Sinclair Coefficients

The Sinclair Coefficients are a method to compare different weight classes in Olympic weightlifting. It replaced Hoffman's formula, which was the first statistical analysis of this type.

The method provides 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?", given by the formula: ACTUAL TOTAL × SINCLAIR COEFFICIENT = SINCLAIR TOTAL.

Since 1 November 2018, there are ten bodyweight categories for each gender. For men, they are 55 kg, 61 kg, 67 kg, 73 kg, 81 kg, 89 kg, 96 kg, 102 kg, 109 kg, and +109 kg, and for women: 45 kg, 49 kg, 55 kg, 59 kg, 64 kg, 71 kg, 76 kg, 81 kg, 87 kg and +87 kg.

There are two types of lifts: snatch, and clean and jerk. However, at most championships, medals are presented for both lifts and the 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.

The Sinclair Coefficient is ${\displaystyle 10^{A({\log _{10}{(x/b)}})^{2}}}$ 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 2017 to 2020, a calculation of the Sinclair Coefficient is as follows given A=0.751945030 and b=175.508 kg for men and A=0.783497476 and b=153.655 kg for women.

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(61.9/175.508) = −0.4526062683
A(X^2) = 0.751945030 × (-0.4526062683) ^ 2 = 0.751945030 × 0.204852431 = 0.1540377697
10^(A(X^2)) = 10^0.1540377697 = 1.4257315812

Sinclair Total = Actual Total × S.C. = 320 kg × 1.4257315812 = 456.234