Sinclair Coefficients

The Sinclair Coefficients are a means to compare different weight classes in olympic weightlifting.

The answer to the question "What would be the total of an athlete weighing x kg if he/she were an athlete in the heaviest class of the same level of ability?" is given by the formula: ACTUAL TOTAL × SINCLAIR COEFFICIENT = SINCLAIR TOTAL.

There are eight bodyweight categories for male athletes: 56 kg, 62 kg, 69 kg, 77 kg, 85 kg, 94 kg, 105 kg and +105 kg, and seven for female athletes: 48 kg, 53 kg, 58 kg, 63 kg, 69 kg, 75 kg and +75 kg.

There are also two types of lifts: snatch, and clean and jerk. However, at the championships, medals are presented in both lifts separately, and in total (the combined result of the best snatch and the best clean and jerk).

To compare and rank the results, especially between bodyweight categories, the International Weightlifting Federation uses the Sinclair Coefficients which are derived statistically and calculated for one Olympic cycle (for four years, starting in the Spring of each Olympic year).

The total for each bodyweight category is a projection of the Total for that weightlifter if he/she were a competitor in the heaviest bodyweight category with the same level of ability. It is done in four body weight categories for the males (56 kg, 69 kg, 77 kg, +105 kg). For the other four categories (62 kg, 85 kg, 94 kg, 105 kg) the Sinclair Total represents the World Standard because nobody as of March 2008 has lifted the predicted total. Those projections using the Sinclair Total are shown below.

The Sinclair Coefficient is 10^{A({\log_{10}{(x/b)}})^2}. If x<b where x is the weightlifter's bodyweight, b is the world record holder's bodyweight (in the heaviest category) and A is the coefficient for this Olympic cycle, or 1.0 if x≥b.

Then, the Sinclair Total is simply the obtained total multiplied by the Sinclair Coefficient.

For example, from 2013 to 2016, a calculation of the Sinclair Coefficient might look like this:

A=0.794358141 for males
A=0.897260740 for females
b=174.393 kg for males
b=148.026 kg for females

Assume that we are assessing a male weightlifter weighing 61.9 kg with a total of 320 kg.
Then, x=61.9 kg, and we have
X=log10(x/b)=log10(61.9/174.393)=-0.449838400
A(X^2)=0.794358141*(-0.449838400)^2=0.794358141*0.20235459=0.160742013
10^(A(X^2))=10^0.160742013=1.447911485

Sinclair Total = Actual Total x S.C. = 320 kg x 1.447911485 = 463.332

To understand the whole idea, here is the chart with all male bodyweight categories (in kg) and its world record Totals, Sinclair Coefficients, and Sinclair Total. By looking at the Sinclair Total we can determine the RANK. * denotes a World Standard rather than a world record.

# Weight Class (kg) World Record (kg) Sinclair Coefficient Sinclair Total Rank
1 56 305 1.560756 476.030580 6
2 62 332 1.446243 480.152676 2
3 69 359 1.345260 482.948340 1
4 77 380 1.259304 478.535520 3
5 85 394 1.195035 470.843790 8
6 94 418 1.140840 476.871120 4
7 105 436 1.092863 476.488268 5
8 +105 472 1.000000000 472.0000000 7

The same is done for the seven female body weight categories.

# Weight Class (kg) World Record (kg) Sinclair Coefficient Sinclair Total Rank
1 48 217 1.639226 355.712042 2
2 53 233 1.508444 351.467452 5
3 58 251 1.407877 353.377127 4
4 63 261 1.328918 346.847598 7
5 69 286 1.254860 358.889960 1
6 75 296 1.197376 354.423296 3
7 +75 348 1.000000000 348.0000000 6

Notable Sinclair Totals throughout the History of Modern Weightlifting

Naim Süleymanoğlu achieved a Sinclair Total of 504 at the 1988 Summer Olympics in Seoul, South Korea - an all time world record.[1]

Yurik Vardanyan set a 491 Sinclair Total in 1984 in Varna, Bulgaria.

Yury Zakharevich set a 490 Sinclair Total in 1983 in Odessa, Soviet Union.

See also

References

  1. ↑ Ledder, Glenn (2013). "Mathematics for the Life Sciences" p. 16. http://books.google.com/books?id=0VeRAAAAQBAJ&lpg=PA16&ots=QfYf6PjYmn&dq=Sinclair%20Coefficients%20naim%20suleymanoglu&pg=PA16#v=onepage&q=Sinclair%20Coefficients%20naim%20suleymanoglu&f=false

External links

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