Understanding the weighting factors used in KCBS judging
By JOE
O'CONNELL, cbbqa past
President
Updated April 21, 2002
The
Kansas City Barbecue Society (KCBS) currently weights the raw scores of
judges at contests. Each raw appearance score is converted to a
weighted score by multiplying it by 0.5714; each raw taste score
is converted to a weighted score by multiplying it by 2.2858; and
each raw tenderness score is converted to a weighted score by multiplying it
by 1.1428 -- as explained in the applicable KCBS Rules, which is
KCBS Rule 19.
Reason for the strange numbers
There is a historical reason for the seemingly strange weighting
factors that are used in KCBS scoring. The history may be told
very briefly as follows.
Originally taste was given twice the weight
In the beginning, the appearance, taste and tenderness scores were given the
range of from 9 to 1, with 9 being highest. However, the taste score was
doubled (multiplied by 2), because in those days KCBS wanted to give twice as
much weight to the taste score as it gave to the appearance and tenderness
scores.
Originally 180 was a perfect score
Therefore, if a single judge scored an entry with 9-9-9, the entry would
receive a total of 36 points from that judge.
Note: in this and elsewhere, scores are always
listed in the order of appearance, taste and tenderness.
Under the KCBS rules, the low score was disregarded ("thrown out")
in calculating an entries total score. Thus, if an entry received scores
of 9-9-9, 9-9-9, 9-9-9, 9-9-9, 9-9-9 and 2-2-2, the low score would be
disregarded. Therefore, the highest possible score would be 180 points - a
perfect 180 - equal to 36 points times 5 judges.
New rule changed the weighting
In 1999, KCBS changed the weighting system. Prior to 1999, taste was
given twice the weight as appearance and tenderness, and it was a simple matter
to double the taste score and then add the appearance and tenderness scores to
determine the final weighted scores. For example, a raw score of 8-8-9
became a weighted score of 8+(8+8)+9 or 33.
For 1999, KCBS decided to change the weighting so that tenderness is given
twice the weight as appearance and taste is given twice the weight as
tenderness.
However, KCBS also decided not to change the fact that the raw scores must be
from 9 to 1, that the highest possible score by a single judge must be 36
weighted points, and that the highest possible score by all judges must be 180
weighted point - a perfect 180.
This created a mathematical conundrum: what numbers to use as weighting
factors that would keep a 9 to 1 range of raw scores, a 36 point weighted score
maximum per judge, and a 180 point weighted score maximum per entry?
Rule of 7
The Rule of 7 solves the problem. To understand the Rule of 7, consider
that, if 4 is the taste, 2 is the tenderness, and 1 is the appearance, then the
taste is worth twice the tenderness, and the tenderness is worth twice the
appearance.
Thus, the taste score will have, as one of its elements, the factor of 4
divided by 7, or 4/7; similarly, tenderness will have 2/7; and
appearance will have 1/7. Since all these ratios use a common denominator
of 7, this is called the Rule of 7.
The Rule of 7 solves the issue of how to weight taste to equal twice as much as
tenderness, and tenderness to equal twice as much as appearance. But the Rule of 7
has to be tied into the maximum weighted limitations of 36 points per judge.
Factor of 4
To tie the Rule of 7 into the maximum of 36 points per judge, consider that,
in the old system, a score of 9-9-9 was converted by doubling the taste score
into 9+(9+9)+9. This means that, if a judge awards 9-9-9 under the new
system, the new system has to convert the score into 36 points.
That is, the Rule of 7 succeeds in weighting each of the raw scores from 9 to
1, but these must then be multiplied by 4 in order to total a weighted score
from a single judge of from 36 (a perfect score) to a disqualification score.
To do so, the raw scores have to be weighted as follows: the ratios
under the Rule of 7 must be multiplied by 4, and that result must be multiplied
by the raw score in each of the three areas of appearance, taste and tenderness.
Weighting factors
Based upon the Rule of 7 and the Factor of 4, the weighting factors can be
constructed as follows.
In the case of appearance, the raw score is converted to a weighted
score by multiplying the raw
appearance score by 1/7 times 4. In the
case of taste, the raw score is converted by multiplying the raw taste score by
4/7 times 4. In the case of tenderness,
the raw score is converted by multiplying the raw tenderness score by 2/7 times 4.
By using these weighting factors, a perfect raw score of
9-9-9 by a single judge will be converted into a perfect weighted score of 36, as follows:
A raw score of 9 in appearance times 1/7 times 4 equals a weighted
appearance score of 5.14285714285714285714285714285714
A raw score of 9 in taste times 4/7 times 4 equals a weighted taste score
of 20.5714285714285714285714285714286
A raw score of 9 in appearance times 2/7 times 4 equals a weighted
appearance score of 10.2857142857142857142857142857143
These three weighted scores added together equal a total weighted score of 35.9999999999999999999999999999956
Rounding rules
As shown above, using more than 30 digits is even insufficient to exactly equal 36
points. KCBS studied these factors and realized that, if the factors were
rounded to four places, then a perfect score of 36 was possible. Here's
how.
The ratio of 1/7 times 4 equals 0.571428571428571428571428571428571. This
can be rounded to 0.5714 (using the normal rules of rounding up and rounding
down), which is set forth in KCBS Rule 19 as the appearance weighting factor.
The ratio of 4/7 times 4 equals 2.28571428571428571428571428571429. This
can be rounded to 2.2857 (using the normal rules of rounding up and rounding
down), but KCBS uses a slightly different factor of 2.2858, which is set
forth in KCBS Rule 19 as the taste weighting factor.
The ratio of 2/7 times 4 equals 1.14285714285714285714285714285714.
This can be rounded to 1.1429 (using the normal rules of rounding up and
rounding down), but KCBS uses a slightly different factor of 1.1428,
which is set forth in KCBS Rule 19 as the tenderness weighting factor.
Application of KCBS Rule 19
When a single judge awards a perfect score of 9-9-9, the weighting factors
have the following results:
A raw score of 9 in appearance times the appearance weighting factor of 0.5714 equals a weighted appearance
score of 5.1426
A raw score of 9 in taste times the taste weighting factor of 2.2858 equals a weighted taste score of 20.5722
A raw score of 9 in tenderness times the tenderness weighting factor of
1.1428 equals a weighted tenderness
score of 10.2852
These three weighted scores added together equal a total weighted
score of 36.0000.
Therefore, the application of the KCBS Rule 19 weighting factors converts a
perfect raw score by a single judge of 9-9-9 into a perfect weighted score by a
single judge of 36. Furthermore, this results in the conversion of a
perfect score of 9-9-9 by all five judges (with the score of the six judge being
discarded) into a perfect weighted score of 180 weighted points, which is called
the Perfect 180.
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