# The Deficiencies of the Graders Rule

The Graders Rule is a device with which beef graders estimate and report yield in beef carcasses. For most purposes the graders simply report the Yield Grade as Y1, which is any carcass with a yield of 59% or better, Y2, which is a yield of 54 to 58% and Y3, which is a yield of less than 54%. An actual yield percentage can also be estimated.

The Rule is a failed attempt to make practical use of the following Lean Meat Yield Formula:

The ruler is depicted below and I will describe shortly how it is used.

**Shortcomings of The Yield Ruler**

In 2006, 62.5% of all youthful carcasses within the A and Prime grade series were Yield Grade 1; 26.6% were YG 2 and about 10.9% were YG 3.

The first deficiency is obvious. A classification system for such an important characteristic as Yield, that is not divided into more than 3 categories (the American system has five) and that is not reasonably cantered on the normal distribution of carcass yield is not useful as a guide to improvement. It is reasonable to assume that within the almost two out of every 3 carcasses that are classified as Y1 there must be considerable variation that could form the basis for selection and for genetic and management improvement. But this information cannot easily be obtained.

The rebuttal will be that the graders rule also allows the grader to indicate the percentage yield of the carcass but the deficiencies in that system are that the arbitrary maximum yield is 65% and the minimum yield is 49%.

I want to emphasize that the comments in this analysis are not a criticism of the grader. The grader does the best that can be done with the Grader’s Rule. It is the ruler itself that creates inaccurate yield estimates.

Yield is determined by first measuring the length and width of the Longissimus Dorsi (LD) muscle to determine a “Muscle Score”. Note on the ruler depicted above that there are two little green boxes marked on each edge. They are exact duplicates and only one set is necessary. The length of the LD muscle is measured along its long axis from the sharp point on the bottom (left) edge of the ruler above. If the length of the LD muscle is less than the distance from the sharp point on the ruler to the most distant green box the length is taken as a “1”. If the length falls within that green box the length is taken as a “2” and if it the length of the LD muscle extends beyond the end of the green box the length is a “3”. The width of the LD muscle is also measured, and awarded either a “1” or a “2” or a “3” depending upon whether the LD muscle width is less than, within or longer than the 7 mm wide green box that is closest to the sharp point on the rule.

The next step requires reference to the Table labelled “Muscle” on the face of the ruler. If both measures of length and width are 1 or if there is a combination of a 1 and a 2 (or a 2 and a 1) we have a Muscle Score of 1. If the length is 2 and the width is 2 the Muscle Score is 2. Also a (3, 1) or a (1, 3) combination of length and width results in a Muscle Score of 2. A (3, 2) or a (2, 3) on length and width results in a Muscle Score of 3 while a (3, 3) combination means a Muscle Score of 4. One can see at once that the Graders Rule compresses three lengths and three widths, which should be expected to yield 9 combinations, into just 4 Muscle Scores.

A further point to note is that no minimum or maximum width and length is recorded. Thus, according to the ruler one cannot have a yield below 49% nor one above 65%. I am not much concerned about yields that are below 49% as that is bad enough. But yields above 65% likely occur with some frequency and these are exceptional carcasses that should be noted.

As already noted the grader does not actually measure the length and width of the LD muscle. For purposes of making calculations I did so.

The length at closest edge of the most distant 2 block is 14.1 cm and to the outer edge it is 15 cm. The width of the 2 block is 0.9 cm. For computational purposes I suggest that the minimum length would be 14.1-0.9 or 13.2 cm and the maximum length would be 15+0.9 or 15.9cm.

The width length at closest edge of the inner 2 block is 6.4 cm and to the outer edge it is 7.1 cm. The width of the 2 block is 0.7 cm. For computational purposes I suggest that the minimum would 6.4-0.7 or 5.7 cm and the maximum length would be 7.1+0.7 or 7.8 cm.

If one computes the area of the rectangles represented by these lengths and width’s one finds that there is a large degree of overlap in the areas described as Muscle Scores 1 to 4. I recognize that I am computing the area of the rectangle and not of the contained LD muscle but it is sound to assume that the LD contained in the rectangle is a fairly constant fraction of the area of the rectangle.

I found that the range of rectangular areas were as follows

For Muscle Score 1 from 75.2-99.4 sq cm.

For Muscle Score 2 from 86.7 to 109.2 sq cm.

For Muscle Score 3 from 96.6 to 117.0 sq. cm., and,

For Muscle Score 4 from 108.7 to 124.2 sq. cm.

Muscle Score 1 overlaps Muscle Score 2 by 56.4% and even overlaps Muscle Score 3 by 12%. Muscle Score 2 overlaps Muscle Score 3 by 61.8% and overlaps Muscle Score 4 slightly. Muscle Score 3 overlaps Muscle Score by 53.5%.

What this degree of overlap means that a carcass graded Y1 by the grader could be a Y2 in over half the cases while a carcass graded Y2 could as easily be a Y1 or a Y3. Similarly, a carcass assigned a Y3 grade might just as often actually be a Y2.

The area of the Longisimus Dorsi Muscle contributes positively to yield. In the formula above the factor is (0.212 x REA in Sq Cm). The rectangular areas that I have cited above represent the area of the rectangle that contains the LD muscle (i.e. L x W). In other work that I have done I have determined that on average the REA is equal to L x W x 0.78. This was an interesting determination inasmuch as the area of any circle contained in a square is a mathematical constant of 0.7854. In any case we can now calculate the contribution that Muscle Score as a proxy for REA makes to Yield. I will show the calculations for the Muscle Score 1 range and then just the ranged for Muscle Scores 2,3 and 4.

Muscle Score 1 = 0.212 x(75.2 x 0.78) = 16.0

to

0.212 x (99.7 x 0.78) = 21.1

Muscle Score 2 18.4 to 23.2

Muscle Score 3 21.1 to 24.8

Muscle Score 4 23.0 to 26.3

Again we see the pronounced degree of overlap.

This degree of overlap renders the Muscle Score component of the grading system useless as a reliable predictor of Yield Class to say nothing of Yield Percent.

A much more accurate approach would be to actually measure the length and width of the LD muscle and multiply the two. This will rank carcasses much more correctly on LD area than the Muscle Score system. In fact, making actual measurements of muscle length and width should be no more time consuming than using the grader’s rule and the dimensions can easily be entered into a simple hand held calculator along with fat thickness and carcass weight to complete a pre-programmed yield formula. This would result in a much more accurate and consistent yield estimate.

**No Consideration of Carcass Weight**

A final deficiency with the Grader’s Rule is that it gives no consideration to the negative relationship between carcass weight and yield. In the Blue Tag Formula yield is reduced by a factor of 0.032 x the Hot Carcass Weight in kg. This means that an increase of 100 pounds in carcass weight over the average reduces yield by 3.2 percentage points while a carcass weighing 100 pounds less than average would increase yield by 3.2 percentage points. The Grader’s Rule ignores this consideration.

The differences between the methodology used in applying the graders rule and use of actual measurements clearly indicate the superiority of actual measurement over the consolidation of classes. We are using an adaptation of the old Blue Tag Formula and our measurements of Hot Carcass Weight (HCW), length and width of the LD muscle and fat thickness are precise. The graders rule ignores HCW and classifies Fat Thickness into categories that are 2 mm wide. A 1 mm increase or decrease in average fat thickness decreases or increases the yield estimate by 0.68 of a percentage point.

The real deficiency comes with the strange practice of classifying Rib-Eye Length and Width into only three categories and deriving from that a muscle score that causes both an unnecessary imprecision and an overlap in the yield estimates.

Recording the actual dimensions of the LD and Fat Thickness takes no more time than the current practice, and is markedly more accurate.

Yield is too important a characteristic of beef carcasses to be estimated in such an imprecise manner.