The omnium is a multi-discipline track cycling event which has debuted at the Olympics this year. It is made up of six events (flying lap, points race, elimination race, individual pursuit, scratch race and time trial) and has a fairly simple point scoring system to determine overall placings: for each event the rider who places first scores 1 point, second 2 points, and so on, with the rider with the lowest total number of points across the 6 events being the winner.
In the men’s event, British rider Ed Clancy won the 1km time trial with a time of 1:00.981 (a time which would have won Olympic gold in the 1km time trial at the 2000 Olympics). This was over a second faster than all other riders in the omnium, a sizeable margin over such a short distance, but in the omnium the size of the margin is immaterial – Clancy only need have won by the smallest of measurable margins to still take just one point.
This had me wondering how the omnium might work differently if it were scored in the manner of the athletics multi-discipline events, the heptathlon and decathlon. In these events, heights, distances and times are converted into point scores according to a formula for each individual event. Basically, the faster you run/farther you throw/etc the more points you get. For the omnium, this would require the devising of a points system for each event. For the events contested against the clock (flying lap, individual pursuit, time trial) this would be feasible, but the performance of the riders in the bunch races (points race, elimination race, scratch race) is relative to one another, for example the results of the elimination race (in which the last placed rider is eliminated every 2nd lap) is simply a ranking. Thus for these races it would be difficult to devise a performance-based points system and so the ranking-based system makes sense.
However, we can apply the omnium points system to the results of the heptathlon at the 2012 Olympics. The different rankings (HR = heptathlon points system rankings, OR = omnium system rankings) are shown in this table (full spreadsheet here.)
|Jessica Ennis (GBR)||1||1|
|Lilli Schwarzkopf (GER)||2||2|
|Tatyana Chernova (RUS)||3||4|
|Lyudmyla Yosypenko (UKR)||4||3|
|Austra Skujytė (LTU)||5||11|
|Antoinette Nana Djimou Ida (FRA)||6||7|
|Jessica Zelinka (CAN)||7||5|
|Kristina Savitskaya (RUS)||8||6|
|Laura Ikauniece (LAT)||9||10|
|Hanna Melnychenko (UKR)||10||8|
|Brianne Theisen (CAN)||11||9|
|Dafne Schippers (NED)||12||13|
|Nadine Broersen (NED)||13||16|
|Jessica Samuelsson (SWE)||14||14|
|Katarina Johnson-Thompson (GBR)||15||12|
|Sharon Day (USA)||16||17|
|Yana Maksimava (BLR)||17||19|
|Eliška Klučinová (CZE)||18||20|
|Ellen Sprunger (SUI)||19||18|
|Olga Kurban (RUS)||20||21|
|Marisa De Aniceto (FRA)||21||24|
|Györgyi Farkas (HUN)||22||25|
|Grit Šadeiko (EST)||23||22|
|Sofia Ifadidou (GRE)||24||28|
|Ivona Dadic (AUT)||25||27|
|Sarah Cowley (NZL)||26||31|
|Louise Hazel (GBR)||27||26|
|Ida Marcussen (NOR)||28||29|
|Chantae McMillan (USA)||29||23|
|Jennifer Oeser (GER)||30||15|
|Julia Mächtig (GER)||31||30|
|Irina Karpova (KAZ)||32||32|
A Spearman’s rank correlation coefficient of 0.9242 shows that the two rankings are strongly correlated as we’d expect, but for individual athletes the change of system can make quite a difference. Under the omnium system, the Russian Tatyana Chernova would lose her bronze medal to Lyudmyla Yosypenko of Ukraine. Other athletes can fall or rise a considerable number of places. Lithuanian Austra Skujytė, strong in the field events, finds the gains from her vastly superior shot putting limited as she drops 6th places. Meanwhile, for Jennifer Oeser of Germany, her considerable losses from the 800m (which she failed to finish, and so scored 0 points) are limited so much that she climbs 15 places.
It should be noted that the athletes perform in the heptathlon with knowledge of the rules and their performances will be affected accordingly. However, the heptathlon points system is probably viewed as being fairer in that greater efforts reap greater rewards irrespective of how other athletes have performed. It also enables heptathletes to contest for world records as all other track and field athletes can.
I’ve only looked at one heptathlon competition here, and one could look at more to see what effect an omnium-style points system has in those cases. It could also be applied to other multi-discipline events such as the decathlon, modern pentathlon and the individual and team all-around gymnastic events (how the system would apply in the team all-around is another question: would gymnasts be ranked individually in each event or would their scores be combined and then the teams ranked in each event?)
Note: to break ties in the individual events, where possible I have used standard tie-breaking rules for those events, i.e. looking at next best throws/jumps in the long jump/javelin/shot put and using ‘countback’ for the high jump.