The table for the heights and masses of the currently listed male an female vaulters in the world top twenty pole vaulters show their height to be very similar (homogeneous: variance is very small in range for each gender but relatively larger across genders). The most frequently occurring height for females is 170 cms and males 188cms (difference of approximately 7 inches).
Given that limb lengths do have proportional length relationship to standing height then standing on the takkeoff leg toe tip, the maximum vertical reach attainable is related in proportion to stature. Grip length along the pole and the maximum vertical reach by the uppermost part of the top hand are the fundamental geometric determinants of the distance out from the back of the box of the takeoff point, when the tip of the pole is held in the back of the box at a particular grip length and vaulter is at maximum vertical reach height..
The expertise level of the vaulter therefore becomes the variable parameter that enables the vaulter to grip further along the pole and, all other things being equal, enable the vaulter to takeoff at a greater distance out from the back of the box whilst assuming a postural configuration that provides close to maximum vertical reach height. Hence the interaction between expertise and stature becomes the key causative relationship between effective grip length along the pole and the takeoff point location distance out from the back of the box. Not surprisingly then does one find strong similarities between vaulters gripping along the pole at the same length and the distance out,from the back of the plant box, at which they takeoff. At world class level, where athletes can be assumed to be performing close to the upper limits of their capacity, they will tend to be relatively homogeneous in stature and stature dependent measures.
As one samples closer to the upper or lower tail of the normal curve of distribution for any performance parameter measures, the smaller the variance becomes between individual cases in that sample in the normal distribution on those measures. For data to be robust in dealing with a wide variation of the measures the sample has to be representative of the population it wishes to make predictions about ie a representative sample will have a variance range that is similar to that expected to occur in the population based on laws of probabilty. DJ has developed the chart based on selected small sampling of quite similar vaulters and levels of expertise and used the data assuming linearity of relationships based on astute observation and on the ground measurement.
The sampling and sample variance therefore is relatively small and hence DJ's generalizing of his results to the entire poulation of vaulters of all sizes and levels of expertise is an endeavour fraught with hazard, especially when applied to particular cases. This is not to say that he is not able to give a "ball park" prediction as to where a particular 6 step check mark should be for a particular individual. The size of the ball park in relation to the precise location of the 6 step mark is the measure of the robustness of the prediction reliability in relation to the chart and a specific individual.
All of the above I hope will have cleared the ground to establish why the Dartfish video example put up leads to correct observation but false conclusions and the positing of a flawed theory.
The table below shows the time for the last 6 steps calculated on the basis of average speed over the 6steps divide by the average step length (average step length is the distance from takeoff to the 6 step check mark divided by 6 steps). Also shown is the number of frames required for each vaulter to complete the 6step to takeoff when viewed at 30, 60, and 120 frames or pictures per second (pps).
Code: Select all
6 step time 30 60 120
seconds pps pps pps
Female 4.20m 1.442 43 87 173
Male 5.30m 1.449 43 87 174
Male 5.70m 1.446 43 87 174
Bubka 6.10m 1.356 41 81 163
Mack 5.90m 1.381 41 83 166The frame rates are for NTSC standard rates for video capture and playback.
The data show that is not possible to differentiate between the variables of interest (especially step rate) in the performances of Bubka and Mack with any confidence until the original video is recorded at 60pps. It is possible to de interlace the video taken at 30 frames per second and produce a playback at the equivalent of 60 frames per second. This still only gives a time resolution of + - 0.0167 seconds and not the 0.001 seconds claimed! For the female and the male to be confidently differentiated with respect to the step rate and length, the original video would need to have been recorded at at least 120 frames(pps) to be confident about the observed similarities or differences. In a nutshell, at 30pps it is not possible to see with any confidence known differences in step length and rates between individuals who are relatively similar in grip length on the pole.
Other factors related to the recording of the original video source material also confound the problems of using Dartfish in this way.
DJ and others can be forgiven because the visual effect of the video is indeed very powerful and easily misleads those holding shared beliefs in regard to Grip height and the 6 step check mark invariant relationship.
Dartfish was used like a drunk uses a lampost for support rather than illumination!
Although not done to intentionally mislead, it is my contention that the inferrences that have been drawn from the video evidence are fallacious.
Therefore my conclusion remains that DJ's chart is a useful working tool to be used with care and the recognition it is not a panacea to cure all ills associated with the approach run in pole vault.
(Edit on 6-19-08 was to make chart columns functional.)
