__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 99.9^{th} percentile for his age. By contrast the percentiles for the 7 adult males actually given first place awards ranged between the 83^{rd} and 96^{th} percentiles. There were also two individuals at the 97^{th} 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 99.9^{th} __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 1^{st}, 2^{nd}, 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 1^{st} place award and another runner travelling at 11 mph receives a 3^{rd} 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:

- 50: 50 finish records randomly selected from each of 1283 races
- 100: 100 finish records randomly selected from each of 1283 races
- 200: 203 races (161-256 total finishers); median race size was 200
- 400: 204 races (323 and 458 total finishers); median race size was 400
- 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: