Dr Mel Siff Blog

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It was most interesting to note in the latest issue of the NSCA’s Journal of
Strength & Conditioning Research that several well-known Finnish scientists
have developed another weightlifting comparison formula after analysing those
developed by others such as Sinclair and myself. In certain places I have
considered it appropriate to comment on this paper, either to make
corrections or to simplify what was written.

I have included only the most relevant excerpts for my commentary – those who
wish to read the entire article can do so in the Journal.

—————————

Kauhanen H, Komi PV & Haekkinen K. Standardization and validation of the body
weight adjustment regression equations in Olympic weightlifting.

J of Strength & Conditioning Research: Vol 16, No 1, pp 58-74

ABSTRACT

The problems in comparing the performances of Olympic weightlifters arise
from the fact that the relationship between body weight and weightlifting
results is not linear. In the present study, this relationship was examined
by using a nonparametric curve fitting technique of robust locally weighted
regression (LOWESS) on relatively large data sets of the weightlifting
results made in top international competitions. Power function formulas were
derived from the fitted LOWESS values to represent the relationship between
the 2 variables in a way that directly compares the snatch, clean-and-jerk,
and total weightlifting results of a given athlete with those of the
world-class weightlifters (golden standards).

A residual analysis of several other parametric models derived from the
initial results showed that they all experience inconsistencies, yielding
either underestimation or overestimation of certain body weights. In
addition, the existing handicapping formulas commonly used in normalizing the
performances of Olympic weightlifters did not yield satisfactory results when
applied to the present data.

It was concluded that the devised formulas may provide objective means for
the evaluation of the performances of male weightlifters, regardless of their
body weights, ages, or performance levels.

Siff Formulas (sic)

….. Siff (33) regressed the mean values of the 10 best total results made
up to 1988 in each weight category by using this power function and found the
following parameters for men: a = 512.245, b = 146,230, and c = 1.605. Thus,
the world-class normal value for the athlete of a given body weight could be
obtained by the following formula:

R = 512.245 – 146.230*M^ -1.605 ………….. (13)

and the actual result could then be compared with this predicted result,
yielding the relative performance of the athlete.

The advantages of Siff’s power function formula are that it is easy to apply
and upward sloping for all body weights, thus giving comparable results also
for the heavier athletes. A drawback, however, is that the regression does
not pass through the origin. Hence, the formula may only be used for adult
athletes because the normal values the formula gives are unrealistically low
for the body masses less than 50 kg (and even negative if the athlete’s body
mass is less than 33.9 kg), thus favoring very light-weight athletes.

[*** Mel Siff: This comment about the formula not passing through the origin
displays a woeful ignorance of the basic fact that no lifters ever weigh
ZERO! My formulae were devised to compare the actual lifting performances
or real athletes in officially designated bodymass divisions, not virtual
humans whose bodymass is ZERO. That is why I specifically discarded any
formula which passed through the origin (0,0) and clearly restricted its use
to adult lifters in actual Weightlifting divisions from 52 kg upwards. I
deliberately devised other formulae for juveniles and women. Of course, I
knew that my formula gave unrealistic results for humans weighing less than
about 45kg - that is why I devised different equations for different ages
and genders, whose physiological differences clearly have shown that their
strength performances do not mirror that of adult males. I have never come
across any adult male lifters who weigh less than 45kg, so there was no need
to have any equation for adult males start at that unrealistically low
bodymass. ]

…..Being aware of this limitation, Siff (33) modeled the results of the
best performances of both juvenile (<18 years between the body weights of 33
and 90 kg) and senior weightlifters (between the body weights of 52 and 135
kg) using the Gompertz function. Despite its rather complex computation, the
Gompertz function is frequently used in describing biological systems,
especially growth curves, because it is thought to be advantageous in terms
of both mathematical and biological validity. Because of its multiple
exponential (exponential of an exponential) form, the Gompertz function
yields a sigmoid (S-shaped) curve that, however, does not need to be
symmetric around its point of inflection. This makes the Gompertz function
flexible to use with those data sets, which are upward sloping with varying
slopes. The original Gompertz function is of the following form:

[ y = a special exponential of an exponential ]

Siff compared the differences between the actual and predicted results
obtained with this formula and concluded that “In the case of senior
weightlifting, the Gompertz function proves to be superior to any equations
yet deduced to relate lifting strength to body mass in terms of simultaneous
mathematical accuracy and relationship to growth models used in biology
(33)”. However, no updating of the parameters has been provided since 1988….

[*** Mel Siff: The authors based their analysis of my work on publications
from 1980 and 1988 and did not check to ascertain if I had carried out any
subsequent research on the same topic. As can easily be seen form
"Supertraining" or from a simple search of several websites, they could have
discovered my more recent formulae of some 5 years later, including my
decision to no longer use the Gompertz formulae. My later work found that
simper equations produced equally good results and all highly complex
formulae were subsequently jettisoned. Consequently, these comments about my
formulae warrant some revision.]

Methods

….The data for the study were selected from the weightlifting results made
in the World Championships and the Olympic Games during 1973–1999 with the
respective body weights measured at the official weigh-in before each
competition (18) . The results of the 6 best male weightlifters in each
weight category were divided into 3 different data sets of the snatch (s),
clean-and-jerk (cj), and total (tot) results according to the respective
ranking positions in each particular lift. Descriptive statistics and
individual results for the 3 data sets are shown in Table 1 and
Figure 2 , respectively…..

[*** Mel Siff: Note that the authors without giving me any direct credit for
introducing the approach of taking the mean of 10 or 6 of the best ever
performances in every division, rather than the world records in each cases,
simply adopted the same method as if they had produced it! Nobody else in
the world had ever formulated such an approach, so I would have thought that
this offered some recognition for originality. ]

Results

Relationship Between Body Weight and Weightlifting Performance

Figure 2 shows the scatterplots of the snatch (s), clean-and-jerk (cj), and
total (tot) weightlifting results superimposed by their respective LOWESS
fits. Apparently, the results of the very heaviest athletes tend to distort
the otherwise smooth parabola-like fits in all 3 data sets. This clearly
cannot be considered to be a normal behavior of the regression model between
the 2 variables but rather an artifact that results from the small number of
athletes being heavier than 160 kg. Fortunately, the results and the body
weights of the heavier athletes (>110 kg) seem to be normally distributed,
which was also verified statistically. This gave justification to average
these values (separated by the dashed lines in Figure 2 ) to yield one
representative data point for the superheavy (+110-kg) athletes. The result
of this averaging is shown for total weightlifting in Figure 3 ……

Model Parameterization

The desired consequence of this adjustment was a smooth, upward-sloping fit
in each of the 3 data sets, suggesting that the best-fit parametric models
were most likely to be formulated by using power function (Equation 12) with
some reasonable estimates for the parameters a, b, and c. However, rather
than merely formulating the relationship between body weight and
weightlifting results, the aim was to devise formulas that could be used in
the evaluation of the weightlifting performance of a given athlete without
the need to use coefficients or to make any further comparisons. These
formulas were obtained by using Equation 18, which minimized the RSSs from
the fitted LOWESS values while using 100/fitted value as the dependent
variable. The results of this minimization are shown in Table 2 .
Substituting the parameter estimates into Equation 19 yielded the following
formulas:

Ps = Rs (0.5086 + 81.782*M^-3.0870) …………….. (20)

Pcj = Rcj (0.4196 + 70.635*M^-3.1143) …………….. (21)

Ptot = Rtot (0.2314 + 42.195*M^-3.1286) …………… (22)

where P is the percentage of a given lift (s, cj, or tot) from the golden
standard (100%), R is the actual lifting result (in kilograms), and M is the
body mass (in kilograms) of the lifter. For these formulas, the following
analogy holds:

Golden Standard GS = 100*(Ri * Pi^-1)

[*** Mel Siff: which simply means GS = 100*(Ri / Pi) ..... by the way ]

where GS is the golden standard and i is the lift (s, cj, or tot). Thus,
formulas 20-22 give direct percentage indices for the evaluation of the
relative weightlifting performance of each individual male weightlifter,
regardless of his age or performance level.

The goodness-of-fit statistics (Table 2 ) indicate that the devised formulas
follow extremely well the true nonparametric manifestations of body weight
and weightlifting results in all 3 data sets (R2 = 0.9999). The validity of
the formulas is further confirmed in Figure 4 , which shows the percentage
residuals of the total results when calculated from both the nonparametric
LOWESS and golden standard values and regressed against the respective total
results in each of the 25 weight categories, which have been used in the
history of weightlifting since 1973. In each individual weight category
(except for the heaviest ones), the values overlap perfectly and are arranged
in a linear fashion with decreasing slopes with the increase of the weight
categories. The more scattered locations and the poorer overlapping of the
values in the heaviest weight categories are due to the wide distribution of
the data and the adjustments made before the formulation as described
earlier…….

Except for the 2 formulas of Siff, the goodness-of-fit statistics yielded
relatively high R2 [correlation coefficient] values (>0.87) for all models
when calculated from the initial data (column I in Table 6 ). When regressed
against the golden standard, the R2 values even tended to rise, being higher
than 0.95 in all cases, except for the second-order polynomial (column II in
Table 6 ). However, assuming that the golden standard is the optimal model
for the data, the best goodness-of-fit indicators would be the R2 values and
the percentage prediction errors (PPEs) calculated directly from the
predicted golden standard values (column III in Table 6 ). In this case, the
mean percentage prediction errors for most of the models were less than 1%,
and, except for the second-order polynomial and the 2 formulas of Siff, the
R2 values were higher than 0.95.

The right-side graphs in Figure 6 show the behavior of the models as a
function of body weight. The ordinates are the percentage differences between
the model and golden standard for a given body weight (PPE). It should be
noted that the ordinates have different scales and, therefore, are
incomparable to the true differences between the models being far more
substantial…… Larger errors were found with the commonly used
handicapping formulas, especially with those of Siff. The Sinclair formula
yielded moderate results (±2% error), whereas both Siff formulas considerably
underestimated all body weights, with an increasing trend toward the heavier
athletes…….

[*** Mel Siff: Note very well what the authors mention: "However, assuming
that the golden standard is the optimal model for the data,...." Their
entire analysis of other weightlifting formulae is based upon this
assumption. ]

[*** At this point the authors constructed Table 3 to compare the results of
top weightlifters in different bodymass divisions using the Siff and Sinclair
formulae, but it is noteworthy that they did not include a column to show how
well their formula applied to actual world class lifts. I am sure that
readers of the journal would like to have seen their formulae as used in
practice. Maybe their formulae do represent an improvement over those
devised by others, but it certainly would be helpful to readers to see some
practical examples of those equations on all world records for all lifters,
as they state "irrespective of his age or performance level".]

An important feature that one should be aware of in these analyses (likewise
in those made by Lietzke) is that the actual body masses of the athletes were
not known, and therefore, the upper limits of the weight categories had to be
used as the independent variable. For this reason, the superheavy (unlimited)
weight category also could not be included in the analysis. There is,
however, some evidence that the exponent found by regressing the
log-transformed values decreases when including the superheavy lifters in the
analysis. Croucher, when analyzing the 1982 world records, approximated the
normal body weight for a superheavy weightlifter to be 145 kg and found the
exponents 0.584 and 0.577 for the snatch and clean-and-jerk, respectively. To
our knowledge, the only study in which both the actual body masses and the
superheavy lifters have been included in the log-linear analysis is that of
Batterham and George, who modeled the results of the medalists in the Women’s
and Men’s World Weightlifting Championships of 1995…..

[*** Mel Siff: This is also incorrect - even my early comparison formulae
were based upon the performances by the superheavy lifters for their actual
bodymasses, which I obtained from official competition sheets. As a matter
of interest, I intentionally omitted providing all details of the lifts and
actual bodymasses of the superheavies way back then, because I was aware that
other scientists might borrow that approach to produce their own "unique"
formulae.

Here is a relevant excerpt from my 1988 paper (SA Journal of Sports Sci, Phys
Ed & Recr (11)1: 81-92

"The next step was to establish a data base of these Totals for both sports
which is valid for body masses beyond the range used by all previous
researchers and which is not seriously changed every time a world record is
broken. This was achieved by obtaining the official records from the
international governing bodies for both these sports and extracting the ten
highest Totals ever achieved in every body mass division. The mean of these
ten best Totals was calculated, as world records or world best performances
over a few years can change very frequently and are sometimes set by a
'freak' (such as Bob Beamon of long-jump fame), whose lone performance does
not reflect fairly the consistent ability of the world's best competitors.

Other workers had to exclude data from the + 110 kg (over 110 kg) division in
weightlifting (125 kg in powerlifting), as a lifting Total could not be
related to a division which involved an extensive variety of body masses with
no upper limit. In this investigation it was possible to obtain the exact
body mass for the top twenty lifters in this division and regression analyses
of the Totals recorded at these body masses were performed. It emerged that
it was similarly informative to determine the mean of the top ten Totals in
the + 110 kg division and relate it to the mean of the body masses of the
lifters who achieved these results. This method immediately produced the
missing data point necessary to extend the range of validity of strength
equations beyond the former limit of 110 kg in weightlifting and 125 kg in
powerlifting. Initially a cubic spline regression was used to fit the best
possible curve through all the data points as a guideline to narrow down the
search for a suitable equation to the most likely types of mathematically
continuous regression...." ]

Why should we use such large data sets and not the results of the winners or
just the existing world records in the modeling? The main reason is to avoid
the bias caused by the heteroscedasticity in the data (the variance of the
residuals increases with the increase of body weight; Fig 2 ). Of even more
concern is the relative heteroscedasticity, suggesting wider percentage
distribution of the residuals in the light and heavy weight categories
compared with the middle weight categories. Similar observation has been made
earlier by Dooman and Vanderburgh. Thus, when using the models derived solely
for the winners, the performances of the 6 best lifters in both extremities
of the data set were found to be much lower than those in the middle of the
data set (Fig 8A ).

[*** Mel Siff: Here the authors make it sound as if they uniquely and
originally discovered the heteroscedasticity problem associated with basing
any comparison formulae on a single data point (world record) in each
bodymass division. The fact is that even my earliest publication (1980) in
the field of weightlifting formulae showed that I introduced methods based
upon the mean of the top 6 or 10 best performances ever achieved in
weightlifting. They did nothing original here, and it is rather
unprofessional that the wording of their paper implies that nobody else
preceded them by over two decades in this approach. --- see the above excerpt
from my 1988 paper ]

However, assuming that the world-class weightlifters from different weight
categories should display equal abilities and thus equal relative
distribution of the performance, the present models derived for more
extensive data sets may provide more fair criteria for the scaling, since the
relative variance remains rather constant throughout the whole range of the
weight categories (Figure 8B ). Another reason for using larger data sets
instead of the winners was to reduce the impact of exceptional results on the
model. Including the results from the extensive period in the model also
makes unnecessary the updating of the parameters regularly.

[*** Mel Siff: This once again is exactly what I stated in my earliest
papers, where I stressed that a single exceptional increase in a world record
could exert a profound impact on the equations. This was my original
approach and the authors created the impression that their work was original.
--- see the above excerpt from my 1988 paper again.]

The rather low convergence of the handicapping formulas of Siff and Sinclair
is most probably due to the different materials used in the modeling. Siff
(33) modeled the mean values of the 10 best results ever made in each weight
category up to year 1988. Obviously, these models represented a higher
ultimate performance level compared with those of the present study, leading
to the underestimation of all body weights when applied to the present data.
Still, the prediction of the Sinclair formula, even though the parameters
were derived from the recent world records, such an underestimation was not
observed probably because the baseline was adjusted according to the mean
Sinclair scores a priori (Equation 26). Still, the predicted results of the
Sinclair formula yielded ±2% error, which, with those lifters totaling 400
kg, may be as much as 8 kg. This error most likely accounts for the fact that
the Sinclair formula is constrained to be of polynomial form, which differs
from that of the present nonlinear power function derived from the
nonparametric fits of a more extensive data set. Of particular concern in
both the Siff and Sinclair formulas is the inconsistency observed in the
prediction errors throughout the different body weights (Figure 6 )……..

[*** Mel Siff: Note what was written: "The rather low convergence of the
handicapping formulas of Siff and Sinclair is most probably due to the
different materials used in the modeling. Siff modeled the mean values of the
10 best results ever made in each weight category up to year 1988. Obviously,
these models represented a higher ultimate performance level compared with
those of the present study, leading to the underestimation of all body
weights when applied to the present data." Correct, the differences lie in
the choice of different materials used in the modelling and whenever one
encounters their comments about my formulae having a low correlation
coefficient, this is because the correlations of my formulae are measured
according to the different standards chosen by the authors. All of my
formulae displayed a correlation coefficient of over 0.996 when compared with
the original means across all divisions. Similarly, I could conceivably
deduce that their formulae may not correlate well according to my selected
standards. At least the authors admitted that their analysis could have been
influenced by this fact.]

Practical Applications

The present formulas for the snatch, clean-and-jerk, and total results
(Equations 20-22) may easily be implemented on a computer or a pocket
calculator, thus providing a simple and suitable tool for the evaluation of
the relative weightlifting performance of each individual male weightlifter,
regardless of his age or performance level.

In those situations where it is not possible to calculate the indices
directly from the equations, golden standard tables may provide a quick
overview of the performance. These tables can easily be produced by the
following calculations:

Rs = P(0.5086 + 81.782*M^-3.0870)^-1 ……… (29)
Rcj = P(0.4196 + 70.635*M^-3.1143)^-1………… (30)
Rtot = P(0.2314 + 42.195*M^ -3.1286)^-1……….. (31)

where R is the required result (in kilograms) for a given lift (s, cj, or
tot), P is the normalized result (percentage of a result from the golden
standard), and M is the body mass (in kilograms). An example of such a table
is given in Figure 10 , which shows the results required for different
relative indices (65-120% of the golden standard) of the total weightlifting
performance in a selected array of body weights (50-110 kg with 1-kg
intervals). Selecting the athlete’s total result from the row corresponding
to his body mass and following the column upward yields the normalized value,
which can be read from the first row.

[*** Mel Siff: This statement of their findings is worded rather tediously.
What the authors essentially mean here is that the lifter's performance as
calculated as a percentage of the mean of the world's best 6 performances may
be determined from the following formulae (I am just showing the one for the
Total):

P = Total * (0.2314 + 42.195*M^ -3.1286)

I have already placed their formulae into Excel and, when the time permits, I
hope to compare how well their formulae work in practice alongside other
formulae, including mine. If others have the time to do the same before I
manage to do so, your efforts will be appreciated. ]

Dr Mel Siff
Denver, USA
http://groups.yahoo.com/group/Supertraining/

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