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.

 

WMA Age-Grade Standards for Winners of the 30-34, 35-39, and 40-44 Age Groups

Current WMA Age-Grading Standards are extremely aggressive. In fact, in the entire modern era of sports statistics, only about a half dozen isolated performances have met the Standard for 5K road races.  The great majority of single age world record holders have never had a performance that met the Standard.  Consequently, ordinary athletes may have difficulty connecting with these Standards.  The purpose of this article is to re-express the WMA standards in terms that almost every 5K participant can relate to:  the age-group winner.

For road and track racing as well as other sports, World Masters Athletics (WMA) has developed and maintains performance standards for each single year of age. Athletes of various ages are evaluated in terms of how well they stack up against the event standard for their age.  For example, a runner in a 5K road race might be 70% as fast as the standard for his or her age.  Based on how well an athlete compares to the standard for his or her age, WMA has created labels for various levels of performance as follows:

  • Above 90%     World Class Level
  • Above 80%     National Class Level
  • Above 70%     Regional Class Level
  • Above 60%     Local Class Level

This begs the question of how we might relate these various levels, especially the Local, Regional, and National classes, to concrete performances that are familiar to the athletes that are somewhat below World class. For example, if you are a “Regional” class athlete, how often might you win your age group in a 5K road race?

One of the most complete sets of WMA age standards and probably the best known is the WMA Age-Grading Calculator.  This calculator is also the basis for many (almost all?) of the other on-line age-grading calculators.  And although the methodology produces significant biases for the youngest and oldest race participants (see Racing Among the Ages), it appears to be reasonably consistent within gender across a wide spectrum of abilities in the heart of the age range, i.e. between the ages of 30 and 44.  Consequently, in this post we will look at the following age groups:  30-34, 35-39, and 40-44.

Computational Example

[If you are not interested in the computational details, skip to the results section below.]

As an example, consider “Joe”, a 32 year old male who can run a 5K in 21:33. The WMA 2015 standard for a 5 km road race is 13:05.  With a time of 21:33, Joe will perform at 60.7% of the standard, and hence is just above the threshold for a “local class” athlete.  We will also note that a time of 21:33 also corresponds to the 87.29th percentile among 32 year old males.

Among all male and female 5K finishers of all ages, 4.9% are males between 30 and 34[ref].  Suppose “Joe” decides to participate in a very small race expected to have just 40 total runners in addition to himself.  He would then expect to compete against an average of 40 x 4.9% = 1.96 other runners in the M30-34 age group.  If the expected 40 runners are a representative sample of all runners, then the actual number of runners in the M30-34 age group will follow a Poisson distribution with mean 1.96.

Using Poisson distribution with a mean of 1.96 suggests there is a reasonable probability (0.141) that no other competitor shows up for Joe’s age group and he will then have a 100% chance of winning his age group. There is a probability of 0.276 that exactly one other competitor shows up in the M30-34 age group.  Since Joe is calculated to be at the 87.29th percentile among his peers, he will have a 0.8729 probability of defeating this competitor.  Thus the probability that exactly one other age group competitor shows up and that Joe beats him is 0.276 x 0.8729 = 0.241.  The Poisson probability that Joe has exactly 2 competitors is 0.271 and the probability that he beats both is 0.8729 x 0.8729 = 0.7620.  Thus, the combined probability that exactly 2 competitors show up and that Joe beats them both is 0.271 x 0.7620 = 0.206.

It is possible to make similar calculations for every possible number of competitors for Joe in the M30-34 age group, i.e. for 0,1,2,3,4,5,6 . . . etc. When we add up the probability that Joe wins his age group across all possible numbers of competitors, we can calculate that Joe’s overall probability of winning is 0.141+0.241+0.206+0.118+0.050+0.017+0.005+. . . = 0.779.  Thus, a male between 30 and 34 who competes at 60.7% of the WMA standard will have approximately 0.779 chance of winning his 5-yr age group in a race expected to have a total of only 40 other participants.  Since Joe, competing at 60.7% of the WMA standard, will usually win his age group in these very small races, we can correctly state that a 60.7% age-grade is significantly superior to the typical age-group winner in a race with just 40 participants.

Now suppose that Joe participates in another race expected to have 110 total participants in addition to himself. In this case, if we go thru the above calculations for the larger race, we find that Joe will have “only” a 0.501 probability of winning the M30-34 age group.  Thus, half of the time Joe will win his age group and half the time he will not.  Consequently, we can conclude that, among males 30-34, a 60.7% age-grade is equivalent to the median or typical age-group winner in races having a total of 110 participants.

Results_:_WMA Age Grade for Age-Group Winners in 5K Races

The graph below is based on the age group winners for six age groups: F30-34, F35-39, F40-44, M30-34, M35-39, and M40-44.  For each of these age groups the median WMA Age Grade was calculated for each of three race sizes: 110, 500, and 3,000.  The averages are as follows:

Total Race Participants                  Avg. WMA AG for Age Group Winners

  •            110                                                  60% (Local Class Level)
  •           500                                                  70% (Regional Class Level)
  •        3,000                                                  80% (National Class Level)

In the graph you will note that, although the combined average of males and females match the WMA classes very well, the WMA Age Grade assigned to female age group winners is consistently below that given to males. For example, for races with 110 total participants, the average AG assigned to males is 3.5 percentage points below that assigned to females.  For races with 500 participants the difference is 4.9% and for races with 3,000 participants the difference is 3.4%.

Consequently, within the range of abilities and the range of ages considered here, there is an average bias of about 4% against the females. If the WMA AG of males and females are directly compared, 4% should first be added to the female AG.  For example, a female with a 66% AG is performing at a level equivalent to a 70% male AG.