# 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 xb.

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 x S.C. = 320 kg x 1.4257315812 = 456.234
```

## Men's Sinclair chart

To understand the whole idea, here is the chart with the men's bodyweight categories (in kg) and their world record Totals, Sinclair Coefficients, and Sinclair Total. By looking at the Sinclair Total, we can determine the RANK.

# Weight Class (kg) World Record (kg) Sinclair Coefficient Sinclair Total Rank
1 55 293 1.552231 454.803 7
2 61 317 1.440117 456.517 5
3 67 332 1.353700 449.428 10
4 73 360 1.285695 462.850 4
5 81 374 1.215696 454.640 6
6 89 387 1.162510 449.891 9
7 96 416 1.126229 468.511 2
8 102 412 1.100963 453.597 8
9 109 435 1.076911 468.456 3
10 +109 474 1 474 1

## Women's Sinclair chart

# Weight Class (kg) World Record (kg) Sinclair Coefficient Sinclair Total Rank
1 45 191 1.670561 319.077 10
2 49 209 1.559644 325.966 6
3 55 232 1.432118 332.251 1
4 59 237 1.365809 323.697 8
5 64 252 1.298241 327.157 4
6 71 267 1.224840 327.032 5
7 76 272 1.183684 321.962 9
8 81 283 1.149684 325.361 7
9 87 294 1.116377 328.214 3
10 +87 330 1 330 2

## Notable Sinclair Totals throughout the history of modern weightlifting

The highest men's Sinclair Total was set by Naim Süleymanoğlu at the 1988 Summer Olympics in Seoul, South Korea, with 500.705. [1]

Yurik Vardanyan set a 489.643 Sinclair Total in 1984 in Varna, Bulgaria.

Yury Zakharevich set a 489.232 Sinclair Total at the 1988 Olympics in Seoul, South Korea.

The highest ever women's Sinclair total was set by Tatiana Kashirina at the 2014 World Championships in Almaty, Khazakstan, with 364.529.