# 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 xb.

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

For example, from 2009 to 2012, a calculation of the Sinclair Coefficient might look like this:

A=0.784780654 for males
A=1.056683941 for females
b=173.961 kg for males
b=125.441 kg for females

Assume that we are assessing a male weightlifter weighing 56 kg with a total of 305 kg.
Then, x=56 kg, and we have
X=log10(x/b)=log10(56/173.961)=-0.49226387
A(X^2)=0.784780654*(-0.49226387)^2=0.784780654*0.242323718=0.190170966
10^(A(X^2))=10^0.190170966=1.54942645

Sinclair Total = Actual Total x S.C. = 305 kg x 1.54942645 = 472.5751


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 1.558521584 475.349083 2
2 62 327 1.441035030 471.2184548 7
3 69 358 1.338020780 479.0114392 1
4 77 380 1.250896723 475.3407547 3
5 85 394 1.186208968 467.3663333 8
6 94 418 1.132098286 473.2170835 4
7 105 436 1.084720914 472.9383185 5
8 +105 472 1.000000000 472.0000000 6

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 1.527286404 331.421150 3
2 53 230 1.405834156 323.341856 6
3 58 251 1.313997403 329.813348 4
4 63 257 1.243171779 319.495147 7
5 69 286 1.178167275 336.955841 1
6 75 296 1.129083982 334.208859 2
7 +75 328 1.000000000 328.0000000 5

## 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.

A man who set 35 world records during his career, Yury Zakharevich, did a 490 Sinclair Total in 1983 in Odessa, Soviet Union.