'Age grading' is the word for a calculation used in masters athletics (formerly called veterans athletics). The first goal was to get relevant results in multi events, because the common IAAF scoring of multi events lead to zero points for good results of old athletes.
Statistical basisFor a statistical analysis roughly two strategies can be chosen. Above I have looked at extreme values, i.e. the age records of the high jump. I myself collect those data, they can be found at my website. For other disciplines less data are available, age records per 5 year age groups are on wikipedia.
Another way is not to take extremes but means of for example the top ten per age group. The idea is that when more data have been used exceptional results will have less influence, which would give a better view on trends. Below you see them, they are taken from the inofficial all time world rankings (situation early 2011). A linear trend line has been added and it is clear that this line is not essentially differing from trend lines in earlier graphs.
Remarkable is that in every age group the cloud of ten dots looks about the same. In older age groups differences in centimeters are about the same as for young masters, although one centimeter relatively is a bigger difference for old jumpers than for young ones.
Trend lines change when a polynomial of order 3 is taken, nevertheless for men the difference is small. Why not for the women's records? A real effect or accidental? I did not look for an answer on these questions and from now on only age records are used, not the rankings.
Three systems of age gradingsThe international organisation of masters athletics WMA (formerly WAVA) is using its third set of age gradings:
1. Published 1989, revised 1994, designed by Al Sheahen et al.
2. Published 2003, last revision 2007, made by Rex Harvey et al.
3. In use from 2010 (a bit earlier in Germany), made by Bernd Rehpenning et al.
Use af age gradings is simple: take a masters result, multipy by a certain factor for that age and what you get is a result in the normal range for twens, called the Open Class (OC).
To compare all three sets of age gradings I've made two graphs per discipline. The first one shows the world records (blue line) and a purple line through two records such that all other records are below this line. There also is a green line, more about that later. Vertical is not an athletic performance but a percentage. What counts as 100% will follow in a moment.
The purple line is also present in the second graph, but here it is horizontal. The colored lines show how the three gradings (their last revision) compare to the purple line. Orange is system 1, blue is system 2 and green is today's system 3. A line higher in the graph means that with this grading it is harder to get 100% (that is, one gets less points in a multi event). The trend in these three systems is that they shift upwards in the graph -- logical, records are improved and become better than makers of a grading system had expected.
At the right side of the graph gradings go down, more about that later.
Hundred percentTo get the same kind of graphs for all disciplines meters and seconds have been recalculated into percentages. For jumps and throws the calculation is: 100 times master performance divided by OC-record is percentage. For runs this would lead to a percentage over 100%, so here the calculation is inversed: 100 times OC-record divided by master performance is percentage.
Something has to count as 100%, which can be:
A. The OC world record
B. The world record of the youngest masters (M35 and W35)
C. The mean of the top ten of the all time list of M35 and W35 and count this as 95%
In other words, you can take extremes, means and much more. 'A' would be the simplest choice, but it is not as simple as it seams and the main reason is doping. Especially the women's world records sometimes are severely influenced by doping.
Some facts and opinions about records and doping:
a. All OC records are influenced by doping
b. Especially some records are severely influenced by doping
c. Among the master records of the younger age groups there are influenced records
d. Even some older masters have been found cheating, among them holders of strong masters world records
e. Atletes having been on drugs when young will have better results as a master than they would have had without doping, even long after stopping taking drugs.
All these things are making it difficult to stamp a certain result as 100%. Happily comparing age groups with each other is not affected, but the numbers, the percentages are. Records that stand out in the graphs maybe are affected by doping, but that cannot be proved. Nor can it be said how much they are affected -- athletes with records but on drugs are very gifted anyway.
Throwing implements and hurdle heightsThe youngest masters use the same throwing implements as the Open class, but older groups throw with ever lighter implements. A simple formula is used to reduce all age records to comparable results. After multiplying with the square root of the weight difference mostly neat graphs are obtained. For example: an M90 reaches 9.00 m in shot put with an implement weighing 3 kilograms; weight for the open class is 7.26 kg, so 9.00 times square root (3 / 7.26) gives a distance of 5.78. This distance is used in the graphs.
With this formula also existing age gradings have been recalculated. This should lead to regular graphs, but this is not always the case. Two possibilities: the formula has not been used in desigining the age gradings, or the formula isn't good enough.
In hurdle races for older athletes both hurdle height and distance between hurdles change. A simple formula to make all records comparable is not at hand, therefore for the time being hurdles (and steeple chase) are not looked at in this study.
On a certain ageNobody can beat ageing, there are a lot of body processes that change and lead to older, lower, slower. At a certain age decline will accelerate and for everyone this is at another age, genetically. In the long run age records will all be set by masters whose accelerated decline happens on a very high age. The high jump graphs above show a nearly linear decline for men up to at least 94 and for women up to at least 80 years. When I started those graphs in 1998 it was quite different. The linear decline really continues into higher ages now.
Linear?In the first grading system for runs an approximately linear decline was adopted, but for the technical disciplines the same percentage decline each year has been supposed. (Therefore the orange line in the graph was convex for a big part.) This sounds logical, but soon it turned out that masters records didn't like the theory, the decline looked more like a linear decline in these disiplines too. The gradings of the second system therefore were data driven: the gradings have to follow the known records.
In the high jump decline indeed looks linear, but not so for the 100 m for men:
A tangent line can always be found but in this case two points quite close to each other have to be chosen. Records for both the younger age groups and the older ones lie beneath the straight purple line. It could be accidental, just the situation of the records at this moment, on the other hand the 100 m of the men is the most practiced discipline and the blue graph is the smoothest of all disciplines. In stead of the purple straight line a curved line a bit concave would fit better -- which implies that decline is not linear.
The green line by the way is for the gradings of the current system. It hoovers a bit above all age records because Bernd Rehpenning wanted to make the gradings future proof: it should have a bit room for record improvements, so it will take some time before someone scores over 100%. This principle seems not to have been implemented for all disciplines.
The reverse of a concave decline can be seen in some throws of the women. The tangent line goes through two points at the far ends. Here a convex curve seems to be the best solution.
What can you do with gradings?A. The simplest calculation goes like this. The 50 year old women of the second graph jumped 1.40 and that turns out to be 32.4 cm less than the green line for age 50 (1.724 m) and so ... calculate ... calculate ... she does 81.2 % of the supposed world record for her age. Age grading is 81.2.
B. A step further is supposing that all age records in fact are just as good. The OC world record is 2.09 m (Stefka Kostadinova), the green line gives 1.724 for age 50 and so you have to multiply all results of women age 50 by 2.09/1.724 to grade them. Age factor then is 1.212. Control: 1.2121 times 1.724 gives 2.09, correct! A jump over 1.40 then has a value of 1.2121 times 1.40 is 1.697 meter.
C. The original humble intention of age gradings was to get relevant points in multi events. This can be reached easily with the factor 1.2121 found under B: a W50 jumped 1.40 in the heptathlon, multiply with 1.2121, result 1.818, round down to 1.81, look up 1.81 in the IAAF scoring tables and she gets 991 points.
D. A step further would be to do the calculation under A for all W50 in a masters championships to find out who is the best of them.
E. Another step further is to age grade al participants of all age groups of a championship and compare them via their percentages.
F. It is also possible to do calculation B for all to see what they 'in fact' have ran, jumped or trown. It will turn out that some masters in my country (the Netherlands) are better athletes than our open class athletes, because they 'in fact' have better scores. The numbers say so. Or not?
LongitudinalTo prove or disprove this I look at myself. At age 60 I jumped 1.47, according calculation B this 'in fact' is 2.02 m, according to the current age grading of Bernd Rehpenning it also is 2.02, according to the earlier gradings of Rex Harvey it is 'in fact' 2.10. But in reality the OC world record is only 2.09 and our national OC record is 1.92. Something strange is happening.
A big problem in all studies of ageing in sports is the fact that we hardly have longitudinal data series. Longitudinal means that results of a certain athlete are known for a very long period, results that have to be comparable even in their details: the same intensity of training etcetera. The older record holders are without doubt gifted athletes, but are they of the same class as Bolt, Beamon, Bubka, Blankers, Bekele, Dibaba?
In most cases: no, they were not that good. Or it is completely unknown how they were in their youth because they started to do athletics at age 65 or 85. Athletes like that exist!
One of the best age records of women in the high jump is 1.76 of Debbie Brill, which she jumped as a 46-year old. According to calculation B that 'in fact' is 2.038. The current gradings have factors per 5 year (older gradings per year) which gives 2.044 for Debbie. She is one of the few real top athletes who also have results as a master (unfortunately she has stopped jumping) and her OC best is 1.99. Very good, but not 2.03 or 2.04. On the other hand: the OC world record of Debbie's days wasn't 2.09 but 2.01.
Another example; discus thrower Gabre Gabric threw 12.86 as a 95-year old with a discus weighing 0.75 kg. With the square root formula given above this becomes 11.14 for a discus of 1 kg. Interesting of her is that she competed in the discus throw at the Olympics of 1936. She wasn't the world record holder at the time, but she was one of the top throwers of the world. The current gradings say she 'in fact' is throwing 57.51 m now, which is quite comparable to what she did in the past. We should like to have more of such longitudinal data. WANTED!
Gradings comparedTo conclude this introduction: it will be clear that designing a system of age gradings is not a straightforward process, many choices have to be made and many of them are arbitrary. To study this look at the following pages:
Masters world records
Three systems of age grading compared
Differences between disciplines
A mathematical model of gradings
The model in use
Tests, fine tuning, problems
Weia Reinboud (weiatletiek (at-symbol) xmsnet (dot) nl)