A question addressed to Part 1 of this post indicated that the development of a definition of competitiveness was lacking. I agree and provide the following in an attempt to elucidate the basis in a more complete way. The “statement of competitiveness” in Part 1 of this post is the following:
“The most defensible metric for such comparisons is the distribution of finishers as a function of percent back from the winning time.”
There is much background to this statement but I will summarize by pointing out that it is often misunderstood what ‘competitive’ is. An individual sport is competitive when the tail of the performance distribution is populated, i.e. the best talent has been attracted to the sport and this talent regularly performs at or near the individual’s attainable level. This axiom is based on the reality that individual athletic performance is the result of the interaction of many variables (talent (however one wishes to define it, but likely to be based on physiology), training, stress (physical and emotional), health, experience, etc.) and yields an approximately normal (or Gaussian) distribution of performance. Such a distribution has a ‘high performance tail’ that informs one as to the extent of the competitiveness of the sport. This tail is populated by athletes who perform at 3+ standard deviations from the mean. Here we are speaking of athletes who’s performance is beyond the top 0.27%. If this tail is populated, and provided there are a sufficient quantity of participants in the sport to ensure validity, then it is a direct measure of how competitive the sport (or event) is. A sometimes unappreciated derivative of this approach is the reality that such ‘3 sigma’ athletes are rare, very rare, and that the most competitive races will therefore reliably (although not always) exhibit this high performance tail. The 2011 London Marathon data presented in Part 1 of this post is indicative of a highly competitive event where the high performance tail of the distribution is nicely defined. Just ask someone like Max King or Sage Canaday (or any 2:15 marathoner) exactly how superior a 2:05 marathoner is- if they do not use the term ‘exponentially’, then they should as the differences are parametrized by an exponential function.
To further substantiate this approach, presented below is a table of the percent back analysis described in Part 1 for a few additional open* races- the 2012 Chicago Marathon, the 2012 Pikes Peak Marathon, and additional time series data for the Western States Endurance Run (2004-2011). Note the very low proportions of competitors finishing in the top 10% through the top 30% in the road marathons compared to the trail marathon and ultramarathon events. This supports a view that the competitive nature of the these events is likely at an immature state relative to road marathons. These data are not surprising given that the participation in trail and ultramarathon events is just now growing at a (seemingly) fast rate, whereas participation levels in road marathons has essentially plateaued (or are in slight decline). It is expected, as the trail and ultramarathon sports continue to grow, that the ‘high performance tail’ will have increasing probability of populating and statistically ‘superior’ performances will be extant, just as they are in road marathons.
The existence of a group of competitors who compete at a similar level and compose a ‘winning’ population in a sport does not mean that the sport is competitive. Examples of this have been seen in triathlon and cross country mountain biking. The early days of competition in these sports yielded winning finishing times (or speeds, in the case of mountain biking) that today, only 20-30 years later, are mediocre. Technology certainly played a role in the decreased times and speeds but, more importantly, these sports went through substantial growth coincident with significant improvements in performance. This is the result of the attraction of competitors to these sports whose ability and focus allowed for the continued challenge of what would, in times past, be considered ‘superior’ performance. These athletes pushed the boundaries of what was considered ‘possible’ i.e. the tail of the performance distribution was populated and rare, ‘3 sigma’, athletes became an integral part of the sports. There is every reason to expect that the same will obtain in trail and ultramarathon disciplines as participation goes mainstream. Given the current distributional data on ‘percent back’ from winning times (examples of which are provided above), it is apparent that the sport of trail ultra running is, from a performance perspective, in infancy. As stated in Part 1:
“If the 2011 London marathon data are indicative, these ‘sharp end’ ultramarathon competitors would be few and significantly better than the rest.”
At this point, statistically, the ‘sharp end’ competitors in ultramarathons are many and not that much better than the rest.
These data and the associated analysis are provided to add a data-based entry into the on-going discourse on competitiveness in ultramarathons. These comments are specifically intended offer an objective view, independent of individual athlete references.
*note: ‘Open’ races are those that do not involve any world-class time qualification for participation; ‘closed’ races such as world championships, Olympics, and numerous other races typically involve time or team (and sometimes both) qualifications. However, there is data to suggest that even the ‘selected’ populations in ‘closed’ races are self-similar to the at-large populations and therefore exhibit a normal (Gaussian) distribution and the arguments above would apply. This is a subject for another post.