlon got off to an incredible start in the 100m Hurdles. Jess Ennis ran an incredible time of 12.54s, smashing the World Record for the fastest Hurdles ran in a multi-event competition, and taking a quarter of a second off her personal best. Her time was so quick that it would have won the individual gold medal for the Hurdles in Beijing 2008. She scored 1195 points, and had a lead of 17 points over Zelinka in 2nd place. She was almost a second quicker than Chernova, the World Champion in Daegu last year, and took a lead into the second round.
In the next event, the High Jump, Lithuanian athlete Skujyte topped the scoring with 1.92m, earning her 1132 points, and pushing her up into a closely contested 2nd place, but due to a poor performance in the Hurdles, still trailed Ennis by 149 points. In the shot put, Skujyte put out a fantastic score of 17.31m (1016 points), breaking the World Heptathlon Shot Put record by 2cm, to rocket her into Gold medal position, 64 points ahead.
Whilst this was a remarkable round from Skujyte, if we compare it to Ennis’ Hurdles, which were at least as good a performance, arguably better, then we see that the event that Skujyte happened to be remarkable in is a much more advantageous event to be good at than the Hurdles. Both Skujyte and Ennis broke world records in their respective performances, Ennis by a greater margin, but Skujyte’s moved her much further away from the rest of the field. Ennis came a respectable 10th in the Shot Put, and scored 203 fewer points than Skujyte. However, Skujyte came a shocking 32nd in the Hurdles, but only dropped 217 points off Ennis. In other words, despite being in contention in the Shot Put, Ennis lost almost as many points to Skujyte on the Shot Put as she gained off her in the Hurdles, where Ennis had the greatest run a Heptathlon has ever seen and Skujyte was one of the very worst performers in that event. This is because in the current scoring system, the Hurdles is the most under-rewarded and the Shot Put the second most over-rewarded.
After the 200m, Ennis regained her lead, but after that event, Skujyte was still in 2nd place overall despite another 32nd place finish. After the long jump, Tatyana Chernova moved up to 3rd place after a very strong jump of 6.54m (1020 points). Then came the javelin – the most over-rewarded even in the competition. Schwarzkopf performed well, and jumped up from being 100 points behind the podium to being within 10 points of Bronze. Ennis performed reasonably well in her worst event, and went into the 800m with a considerable lead of 188 points – and with Ennis being a very strong 800m runner, the Gold it seemed was already hers. However, the race for the other two podium spots was very interesting: Skujyte was 82 points ahead of 2nd place but not known as a strong 800m runner. 3rd, 4th and 5th were all within 10 points of each other, and despite being 44 points behind a medal spot, Chernova’s strong middle-distance running meant she could not be discounted.
The 800m ended with Ennis out in 1st and with a Gold that in the end was comfortable, winning by a large margin of 306 points. Skujyte did not perform well, and ended up slipping out of the medals down to 5th in favour of Schwarzkopf in Silver (originally disqualified for a lane infringement, but this was reversed on appeal), and Chernova in Bronze.
But what would have happened with PSS?
Ennis still would have won – in fact by even further. She would have 7086 points, a huge 399 points ahead of 2nd place. These extra points come from an additional boost for her fantastic Hurdles time, as well as not being penalised so much on her performances in the Shot Put and Javelin. Schwarzkopf, who leapt up the rankings after the javelin, would now be reduced to 3rd place, but only by 6 points, and Chernova would then take silver. Yosypenko would be unaffected in 4th, and Skujyte would remain in 5th, but be 99 points away from 4th rather than just 19. With PSS, it would not be possible for her to do so well after her poor performances in all three running events. All in all, only 3 of the top 10 would occupy the same position under PSS, with Nana Djimou Ida dropping three places, from 6th to 9th, and medals changing. There is no doubting that PSS would make a difference. But is it fairer?
It feels instinctively wrong that you can break a world record whilst a competitor is in 32nd place, then be nearly as far behind as they were when coming 10th on a separate event. However, we do have some much harder evidence to show that PSS is definitely much fairer than the current scoring system.
The red squares representing the variance in PSS are much closer together than the blue diamonds of the current scoring system, showing that events are more evenly weighted in PSS
Apart from the 800m, which was extremely closely contested in this particular Heptathlon and is therefore anomalous with both scoring systems, PSS is closer to the average variance between 1st and 10th place in every single event. Unlike in the last post, when we were investigating the effects of the scoring system on a Heptathlon from which we derived the system, this is brand new: a perfect testing ground for our methods. And our conclusion is that they work much better than the current system does. This is a modern, elite, competitive Heptathlon, and this is clear proof that our Proposed Scoring System is fairer. If the IAAF are to change the system, then yes, we must consult larger datasets, but this is further proof that our system is fairer for athletes, and should be considered as a very real alternative to the current system.
We hope you have enjoyed this post. If you have, then please check out our last two posts:
The Physics of Diving: Tom Daley and Angular Velocity – How does Tom Daley manage to complete his famous Front 4 1⁄2 dive?
The Physics (And Maths) of Soccer: Offsides, Angles and Backspin - The offside rule is one of the most confusing in soccer. What is it and why are there so many controversial decisions surrounding it?
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Aren’t you assuming that ability to compete in each event is unrelated. Some events benefit more from a change in the event-averaged physique than others. For example whilst specialist 100m hurdlers and 200m sprinters generally have similar body shapes Shot Put specialists have a very different physique. Thus even limited to these three events you would need to weigh the Shot Put more if you wanted to put the same importance on all three events.
There is an advantage in sticking with the current scoring system in that it facilitates comparisons with previous events and atheletes.
Perhaps, rather than trying to influence a change in the scoring system, it would be worth making the coaching teams of the GB athelets aware of it’s consequences so that they can tailor training programs more effectively.
The writer makes a crucial error in that he bases his entire premise on an ‘instinctively perception of 1st vs 32nd place’. If the field is close on one event, 1st or 32nd place could be close in points. Whereas in another event the field might be more spreadout thus resulting in more of a point spread for first and last. You should not base your point system on what other athletes do in the same competition. Don’t sweat it though, statistical intuition is the most overated competence, even professional mathematicians make the same errors in judging these kind of problems.
How would I do it? I agree that excelling in a particular event needs extraordinary points, but I would rather use a system which equalizes the current world record of any event with say 1300points and make more of a fair spread by using historical data of the development of the world record by the decathlon athletes themselves. The idea behind this is that you need to make a relation between the original specialist and the decathlon allrounder. This way you would punish an athlete which underperforms even by decathlon standards, and reward one if he or she excells by world standards…
Thanks for your comment,
I think that it seems strange to base a scoring system on two separate sets of bench marks, namely world records for individual events and multi-event world records. This wouldn’t create a very natural curve, and as a result, the scores could be extremely turbulent at particular points. For example, the individual world record for women’s shot put is 22.63m. The world record for a heptathlete in the shot put was set last by Skujyte last week, at 17.31m. This means that there would be no data points between 17.31m and 22.63m for you to rely on, yet there are several below 17.31m (the previous heptathlon world record was 17.29m). Therefore it would be difficult to formulate a consistent scoring system.
Now how does that phrase go. Lies, damn lies and statistics. Instead of whining about the supposed unfairness of the current scoring system and attempting to devalue the throwing events why not encourage British athletics to embrace such events. Was in not telling that whilst the OBS provided coverage of both the mens and womens javelin competitions in full the BBC were unable to find anybody to offer a commentary. I don’t think Czech television had such a problem.