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.

 

Optimum Age Groupings in 5K races

Summary

Based on the criteria suggested in this article, the most efficient age grouping structures have 3 awards per age group and use the following adult age group divisions:

  • Races with under 70 total finishers:   18,35,50,65+
  • Races with 70 to 129 total finishers:   18,30,40,50,60,70,80+
  • Races with over 129 finishers:  18,25,30,35,40,45,50,55,60,65,70,75,80+

Introduction

Most races divide participants into age groups within gender. Awards are then given for the first place and (frequently) for the second and third places in each age group.  (Rarely, some larger races may award more than three places within each age group.)  Typically each age group may span 5, 10, 15 or another number of years.

Race participants place significant value on award ceremonies where the top finishers in each age group are recognized. However, there is a limit to how much time participants are willing to devote to an awards ceremony.  Generally, the interest among participants tends to wane if the ceremony extends beyond about 45 minutes to an hour.

This begs the questions: What is the best way to structure age groups and how many awards should be offered in each age group?  As we will see, the answers depend heavily on the size of the race; i.e. it depends on the total number of finishers in each race.

Example

Let’s look at an example of age grouping – a bad example. Since this is an example of what can go wrong when you have poorly structured age groups, I will not give the identity of the race.  Suffice it to say, several of my friends participated in this race and there was significant dissatisfaction with the way age groups and awards were handled.

Among adults, the age groupings were: 18-24, 25-29, 30-34, 35-39, 40-44, 45-54, 55 and over (This age grouping can be abbreviated as 18,25,30,35,40,45,55+).  The first and second place in each age group received an award.  There was a combined total of 193 finishers which includes Youth, Adult Females, and Adult Males..

In this race, a 79 year old man had a rather remarkable 10K time of 53:05 – but he received no award since he had to complete with much younger men in the 55+ age group. This man’s 10K time (and all other participant’s times) can be converted to their 5K equivalent using the MCMILLAN RUNNING CALCULATOR.   In this case, the 5K equivalent time for this 79 year old is 25:34.  We see from bigdatarunning.com/5k_percentiles/ that this performance places him at the 99.9th percentile for his age.  By contrast the percentiles for the 7 adult males actually given first place awards ranged between the 83rd and 96th percentiles.  There were also two individuals at the 97th percentile, one received no award and one was given a second place award, but both out-performed all of the individuals receiving a first place award.  Clearly, in this case, the age groups and award schedule selected by the race director were problematic.

Age equivalent performance

In order to quantify the differences among runners after adjusting for age, all performances are converted to a 25 year old equivalent basis. This is the age at which top athletes peak and is the average age of Olympic medalists [see Peak Performance, part 2].  For example, a 25 year old male at the 99.9th percentile has a 5K time of 14:02 corresponding to an average speed of 13.28 miles per hour.

Metric

A discrepancy occurs whenever two runners in a race have different age adjusted speeds but both receive the same award, (or equivalently both receive no award at all). A natural way to quantify the discrepancy between two runners in the same award category is to look at the squared difference in their age adjusted speeds.  With this definition, the average discrepancy across all pairs of runners is mathematically equivalent to twice statistical variance among the runners, i.e. it is twice Mean Squared Error (MSE) among the age adjusted speeds.  Consequently, for consistency with conventional statistical terminology, I will define discrepancy in terms of ½ the squared difference in speeds.

The giving of awards for 1st, 2nd, etc. in each age group is intended to correct or reduce the discrepancy among race participants.  Thus the discrepancy between two runners is eliminated when the faster runner receives a more prestigious award than the slower runner.

On the other hand, and especially with poorly designed age groupings, a slower runner may actually be given a better award than a faster runner. In this case, the overall discrepancy is increased in proportion to the squared difference in the rank of the awards given.  For example, suppose someone running at an age adjusted speed of 7 mph was given a 1st place award and another runner travelling at 11 mph receives a 3rd place award.  The magnitude of this discrepancy is then ½*[(11-7)*(3-1)]2 .

Using these definitions of “discrepancy”, an age group efficiency can be defined based on reduction in variance caused by the awarding of metals. For example, if, for a particular age group schedule, the awarding of metals reduces the variance by 30%, then we would say that the age group schedule has an efficiency of 70%.  The tables at the end of this article represent the average of male and female age group efficiencies for hundreds of races.

Data

The data from the 1283 5K races discussed in the book Racing Among the Ages was used to evaluate the relative efficiency of various age grouping schedules.  Based on the total number of finishers, several different race sizes were examined for each age group schedule:

  1. 50: 50 finish records randomly selected from each of 1283 races
  2. 100: 100 finish records randomly selected from each of 1283 races
  3. 200: 203 races (161-256 total finishers); median race size was 200
  4. 400: 204 races (323 and 458 total finishers); median race size was 400
  5. 800: 202 races (645 and 977 total finishers); median race size was 802

Age grouping efficiency is very much dependent on the number of awards  given. However, the aforementioned time constraints as well as a desire not to “cheapen” the awards puts limits on the numbers of awards.  For present purposes, I only look at schedules where less than 50% of finishers receive an award, three or less awards are given per age group, and an average of 36 or fewer total awards are given to each adult gender (18 and over).  Including the awards for the youth, this will be about as many awards as can be given within a ceremony not exceeding an hour.   (Note that the average number of awards given may be slightly less than the number of awards actually offered because some age groups may have fewer participants than the number of awards offered to each age group.)

Results

The tables below show the efficiency for selected adult age grouping schedules. (All of the schedules shown start at 18 years; however, starting them at 20 years gives essentially the same conclusions.)

For races with 50 total finishers, age groups 15 years wide are optimal; for races with 100 finishers, 10 year age groups are optimal; and for races with 200, 400, or 800 finishers, 5 year age groups are optimal. For races of all sizes, the optimal age grouping schedule was associated with 3 awards per age group rather than 1 or 2.

In addition, for races with 50 finishers the top age group should be 65+. For races all other sizes, the top age group should be either 75+ or 80+.

Based on race size, the best age grouping schedules were as follows:

  • 50 Finishers:        18,35,50,65+
  • 100 Finishers:     18,30,40,50,60,70,80+
  • 200 Finishers:     18,25,30,35,40,45,50,55,60,65,70,75,80+
  • 400 Finishers:     18,25,30,35,40,45,50,55,60,65,70,75,80+
  • 800 Finishers:     18,25,30,35,40,45,50,55,60,65,70,75,80+

Perhaps these results may seem intuitively obvious and in fact many races use grouping schedules that are consistent with these results. However, there are many other races that still use very inefficient age grouping schedules.

TABLES: THE EFFICIENCY OF SELECTED AGE GROUPING SCHEDULES

50 Finishers:

100 Finishers:

200 Finishers:

400 Finishers:

800 Finishers:

 

 

Age Related changes in 5K Participation Rates: Implications for Age-Grading

Have you ever noticed how few older individuals participate in 5K races? Have you noticed how many races don’t even have separate age groups for the oldest individuals?  Typically these races might advertise five year age groups which cut off abruptly at 60 years of age, e.g.:

“. . . . . . 25-29, 30-34, 35-39, 40-44, 45-49, 50-54, 55-59, and 60+”

Why would this be? In terms of athletic ability and running speed, the difference between a 70 year old and a 60 year old is much greater than Continue reading “Age Related changes in 5K Participation Rates: Implications for Age-Grading”