Grand Prix Tables and Formulas
We give here the formula and tables used to calculate the
grand prix points awarded for each tournament played in.
The Grand Prix points table for a standard 4-round
tournament
To find your Grand Prix point score in the table below, find
the row for your section and the column for your score in that section.
For example, you scored 3 wins in a 4-round Elementary section. You get 88 points added to your Grand Prix total point score.
|
|
4 |
3.5 |
3 |
2.5 |
2 |
1.5 |
1 |
0.5 |
0 |
|
Championship |
1000 |
707 |
500 |
354 |
250 |
177 |
125 |
88 |
0 |
|
Reserve |
250 |
177 |
125 |
88 |
63 |
44 |
31 |
22 |
0 |
|
Elementary |
177 |
125 |
88 |
63 |
44 |
31 |
22 |
16 |
0 |
|
Primary |
88 |
63 |
44 |
31 |
22 |
16 |
11 |
8 |
0 |
|
4-5 Novice |
53 |
37 |
26 |
19 |
13 |
9 |
7 |
5 |
0 |
|
2-5 Novice |
44 |
31 |
22 |
16 |
11 |
8 |
6 |
4 |
0 |
|
2-3 Novice |
37 |
26 |
19 |
13 |
9 |
7 |
5 |
3 |
0 |
|
K-1 |
31 |
22 |
16 |
11 |
8 |
6 |
4 |
3 |
0 |
|
Grand Prix points tables
for different numbers of rounds are shown later |
|
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Formulas and explanations
Legend
base = the value assigned to a
score of 4 in the Championship section, currently 1000.
#rnds = #rounds played in the section
adj = the
adjustment value for the relative strengths of the sections.
score = the players score for the
section
The basic formula
(for a 4 round tournament section):
points = base /
2**(4-score) (1000 divided
by 2 to the power of 4 minus the score)
Explanation of the
basic formula:
The basic idea is that the difference between the points assigned to a score should grow as a power of 2, thus doubling every two slots, or half-points. Thus, a score of 4 is worth twice what a score of 3 is worth, and a score of 3.5 is worth twice a score of 2.5. You can clearly see these relationships by examining the table shown above. Scores of zero are excluded from the calculation; they score zero points.
For a score of 4 in the Championship section, the basic formula yields
1000 / 2**0 = 1000/1 = 1000, while for a score of 3, it gives
1000 / 2**1 = 1000/2 = 500, which is exactly what we wanted.
Extending the basic formula to all sections
Bare in mind that our goal is to provide a single total point score for a player regardless of what sections he played in during the course of the season. For the proper values to be assigned to the lower sections, we must adjust the basic formula.
To achieve this, we use the idea of an equivalent score. By examining average ratings and the results of section switching in the past, we are able to develop a table of score adjustments:
Section score adjustment
table
|
SECTION |
ADJUSTMENT |
|
Championship |
0 |
|
Reserve |
2 |
|
Elementary |
2.5 |
|
Primary |
3.5 |
|
4-5
Novice |
4.25 |
|
2-5
Novice |
4.5 |
|
2-3
Novice |
4.75 |
|
K-1 |
5 |
This means that a Reserve section score should be awarded the same number of points as a Championship section score that is 2 points less, while an Elementary section score should be awarded the same number of points as a Championship section score that is 2.5 points less, and so on. Moving down the adjustment column, we can see that those playing in the Novice and K-1 sections can not match the lowest point score achievable in the Championship section, but they can match point scores in other sections.
Again, you can see these relationships clearly reflected in the above table. For example, 88 points are awarded for a score of 0.5 in the Championship section, 2.5 in the Reserve, 3 in the Elementary, and 4 in the Primary.
Reflecting the
section adjustment in the formula
This is done by subtracting the adjustment value from the
score used in the formula.
The adjusted formula
for a 4-round tournament section:
points = base/2**(4-(score-adj))
For example, a score of 3.5 in the Primary section would be calculated as
1000 / 2**(4-(3.5-3.5)) = 1000 / 2**4 = 1000/ 16 = 63
Sections other than 4
rounds in length
Sometimes we run sections that are not the normal size. A
4-player section may play only 3 rounds, and we have also had a 6-round K-1
section this year. To handle this, we have extended the formula. The score is
prorated by dividing 4 by the number of rounds. The extended formula and some resulting
tables are shown below.
The extended formula:
points = base/2**(4-(score*4/#rnds-adj))
For example, a score of 3 in a 6 round Primary section
yields
1000/2**(4-(3*4/6-3.5))=1000/2**(4-(2-3.5))=1000/2**5.5=1000/45 = 22
The extended formula
in Excel spreadsheet notation:
=IF(score=0,0,base/POWER(2,4-(score*4/#rnds-adj)))
The IF statement assigns 0 points to a score of zero. To use the formula in Excel, you must substitute cell references for base, score, #rnds, and adj. In the tables, we show all results to the nearest digit.
The Grand Prix points tables for other than 4 rounds
To find your Grand Prix point score, choose the appropriate table below, and then find the row for your section and the column for your score in that section.
For example, you scored 2 points in a 3-round Championship
section. You get 397 points added to your Grand Prix total point score.
|
6 Rounds |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
6 |
5.5 |
5 |
4.5 |
4 |
3.5 |
3 |
2.5 |
2 |
1.5 |
1 |
0.5 |
|
Championship |
1000 |
794 |
630 |
500 |
397 |
315 |
250 |
198 |
157 |
125 |
99 |
79 |
|
Reserve |
250 |
198 |
157 |
125 |
99 |
79 |
63 |
50 |
39 |
31 |
25 |
20 |
|
Elementary |
177 |
140 |
111 |
88 |
70 |
56 |
44 |
35 |
28 |
22 |
18 |
14 |
|
Primary |
88 |
70 |
56 |
44 |
35 |
28 |
22 |
18 |
14 |
11 |
9 |
7 |
|
2-5 Novice |
44 |
35 |
28 |
22 |
18 |
14 |
11 |
9 |
7 |
6 |
4 |
3 |
|
K-1 |
31 |
25 |
20 |
16 |
12 |
10 |
8 |
6 |
5 |
4 |
3 |
2 |
|
5 Rounds |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 |
4.5 |
4 |
3.5 |
3 |
2.5 |
2 |
1.5 |
1 |
|
|
|
|
Championship |
1000 |
758 |
574 |
435 |
330 |
250 |
189 |
144 |
109 |
|
|
|
|
Reserve |
250 |
189 |
144 |
109 |
82 |
63 |
47 |
36 |
27 |
|
|
|
|
Elementary |
177 |
134 |
102 |
77 |
58 |
44 |
33 |
25 |
19 |
|
|
|
|
Primary |
88 |
67 |
51 |
38 |
29 |
22 |
17 |
13 |
10 |
|
|
|
|
2-5 Novice |
44 |
33 |
25 |
19 |
15 |
11 |
8 |
6 |
5 |
|
|
|
|
K-1 |
31 |
24 |
18 |
14 |
10 |
8 |
6 |
4 |
3 |
|
|
|
|
3 Rounds |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
2.5 |
2 |
1.5 |
1 |
0.5 |
|
|
|
|
|
|
|
Championship |
1000 |
630 |
397 |
250 |
157 |
99 |
|
|
|
|
|
|
|
Reserve |
250 |
157 |
99 |
63 |
39 |
25 |
|
|
|
|
|
|
|
Elementary |
177 |
111 |
70 |
44 |
28 |
18 |
|
|
|
|
|
|
|
Primary |
88 |
56 |
35 |
22 |
14 |
9 |
|
|
|
|
|
|
|
2-5 Novice |
44 |
28 |
18 |
11 |
7 |
4 |
|
|
|
|
|
|
|
K-1 |
31 |
20 |
12 |
8 |
5 |
3 |
|
|
|
|
|
|
The Grand Prix points tables for other formats
When the format has changed, such as in the grade based Westchester County Championships, adjustments are made based on the expected ratings strength of likely pairings for the Grand Prix contenders. This adjustment takes into account the likely field sizes; large fields may have big gaps in strength. For a final sanity check, the results are compared to adjustments calculated based on average GP score performance of the contenders from each section’s total possible population. If necessary, modifications are then made.
The following table will be used for the 2011 Westchester County Scholastic Chess Championships:
|
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|
|
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|
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|
|
4 |
3.5 |
3 |
2.5 |
2 |
1.5 |
1 |
0.5 |
|
Adjustment |
|
JHS/HS |
841 |
595 |
420 |
297 |
210 |
149 |
105 |
74 |
|
0.25 |
|
MS |
420 |
297 |
210 |
149 |
105 |
74 |
53 |
37 |
|
1.25 |
|
Elementary |
250 |
177 |
125 |
88 |
63 |
44 |
31 |
22 |
|
2 |
|
Primary |
125 |
88 |
63 |
44 |
31 |
22 |
16 |
11 |
|
3 |
|
K-1 |
53 |
37 |
26 |
19 |
13 |
9 |
7 |
5 |
|
4.25 |