BGS overall grade calculation? Your help is needed.
People often wonder how the overall grade is determined from the subgrades. It is nowhere written officially. In the most cases, it is straightforward, but it can get very unclear in certain unusual combinations of subgrades, and it is hard to pinpoint an exact algorithm.
I am proposing an algorithm as follows. You are welcome to find examples, check it, and let me know if any issues.
Calculating the overall grade from subgrades:
Rank numbers from subgrades in a decreasing order. gap is the difference between the 3rd and 4th numbers in that rank. 3rd means the 3rd number and 4th means the 4th number in that rank. overall means the overall grade.
A) If gap is 0, overall=4th.
B) If gap is 0.5 or greater:
1) If 4th is edge/surface and:
i) gap is less than 1.0, overall=4th+0.5;
ii) gap is greater than or equal to 1.0, overall=4th+1.0, except the following three scenarios,
E1) getting overall 9.5 by adding 1.0 to 4th when gap is 1.0,
E2) getting overall 10.0 by adding 1.0 to 4th, or
E3) 1st-4th=1.5 and 1st is not 10,
where we use overall=4th+0.5 instead.
2) If 4th is centering and:
i) gap is less than 2.0, overall=4th + 0.5;
ii) gap is greater than or equal to 2.0 and less than 4.0, overall=4th+1.0;
iii) gap is greater than or equal to 4.0, overall=4th +1.5.
3) If 4th is corner and:
i) gap is less than 3.0, overall=4th+ 0.5;
ii) gap is greater than or equal to 3.0, overall=4th+1.0.
Examples for scenarios:
B) 1) ii) BGS# 6509367: 4th number is edge, gap is 1.0, overall grade=4th+1.0.
B) 1) ii) BGS# 6082047: 4th number is surface, gap is 1.0, overall=4th+1.0.
B) 1) ii) BGS# 6565554: 4th number is surface 8.5 and all the rest are 10, gap is 1.5, overall=4th+1.0. [Note that this example is not covered in E1) due to the requirement of gap in E1), and also the second condition in E3) makes this example not covered in E3) either.]
B) 1) ii) [special thanks to James Kwon for this example, which prompts me to include the third exception E3) to B) 1) ii)] BGS# 9475095: 1st number is 9.5, 4th number is surface 8, gap is 1.0, it satisfies E3), so overall=4th+0.5.
B) 2) i) BGS# 6812367: 4th is centering, gap is 1.5, overall=4th+0.5.
B) 2) ii) BGS# 7199946: 4th is centering, gap is 2.0, overall=4th+1.0.
B) 2) iii) BGS# 5809940: 4th is centering, gap is 4.5, overall=4th+1.5.
B) 3) ii) BGS# 7358873: 4th is corner, gap is 2.5, overall=4th+0.5.
The first condition in E3) above means that one gets overall that is only 0.5 below 1st, if adding 1.0 to 4th; and intuitively this exception says that the variation of subgrades is too small to warrant a 1.0 addition to 4th.
In summary, corner is punished hardest, centering next, surface/edge the least. How much the overall grade is better than the worst subgrade depends on which subgrade is the worst and also depends on how much the rest three subgrades are better than the worst subgrade, measured by gap.
If you have or come across some unusual combinations of subgrades, please check with the above algorithm to see if your example satisfies the algorithm. If not, please contact me via the spinotron page.
P.S. The existence of my algorithm stems from my assumption that there is a strict albeit complicated algorithm in place for BGS for the internal grading use, and the above tries to capture that in a few lines; of course it could very well be that there is some leeway to allow graders to decide whether to add 1.0 or 0.5 by eyeballing the look of the cards when either addition to 4th would be reasonable.
I am proposing an algorithm as follows. You are welcome to find examples, check it, and let me know if any issues.
Calculating the overall grade from subgrades:
Rank numbers from subgrades in a decreasing order. gap is the difference between the 3rd and 4th numbers in that rank. 3rd means the 3rd number and 4th means the 4th number in that rank. overall means the overall grade.
A) If gap is 0, overall=4th.
B) If gap is 0.5 or greater:
1) If 4th is edge/surface and:
i) gap is less than 1.0, overall=4th+0.5;
ii) gap is greater than or equal to 1.0, overall=4th+1.0, except the following three scenarios,
E1) getting overall 9.5 by adding 1.0 to 4th when gap is 1.0,
E2) getting overall 10.0 by adding 1.0 to 4th, or
E3) 1st-4th=1.5 and 1st is not 10,
where we use overall=4th+0.5 instead.
2) If 4th is centering and:
i) gap is less than 2.0, overall=4th + 0.5;
ii) gap is greater than or equal to 2.0 and less than 4.0, overall=4th+1.0;
iii) gap is greater than or equal to 4.0, overall=4th +1.5.
3) If 4th is corner and:
i) gap is less than 3.0, overall=4th+ 0.5;
ii) gap is greater than or equal to 3.0, overall=4th+1.0.
Examples for scenarios:
B) 1) ii) BGS# 6509367: 4th number is edge, gap is 1.0, overall grade=4th+1.0.
B) 1) ii) BGS# 6082047: 4th number is surface, gap is 1.0, overall=4th+1.0.
B) 1) ii) BGS# 6565554: 4th number is surface 8.5 and all the rest are 10, gap is 1.5, overall=4th+1.0. [Note that this example is not covered in E1) due to the requirement of gap in E1), and also the second condition in E3) makes this example not covered in E3) either.]
B) 1) ii) [special thanks to James Kwon for this example, which prompts me to include the third exception E3) to B) 1) ii)] BGS# 9475095: 1st number is 9.5, 4th number is surface 8, gap is 1.0, it satisfies E3), so overall=4th+0.5.
B) 2) i) BGS# 6812367: 4th is centering, gap is 1.5, overall=4th+0.5.
B) 2) ii) BGS# 7199946: 4th is centering, gap is 2.0, overall=4th+1.0.
B) 2) iii) BGS# 5809940: 4th is centering, gap is 4.5, overall=4th+1.5.
B) 3) ii) BGS# 7358873: 4th is corner, gap is 2.5, overall=4th+0.5.
The first condition in E3) above means that one gets overall that is only 0.5 below 1st, if adding 1.0 to 4th; and intuitively this exception says that the variation of subgrades is too small to warrant a 1.0 addition to 4th.
In summary, corner is punished hardest, centering next, surface/edge the least. How much the overall grade is better than the worst subgrade depends on which subgrade is the worst and also depends on how much the rest three subgrades are better than the worst subgrade, measured by gap.
If you have or come across some unusual combinations of subgrades, please check with the above algorithm to see if your example satisfies the algorithm. If not, please contact me via the spinotron page.
P.S. The existence of my algorithm stems from my assumption that there is a strict albeit complicated algorithm in place for BGS for the internal grading use, and the above tries to capture that in a few lines; of course it could very well be that there is some leeway to allow graders to decide whether to add 1.0 or 0.5 by eyeballing the look of the cards when either addition to 4th would be reasonable.
