The idea behind the point system. For a full grade upgrade (from 4 to 5 or 7a to 7b), the points of the lower grade are multiplied by 1.75. For example: a "5" gives 21 points. The next full grade is 6a which gives 38 points (21 * 1.75).
Any minor upgrade/downgrade (from 5 to 5- or from 6a to 6a+) adds/subtracts 33% of difference of 2 full grades. For example: the difference from a "7c" (615 points) to an 8a (1078 points) is 463 points multiplied by 0,33 gives 153 points -- added to the "7c" results in 768 points for a "7c+"
I also tried a different factor: "2" for a full grade upgrade but the numbers get crazy big then.
New Approach
Using y = 4^x
Which translate to 4 times more points for a full grade upgrade. Or concretely spoken, you need to ascend a 6a 4 times in order to get the same points as 'cending a single 7a.
For the distribution of the minor grade upgrades (from 7a to 7a+) we use the tangent at the full grade point to calculate the points. It makes the minor upgrades gain less points compared to the graph of 4^x.
PHP code demoing the idea
for( $x = 0; $x <= 8; $x++ ) // grades from 1 to 9 (zero based index) { $y = pow( 4, $x ); echo "\n"; echo "Point: ($x,$y)\n"; for( $x1 = 0.2; $x1 <= 1; $x1 += 0.2 ) // minor upgrades (7a to 7a+) { $x1i = $x + $x1; $m = log(4) * pow( 4, $x ); $n = $y - $m * $x; $y1i = round( $m * $x1i + $n ); echo "Point: ($x1i,$y1i)\n"; } }
Index | Grade | Old system | New system | 4^x | 3^x |
---|---|---|---|---|---|
0 |
10 |
1 |
1 |
1 |
|
1 |
11 |
2 |
2 |
2 |
|
2 |
19 |
3 |
4 |
3 |
|
3 |
20 |
4 |
5 |
4 |
|
4 |
21 |
5 |
6 |
6 |
|
5 |
39 |
6 |
16 |
9 |
|
6 |
40 |
7 |
20 |
13 |
|
7 |
41 |
8 |
25 |
17 |
|
8 |
79 |
11 |
64 |
27 |
|
9 |
80 |
12 |
82 |
39 |
|
10 |
81 |
15 |
99 |
51 |
|
11 |
159 |
18 |
256 |
81 |
|
12 |
160 |
21 |
327 |
117 |
|
13 |
161 |
27 |
398 |
152 |
|
14 |
280 |
38 |
1024 |
243 |
|
15 |
300 |
47 |
1308 |
296 |
|
16 |
320 |
66 |
1592 |
350 |
|
17 |
340 |
82 |
1876 |
403 |
|
18 |
360 |
115 |
2160 |
457 |
|
19 |
380 |
143 |
2444 |
510 |
|
20 |
600 |
201 |
4096 |
729 |
|
21 |
620 |
251 |
5232 |
889 |
|
22 |
640 |
351 |
6367 |
1049 |
|
23 |
660 |
438 |
7503 |
1210 |
|
24 |
680 |
615 |
8639 |
1370 |
|
25 |
700 |
768 |
9774 |
1530 |
|
26 |
1080 |
1078 |
16384 |
2187 |
|
27 |
1180 |
1345 |
20927 |
2668 |
|
28 |
1280 |
1886 |
25469 |
3148 |
|
29 |
1380 |
2353 |
30012 |
3629 |
|
30 |
1480 |
3300 |
34554 |
4109 |
|
31 |
1580 |
4117 |
39097 |
4590 |
|
32 |
2160 |
5775 |
65536 |
6561 |
|
33 |
2360 |
7204 |
83706 |
8003 |
|
34 |
2560 |
10106 |
101877 |
9444 |
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