Race Time Prediction for Selected New Zealand Ultramarathons

Athletes have a natural tendency to want to predict their times over different distances and different events. This is relatively straightforward for most road events, but is considerably more difficult for ultradistance events that might have varying amounts of ascent and descent, be at different elevations, and have different underfoot conditions. This post presents the results of an analysis of actual performances in New Zealand ultramarathons, and provides factors to enable an athlete to predict their race time as a multiple of a standard marathon time.

Adapted from: Andrew Shelley, "Race Time Prediction for Selected NZ Ultramarathons", NZUA News, Issue 6, December 2009.[1]

• Introduction
• Methodology and Data
• Rate of Slow Down
• Race Time Prediction
• References

Introduction

The analysis captures most of the ultramarathons currently available in New Zealand:²

• Heaphy Five-O;
• Hutt River Trail;
• Kepler Challenge;
• Marton-Wanganui;
• Molesworth Run;
• Great Naseby Water Race 50km, 80km, and 100km;
• Saint James Ultramarathon;
• Sri Chinmoy 50km and 100km events (Christchurch);
• Tarawera Ultramarathon (2009 course);
• Taupo 100km (both the 2009 course and pre-2009 course);
• Te Houtaewa 90 Mile Beach run; and
• Triple Peaks Challenge.

The analysis compares results for an individual athlete across different events and distances. Comparison across events and athletes allows us to identify:

• The rate at which the average athlete slows down with longer distances;
• How difficult an event is compared to a “standard” road marathon; and
• A prediction of an athlete’s time for an event, expressed as a multiple of a standard road marathon.

Methodology and Data

For each athlete the result in one event was paired with that athlete’s result in other events. Regression analysis was then used to calculate the average ratio of finish times in an event to finish times in a standard marathon. The methodology ensures that each race result is relevant, even if an individual athlete has not completed a marathon. For example, the results for an athlete who has completed the Kepler Challenge, the Saint James Ultramarathon, and one of the Sri Chinmoy events will contribute to establishing how the times for those three events should relate to each other. Other athletes will have completed both a marathon and one (or more) of the ultramarathon events, and times for those athletes will help establish the relationship to the time for a standard marathon.

The primary data set comprises the race results for the relevant ultramarathons over recent years. Four years of data was used where possible, but for many events fewer years were available. Table 1 shows the years used for each event. The database of ultramarathon race results has one or more race times for 1,269 athletes.

For each athlete in the database of ultramarathon race results a marathon time is also obtained where possible. Marathon times were taken from the Buller Gorge Marathon (2006-2009), the Christchurch Marathon (2006-2009), the Dunedin Marathon (2007, 2008), the Harbour Capital Marathon (2007-2009), the New Plymouth Marathon (2006-2009), the Rotorua Marathon (2007-2009), and the Wairarapa Country Marathon (2006-2008).³ While longer time series were available for some events, a wider date range increases the likelihood that differences in the athlete’s fitness level (and age) would affect the results. All race results were obtained from race websites.

Individuals that were known to be injured or have participated in another ultramarathon in the previous two weeks have had those data points removed. Where an athlete had participated in a particular event in more than one year, the fastest of that athlete’s times was used as the relevant observation.

The final data set consisted of a set of times for athletes who had either participated in a marathon and at least one ultramarathon, or who had participated in at least two ultramarathons. There were 373 athletes in the final database.

The only remaining data that is required is the distance for each race. Distances and sources are summarised in Table 1 below.

Table 1: Race Distances and Years of Data

Race	Distance	Source for Distance	Years of Data
Road Marathon	42.2km	Assumption	2006-2009
Heaphy Five-O	78.4km	Distance on DOC website	2008
Hutt River Trail	60.25km	GPS measurement by author (twice)	2008, 2009
Kepler Challenge	61.3km	Race director private communication with Matt Bixley	2006-2008
Great Naseby Water Race	50.1km	GPS measurement 10.02 km/lap	2008, 2009
	80.16km
	100.2km
Molesworth Run	84.0km	Race website	2006-2008
Saint James Ultramarathon	67.2km	GPS measurement by author (once)	2007-2009
Sri Chinmoy	50.0km	Race website	2006-2009
	100.0km
Tarawera Ultramarathon	90.0km?	No accurate distance available.	2009
Taupo 100km	100.0km	Race website	2006-2009
Te Houtaewa 90 Mile Beach	60.0km	Race website	2008, 2009
Triple Peaks Challenge	47.0km	Race website	2009

Rate of Slow Down

A common approach used for race time prediction is the formula proposed by Riegel (1981a, 1981b):

The factor n is a measure of how athletes slow down over longer distances. Having analysed American data, Riegel proposed factors of n = 1.06 for sub-marathon distance events and n = 1.18 for ultramarathon events. The American results suggest that for sub-marathon distances speed declines by 6% as distance doubles, and that for ultramarathon events speed declines by 18% as distance doubles.

My analysis of New Zealand results suggests a factor of n =1.197 for ultradistance events, i.e. we seem to slow down just a little more than Riegel predicts from American data. An athlete with a “standard” marathon time of 3h30 can then use the Riegel formula and the New Zealand slow down factor to predict a race time over a “standard” 100km event:

According to the formula an athlete who can run 3h30 for a standard marathon should, with appropriate training, be able to run just over 9h50 for 100km.

For the period of the analysis New Zealand had three 100km events: the Sri Chinmoy 100km, the Great Naseby Water Race, and the Taupo 100km. The Sri Chinmoy course is flat and fast and provides the ability to run the “standard” time. The Great Naseby Water Race and the Taupo 100km are slower courses, so the multiplier above will not apply. The following section presents the multipliers for each event – being based on actual results these multipliers reflect the relative difficulty of each course.

Race Time Prediction

The multipliers for each event are presented in Table 2 below. In addition to the actual events, multipliers are included for a “standard” 80km. The Sri Chinmoy 50km and 100km events are conducted on a flat, fast course and can be considered to be the “standard” events for those distances. As calculated earlier, the multiplier for the reference 100km is 2.81.

Table 2: Race Time Prediction Multipliers, Ordered by Multiplier

Event	Distance (km)	Multiplier
Reference 50	50	1.23
Sri Chinmoy (Christchurch) 50	50	1.23
Naseby 50.1	50.1	1.34
Triple Peaks Challenge	47	1.59
Hutt River Trail	60.25	1.73
Marton-Wanganui	66.4	1.88
Te Houtaewa 90 Mile Beach	60	1.93
Reference 80	80	2.15
Kepler Challenge	61.3	2.15
Naseby 80.16	80.16	2.36
Saint James Ultramarathon	67.2	2.69
Molesworth Run	84	2.69
Heaphy Five-O	78.4	2.75
Sri Chinmoy (Christchurch) 100	100	2.81
Naseby 100.2	100.2	3.08
Tarawera Ultramarathon	90	3.18
Taupo 100	100	3.32
Note:(*) Although the precise distance for the 2009 edition of the Tarawera Ultramarathon is unknown, this does not affect the overall multiplier.

A few points that can be drawn from the analysis:

• Even after switching to the new “flatter” course in 2009, the Taupo 100k remained a very tough course with no significant change in the multiplier. Running up both the Waitahanui Hill and the Hatepe Hill in the first half of the race appears to be as hard as the rolling hills encountered on the first half of the old course. The further refinement in 2010 without the Waitahanui Hill and Hatepe Hill should hopefully see an improvement in times with the multiplier dropping closer to 3.0.
• Multipliers for the Heaphy Five-O, the Molesworth Run and the Saint James Ultramarathon are almost identical. The similarity in multipliers between the Molesworth Run (2.69) and the Saint James Ultramarathon (2.69) confirms what the race directors for the Molesworth Run already thought to be true.⁴ The similarity in multipliers between the Heaphy Five-O (2.75) and the Saint James Ultramarathon (2.69) confirms the views of a number of athletes that have run both races.
• Running on sand appears to be quite hard, even if it is well-packed. The multiplier for the 60km Te Houtaewa 90 Mile Beach run is 1.93, in comparison to the 1.73 for the 60.25km Hutt River Trail ultramarathon (which includes a significant hill) and 2.15 for the “standard” 80km event. It is unclear whether the apparent difficulty is accurate, or whether the distance is understated or the event attracts under-prepared runners deciding to “give it a go”.

A range of possibilities exist for further extending this analysis. One possibility is to explore whether the rate of slow down differs between experienced and inexperienced ultrarunners, or with the speed of the runner. Another possibility is to extend the analysis to include other events that may be of interest to ultrarunners, such as some of the longer mountain and trail races. The database could also be used to identify the extent to which there is a common community of runners between different races.

References

For further reading on Riegel’s formula see:
Riegel, Peter S. (1981a) “Athletic Records and Human Endurance”, American Scientist, May-June, 69:285-290.
Riegel, Peter S. (1981b) “A Statistical Analysis of Ultramarathoning Records”, Ultrarunning, September: 12-13.

The Running for Fitness race time calculator has five different race time calculators, including the Riegel method. However, the Riegel calculator has the factor of 1.06 hard coded, so it will be a bit optimistic for ultradistance events.

Endnotes

[1] Thanks to Matt Bixley for helpful comments and contributions to data sources.
[2] The Riverhead Adventures 50km Trail Run was excluded from the analysis because it was unclear whether the same course had been used in each year. The Kaweka Challenge 51km race (“Course 0”) is not included due to not actually having been run during the time period for the analysis.
[3] Results were not included for a number of smaller marathons that were judged by the author as being unlikely to be comparable to a standard road marathon, whether due to the nature of the course or because of communications with athletes casting some doubt on the course length. The Auckland Marathon was not included because (a) results were not available as a csv file or as a spreadsheet, and (b) examination of results available on the internet reveals many errors, including half marathon walkers classified as marathoners. Results for the Harbour Capital Marathon and the Rotorua Marathon were not available as a csv file or as a spreadsheet prior to 2007. Buller Gorge Marathon results for 2006 and 2007 and Christchurch Marathon results for 2006 taken from MarathonGuide.com. Dunedin Marathon results not available on the internet prior to 2007.
[4] Race director private communication with author.