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 87.29^{th} __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 87.29^{th} 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.