In a previous post of mine I had presented the age factors, which aim at adjusting the performance, correcting for age, and which are tailored to master athletes (although age factors can be, and sometimes are, introduced for young athletes as well). I had given there a simple formula for the age factor F
F=C/(A-a)
where a is the age of the athlete and A,C are two parameters. Typically all three a,A,C are expressed in years and F is a dimensionless number.
Age factors are empirically established by the the various masters sports governing bodies. In order to show how well the simple formula above works I present a fit of the age factor for high jump proposed by the World Masters Athletics association.
The quality of the fit is excellent. So the question that naturally arises is how can such a simple formula be so realistic? The answer is to be found in the way the performances decline with age. Here are the results of the men's masters world high jump records.
We observe that the records follow very closely a straight line, over several decades and performances which vary by a factor of more than two. So if the variation of the performance P can be parametrised as
Age factors are empirically established by the the various masters sports governing bodies. In order to show how well the simple formula above works I present a fit of the age factor for high jump proposed by the World Masters Athletics association.
The quality of the fit is excellent. So the question that naturally arises is how can such a simple formula be so realistic? The answer is to be found in the way the performances decline with age. Here are the results of the men's masters world high jump records.
P=B(A-a)
the age factor introduced above corrects precisely for the variation with age.
Once one has the expression of the variation of records with age it is natural to wonder what is the meaning of the quantity A, i.e. the age for which the performance goes to zero. Clearly, this is an indication as to the maximum life span. Assuming that the records are representative of the human race as a whole and that a living person, even at a very advanced age, is capable of locomotion, one can imagine that the total absence of a possibility for an athletic performance occurs only at that person's demise. The records, but even better the age factors, somehow encode this. This is the secret information I refer to in the title.
I must insist here on the fact that the age factors are better suited for the purpose of the prediction of the maximal possible life span as compared to records. The records are the feats of exceptional individuals, while the age factors are normally established based on solid statistical analyses of performances covering several decades. Still these studies do not usually exceed ages around 70-75. One reason is that the population of athletes beyond those ages is too small to allow for a statistical approach. Also, as Tanaka and Seals have observed, there is a notable decline in performances around ages 80-85, in particular for endurance performances. This is most closely associated with reductions in exercise training intensity and volume, probably as a consequence of changes in a number of physical and behavioural factors (e.g. increased prevalence of injuries, and reductions in energy, time and motivation to train). Thus neglecting those advanced ages from the statistics on which are based the age factors is the proper way to go, contrary to what one could think. (And the fact that, at least for some events, the dependence of performance on age ceases to be linear is another reason why one should prefer to consider age factors rather than world records).
So what are the predictions for the maximal life span coming form the study of the high jump age factor. From the expression for F we find a value for A equal to 140. In my original post on age factors I had presented a similar analysis for long jump and the value of A obtained was equal to 126.
Several years ago I wrote a short post on D. Harder's approach to scoring. His system allows, in principle, the comparison of performances not only within a single discipline but between all possible sports. In his monograph "Sports comparisons: you can compare apples to oranges" Harder introduces age factors for various track and field disciplines. I found, after some "reverse engineering", that the one for high jump corresponds to an an expression with A=134. Similar values are obtained for the other disciplines.
At this point one can wonder whether the interpretation of A based solely on athletics' results is well-founded. After all, one could imagine that track and field events are special and that other disciplines could draw a totally different picture. As it turns out this is not the case. In the graphic below I present the age factor for weightlifting. The value of A obtained from the best fit is 137 in total agreement with the ones obtained from athletics.
It is interesting also to look at the age factors used in swimming. Two different age factors are used (well, probably many more, but those two are the best known ones). One is known as the "finnish formula" and the second one is due to A. Rawson. The finnish formula, referred to as age index is a factor meant for multiplying the swimmer's time. (I really cannot understand why people are working with time when the natural, physical, quantity on which to base all analyses is the velocity). From the expression of the ageing index we find that it goes to zero for an age of 109. The Rawson index is a monstrosity involving a polynomial of 6th degree in the athletes' age. Still it can be fitted by the simple formula given at the beginning of this post.
The fit results in a value for A of 110. Does the fact that the values for swimming are significantly lower than those of athletics (or weightlifting) mean that A is not universal? I do not think so. I am convinced that the records of swimming have still a substantial margin of progression. In fact pushing the curve of the decline of records upwards, so as to bring the value of A around 125, would correspond to a 100 m world record of 45 s for a 25 year old swimmer, something that is not unrealistic.
So just by looking at the athletic performances we can get an indication of the maximal human life span. The prediction for its value, given the spread of the values, is something in the 120-130 bracket. This means that just by looking at how the human race performs with advancing age we can set a maximum for the possible life duration.
In his book "Scale" (which is perfectly accessible to a layman and which I highly recommend) physicist G. West asks the question of the maximal human life span and reaches the conclusion that it should be around 125 years. It is amazing that athletic performances offer an independent estimate for this, in perfect agreement with West's estimate.
PS. While preparing this post I ran across an article on the World Athletics site (it was IAAF at that time) with title "Scoring athletic performances for age groups", which does indeed summarise my work. Unfortunately my name does not appear explicitly in the article, but, still, I was glad that the Athletics' instances did take notice of my work.
Once one has the expression of the variation of records with age it is natural to wonder what is the meaning of the quantity A, i.e. the age for which the performance goes to zero. Clearly, this is an indication as to the maximum life span. Assuming that the records are representative of the human race as a whole and that a living person, even at a very advanced age, is capable of locomotion, one can imagine that the total absence of a possibility for an athletic performance occurs only at that person's demise. The records, but even better the age factors, somehow encode this. This is the secret information I refer to in the title.
I must insist here on the fact that the age factors are better suited for the purpose of the prediction of the maximal possible life span as compared to records. The records are the feats of exceptional individuals, while the age factors are normally established based on solid statistical analyses of performances covering several decades. Still these studies do not usually exceed ages around 70-75. One reason is that the population of athletes beyond those ages is too small to allow for a statistical approach. Also, as Tanaka and Seals have observed, there is a notable decline in performances around ages 80-85, in particular for endurance performances. This is most closely associated with reductions in exercise training intensity and volume, probably as a consequence of changes in a number of physical and behavioural factors (e.g. increased prevalence of injuries, and reductions in energy, time and motivation to train). Thus neglecting those advanced ages from the statistics on which are based the age factors is the proper way to go, contrary to what one could think. (And the fact that, at least for some events, the dependence of performance on age ceases to be linear is another reason why one should prefer to consider age factors rather than world records).
So what are the predictions for the maximal life span coming form the study of the high jump age factor. From the expression for F we find a value for A equal to 140. In my original post on age factors I had presented a similar analysis for long jump and the value of A obtained was equal to 126.
Several years ago I wrote a short post on D. Harder's approach to scoring. His system allows, in principle, the comparison of performances not only within a single discipline but between all possible sports. In his monograph "Sports comparisons: you can compare apples to oranges" Harder introduces age factors for various track and field disciplines. I found, after some "reverse engineering", that the one for high jump corresponds to an an expression with A=134. Similar values are obtained for the other disciplines.
At this point one can wonder whether the interpretation of A based solely on athletics' results is well-founded. After all, one could imagine that track and field events are special and that other disciplines could draw a totally different picture. As it turns out this is not the case. In the graphic below I present the age factor for weightlifting. The value of A obtained from the best fit is 137 in total agreement with the ones obtained from athletics.
So just by looking at the athletic performances we can get an indication of the maximal human life span. The prediction for its value, given the spread of the values, is something in the 120-130 bracket. This means that just by looking at how the human race performs with advancing age we can set a maximum for the possible life duration.
In his book "Scale" (which is perfectly accessible to a layman and which I highly recommend) physicist G. West asks the question of the maximal human life span and reaches the conclusion that it should be around 125 years. It is amazing that athletic performances offer an independent estimate for this, in perfect agreement with West's estimate.
PS. While preparing this post I ran across an article on the World Athletics site (it was IAAF at that time) with title "Scoring athletic performances for age groups", which does indeed summarise my work. Unfortunately my name does not appear explicitly in the article, but, still, I was glad that the Athletics' instances did take notice of my work.
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