# Sinclair Coefficients

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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.

There are eight bodyweight categories for men: 56 kg, 62 kg, 69 kg, 77 kg, 85 kg, 94 kg, 105 kg and +105 kg, and eight for women: 48 kg, 53 kg, 58 kg, 63 kg, 69 kg, 75 kg, 90 kg and +90 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, with 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 its 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 56 307 1.531340 470.121 8
2 62 333 1.424167 474.248 5
3 69 359 1.329262 477.205 1
4 77 380 1.248153 474.298 4
5 85 396 1.187282 470.164 7
6 94 417 1.135776 473.618 6
7 105 437 1.090007 476.333 3
8 +105 477 1 477 2

## Women's Sinclair chart

# Weight Class (kg) World Record (kg) Sinclair Coefficient Sinclair Total Rank
1 48 217 1.585087 343.964 4
2 53 233 1.470378 342.598 7
3 58 252 1.381240 348.072 2
4 63 262 1.310596 343.376 5
5 69 276 1.243712 343.265 6
6 75 296 1.191290 352.622 1
7 90 286 1.102253 315.245 8
8 +90 348 1 348 3

## Notable Sinclair Totals throughout the history of modern weightlifting

Naim Süleymanoğlu achieved a Sinclair Total of 500.705 at the 1988 Summer Olympics in Seoul, South Korea, an all-time world record.[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 women's Sinclair total is 352.622, set by Natalia Zabolotnaya at the 2011 President's Cup in Belgrod, Russia.