Age Handicapping Competitive Runners, Part 2: Tables for Speed Handicaps

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Introduction

Can the age-related decline in running speed seen in single age world record holders be meaningfully translated into an age handicapping system for local competitive runners?  I use the term “competitive” runners to designate the subset of runners in local races who prepare for and attempt to give their best performance in the race.  Competitors are essentially distinct from the relatively large group of social and recreational participants who are looking for a “fun” run, an opportunity to share an activity with a friend or friends, or to support some greater community cause.

When we consider the full spectrum of local race participants, whether social, recreational, or competitive, current models based on world records clearly do not work very well as was shown in Racing Among the Ages.  However, perhaps it is inherently less useful to age handicap the recreational and social participant subgroups than it is to age handicap the truly competitive runners who strive for the best performance that is possible for them.  One might suspect that five year age group winners, especially in larger local races, largely consist of truly competitive runners.  Certainly, not every competitive runner will win his or her age group.  However, as we go deeper into the order, it becomes progressively more difficult to distinguish between competitive and non-competitive participants based solely on their time.  Consequently, in this article, the word “local” runner or “local class” refers to data and models based on the records of age group winners in local races.  The term “world class” will refer to models and projections based on single age world records.

With this clarification, the initial question can be reframed as follows: Can the age related decline in speed among world class runners be used to generate an age handicapping system for local class runners (and everyone in between)?

Several popular web sites are constructed on this premise, which is largely untested. Two popular age grading calculators are Aging in Sports and Chess and the WMA Age-grading calculator.  Many other age grading sites are derived, directly or indirectly, from these two sites.  In a 2007 publication, the author of the first site, Ray C. Fair, has questioned “Does a person of average talent … who is in good shape slow down at a similar percent rate as elite athletes?”, p53, (italics added).  The second site also uses a model that assumes a comparable percent decline between world record and more average competitors.  In “Age-graded performances”, the principle author of this second site, Howard Grubb, has stated that “super-veteran (aged over 60 or so) athletes run more slowly at the moment than expected.”

So it is reasonable to be skeptical of the untested assumption that world and local athletes slow down at the same percent with age.  However, there are other ways to model the decline in speed.

A Metric Based on the Absolute Change in Speed.

This article examines a simple alternative to the “Percent for Age” method used by current age grading systems. With the proposed alternative, which I will call “Age Speed Addition”, age related performance changes are modelled as absolute differences in speed, whereas current age grading methods assume age related changes can be expressed on a relative (i.e. percent) scale.

To illustrate these two methods, I started with the single age world records for the male road 5K from the Association of Road Racing Statisticians, www.arrs.net.  The values in this dataset were equalized for the underlying single age population sizes as described in “Age Handicapping Competitive Runners, Part1: Quantifying the Population Effect”. The dataset was also smoothed using the Savitzky-Golay filter as described in the Appendix to this article to give the following equivalent speeds based on world records:

  • World 25 year old male: 14.11 mph
  • World 82 year old male: 8.28 mph

Note that the world 82 year old runs at 58.6% of the speed of the 25 year old and that he is 5.84 mph slower.

The “Percent by Age” method (as used by most current age grading systems) would suggest that the 82 year old competitive runner in a local race should run at 58.6% of the speed of his equivalent 25 year old competitor. The absolute speed method suggests the local 82 year old should run 5.84 mph slower.

To illustrate the application of these methods to local competitors, I will use the single year equivalent performance of male age group winners in 356 local 5K races having between 500 and 999 total participants (see Racing Among the Ages).  As with the world records, these local data were also equalized for population and smoothed per the Appendix.  From this we find that the equalized speed of local 25 year olds is 10.84 mph whereas the equivalent speed of a local 82 year old is 4.76 mph.  The following table summarizes these results:

The “Percent by Age” method suggests that the handicapped speed of the local 82 year old be calculated as  4.76/.586 = 8.12 mph.  On the other hand, the absolute “Age Speed Addition” method handicaps the speed of the 82 year old at 4.76 + 5.84 = 10.60 mph.  As you can see, in this case, the “age speed addition” model provides a handicapped speed that is much closer to the target 10.84 mph of the equalized 25 year old local competitor.

The graph below compares the handicapped speeds for local 5K male competitors between the ages of 25 and 85. The formulas described in Age Handicapping Competitive Runners, Part1: Quantifying the Population Effect were used to get speeds representing the same percentile among the populations for each age.  Consequently a perfect age handicapping system should produce handicapped speeds that are the same for all ages.

In the graph, note that the “Age Speed Addition” method gives handicapped speeds that stay approximately within +/-0.5 mph for the entire range of ages. However, even though it does very well prior to the mid-sixties, the “Percent by Age” method fails rapidly after the mid-sixties, confirming Howard Grubb’s earlier concern.  By way of comparison, the average deviation of speed handicapped by the “Percent by Age” method was 3 times larger than the average deviation of speed handicapped by the “Age Speed Addition” method.

A future article will provide an in depth comparison of the Age Speed Addition method proposed here versus current Age Grading methodology. Suffice it to say here that Age Speed Addition represents a substantial improvement on current methods.

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Tables of Speed Additions for Age Handicapping Competitive Runners

Single age world records for the Road 5K, 10K, Half Marathon, and Marathon were combined to generate the tables shown below. This data was provided by the Association of Road Racing Statisticians, www.arrs.net.  Incidentally, with age, the absolute speed declines comparably for all of these distances, so, for each gender, a single table is applicable for all distances between 5K and the Marathon.  Note that the “Age Speed Additions” are expressed as MPH, Miles Per Hour.

Appendix: Data Smoothing

Alan Jones has done a good job of explaining the current Age Grading methodology in his article “Age grading running races”.  The methodology is used to create a curve which dominates all single age records and still comes as close to the data as possible.

On the other hand, for the “Age Speed Addition” tables developed here, I use a non-parametric (or, more accurately, pan-parametric) data smoothing methodology. This has the advantage of producing a more adaptive curve and also of incorporating information from every data point.  In the area of signal processing, this smoothing technique is called the Savitzky-Golay filter.  The graph below shows the population adjusted world records for the 5K smoothed with a quadratic S-G filter having a range of 9 below age 30 and a range of 21 for age 30 and above.   All population adjustments use the formulas developed in Part 1 of this series and adjust to the equivalent population at 30 years of age.

To get single year equivalent performances based on 5 year age group winners in local races, I used rolling 5 year intervals and interpolated to integer ages. The results were then adjusted for population and smoothed with an S-G filter as indicated above.

 

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