I have recently purchased the History of modern Track and Field by the late R. Quercetani. I already had the 1990 edition, in italian, but the 2014 edition was covering the period up to 2013 and Quercetani is the father of T&F statistics, so I did not hesitate. In fact I may write an article on Quercetani one day.
While perusing the book I stumbled upon this note on one of the last pages. It was an estimate of what women throwers could obtain were they to throw with the men's implement.
Now this is a question which has been treated on various occasions in this blog (and I'm not done with it yet). But I was intrigued since the source of Quercetani was F. Amado. That was not the first time I was seeing that name. Amado is at the origin of what were called the Portuguese scoring tables. I had heard about him already in the 60s. His work will be mentioned when I decide to write the (series of) article(s) on performance scoring. Having seen the reference of Quercetani I had to find the book of Amado.
The matter was further complicated by the fact that after the first, 1956, edition he published what he considered the definitive one in 1962, having expanded it into two volumes. I managed to find the first volume in a rare book bookshop and the second volume in the library of the University of Bordeaux (I requested a loan, I got it a few days later and proceeded to scan it). The part on the comparison of throws with implements of different masses was in the first volume.
Amado does not give any explanation concerning his results. He discusses how one can interpolate between values of the table (something which anybody with a smattering of maths would not hesitate to apply a cross-multiplication rule to) but he does not tell us where his numbers come from. So the only possibility was to try to see whether they are too far off the magic formula, I have written a zillion times about, linking the mass, m, of an implement and the length, L, of the throw.
L=a/(m+f)
Below I give a fit of the data for shot put from Amado's table for p=1000 points. The fit is not bad at all and the resulting value of f, 4.5 kg, quite realistic. My preferred value for this quantity if 6 kg but Amado's value comes sufficiently close. For discus throw the bracket of the values I have found for f is 1.5-2.5 kg, while from Amado's data we find 1.1 kg. For javelin the fit on Amado's p=1000 performances gives f=0.7 kg, while my values are in the 0.5-1.0 kg range. Finally for the hammer throw we find from the fit f=3.8, while my values are around 3 kg.
This gives the impression that all is well. In fact I was surprised by the note of Quercetani, because the predicted world records of women throwing with men's implements were very close to what I would have predicted. However if we apply the same analysis to Amado's data for p=0 we find values for f which are much smaller than those obtained for p=1000, half or even less and in fact a negative value in the case of hammer throw. This is a hint that the table of Amado was constructed empirically based on extrapolations not always well controlled. Still it has the merit of existing and does quite well at high level of performances. And he does better than Willoughby who was convinced that the length of the throw was related to the square root (!) of the mass and was astonished that no theoretical explanation existed.
While perusing the book I stumbled upon this note on one of the last pages. It was an estimate of what women throwers could obtain were they to throw with the men's implement.
Now this is a question which has been treated on various occasions in this blog (and I'm not done with it yet). But I was intrigued since the source of Quercetani was F. Amado. That was not the first time I was seeing that name. Amado is at the origin of what were called the Portuguese scoring tables. I had heard about him already in the 60s. His work will be mentioned when I decide to write the (series of) article(s) on performance scoring. Having seen the reference of Quercetani I had to find the book of Amado.
The matter was further complicated by the fact that after the first, 1956, edition he published what he considered the definitive one in 1962, having expanded it into two volumes. I managed to find the first volume in a rare book bookshop and the second volume in the library of the University of Bordeaux (I requested a loan, I got it a few days later and proceeded to scan it). The part on the comparison of throws with implements of different masses was in the first volume.
Amado does not give any explanation concerning his results. He discusses how one can interpolate between values of the table (something which anybody with a smattering of maths would not hesitate to apply a cross-multiplication rule to) but he does not tell us where his numbers come from. So the only possibility was to try to see whether they are too far off the magic formula, I have written a zillion times about, linking the mass, m, of an implement and the length, L, of the throw.
L=a/(m+f)
Below I give a fit of the data for shot put from Amado's table for p=1000 points. The fit is not bad at all and the resulting value of f, 4.5 kg, quite realistic. My preferred value for this quantity if 6 kg but Amado's value comes sufficiently close. For discus throw the bracket of the values I have found for f is 1.5-2.5 kg, while from Amado's data we find 1.1 kg. For javelin the fit on Amado's p=1000 performances gives f=0.7 kg, while my values are in the 0.5-1.0 kg range. Finally for the hammer throw we find from the fit f=3.8, while my values are around 3 kg.
This gives the impression that all is well. In fact I was surprised by the note of Quercetani, because the predicted world records of women throwing with men's implements were very close to what I would have predicted. However if we apply the same analysis to Amado's data for p=0 we find values for f which are much smaller than those obtained for p=1000, half or even less and in fact a negative value in the case of hammer throw. This is a hint that the table of Amado was constructed empirically based on extrapolations not always well controlled. Still it has the merit of existing and does quite well at high level of performances. And he does better than Willoughby who was convinced that the length of the throw was related to the square root (!) of the mass and was astonished that no theoretical explanation existed.
