Table of Contents

• BURS Responds
• Bricks Official Ranking (BOR)
  1. How does PR work?
  2. How does SR work?

BURS Responds

Note:

• Number of responses: 13; more responses are always welcome.
• Blue Background = players who have teamed in at least one Bricks game.
• Green Background = ascending weighting between Bricks I, II and III.
• Yellow Background = 0% for "Old Competition".
• "Old Competition" = the average score of the forth recent, fifth recent and sixth recent competition. Hence competitions older than 1 year will not take any effect on the ranking.

We take Decision B for modelling our BOR.

Bricks Official Ranking (BOR)

How does PR work?

In PR we only look at players' positions, regardless of their scores. Definitions:

• Decay Rate: the difference in percent in scores between player at position x and player at position x+1. For example if the first player scores 10 points and the decay rate is 10%, then the score of the second player is 10×(1-10%), i.e., 9 points; the score of the third player is 9×(1-10%), i.e., 8.1 points, and so on.
• Team Penalty: the "discount" on score if a player is teamed in a Bricks game*. If the team penalty is 10%, for a 2-player team their scores would be discounted by 10%; for a 3-player team their scores would be discounted by further 10% (of the remaining 90%, i.e., further 9%), and so on.

* From the fifth competition (The Wedge) we have time penalty for teams. Hence we don't impose our Team Penalty on them in all competitions starting from that one.

Constants used in PR:

• Decay Rate = 12%; Team Penalty = 18%;
• B1 Weighting: 23%; B2 Weighting: 19%; B3 Weighting: 15%;
• C4 Weighting: 4%; C3 Weighting: 8 %; C2 Weighting: 13%; C1 Weighting: 18%.

Hence we can generate the following table with the above constants:

For example: an individual player ranked at position 10 in Bricks I has a weighted sub-score of 7.28 for it. If teamed the player would have got only 5.97 points (if teamed with one other player) or 4.89 points (if teamed with two other players).

Notice the series [7.28, 8.27, 9.40, 10.68, 12.14, 13.79, 15.67, 17.81, 20.34, 23.00] is geometric, with the common ratio 'r' of [1/(1-12%)].

In addition, 5.97 is 82% of 7.28; and 4.89 is 82% of 5.97.

Again, the total score of PR is calculated by the sum of the weighted sub-scores of each Bricks game.

To make it more interesting, here we take James Gdowik's results on 17 Jan 2001 as a real example. Three steps:

1. His positions are as follows:

Bricks I: 8 (team of 2); Bricks II: 4 (individual); Bricks III: 6 (team of 2);
Millennium: 6; Pentominoes: 8; The Wedge A: 9; The Wedge B: 16; The Wedge Average*: 12; Orzac: 14; Bubble Fun: 22.

* The Wedge Average is the ranking of [the average score of The Wedge A and The Wedge B].

2. From the above table (or by real calculation), James' PR sub-scores are:

B1: 7.71 (or 0.88⁷ × 0.82 × weighting);
B2: 12.95 (or 0.88³ × weighting);
B3: 6.49 (or 0.88⁵ × 0.82 × weighting);
C4: average of [0 (Bottles) + 0.88⁵ (Millennium) + 0.88⁷ (Pentominoes)] × weighting = 1.25;
C3: 1.96 (or 0.88¹¹ × weighting);
C2: 2.47 (or 0.88¹³ × weighting);
C1: 1.23 (or 0.88²¹ × weighting).

3. Hence his total score is 7.71 + 12.95 + 6.49 + 1.25 + 1.96 + 2.47 + 1.23 = 34.06 (Note: the actual rounding gives 34.05)

How does SR work?

In SR we only look at players' scores, regardless of their positions. Definitions:

• Decay Rate per 0.01%: the penalty incurred as a result of having a score worse than the perfect score (see example below for a practical explanation)
• Team Penalty: (same as that in PR)
• Bricks I Adjustment: a multiple to "Decay Rate per 0.01%" on Bricks I because players score closely in this particular game.

Constants used in SR when it was first started on 17 Jan 2001:

• Decay Rate per 0.01% = 0.11% (NB: Now it is no longer 0.11%; see the ranking section for the current value!); Team Penalty = 8%; Bricks I Adjustment = 5×
• B1 Weighting: 23%; B2 Weighting: 19%; B3 Weighting: 15%;
• C4 Weighting: 4%; C3 Weighting: 8 %; C2 Weighting: 13%; C1 Weighting: 18%.

Hence we can generate the following table with the above constants:

The table reads like this, for example:

In Bricks I, if the total moves needed is 1.00% more than the perfect (which is currently 1762 moves), the player will score 20.60 points for it. 1% from perfect is about 18 points more, i.e., the player has the score of 46220. (Of course, the actual system takes 46220 as input, and produces "1.02%" and hence the corresponding score at around 20.77). Here the "1.02%" is interpreted as "a decay at the 102^nd power". And having the "Decay Rate per 0.01%" at 0.11% we have: score = 23×(1-0.11%)¹⁰² = 20.76861976 ...

OK, this looks correct, right? Answer: correct for all games except for Bricks I! Why? Because we have a Bricks I magnifier! With a magnifying factor of 5, the "1.02%" is actually interpreted as "a decay at the 510^th power", which gives a sub-score for Bricks I of about 13.81 only!

The following table is a good tool to estimate your score roughly, but quickly. Find out the "+??%" which corresponds to your score and look that up from the above table!

Advanced Topic: step-to-move conversion -- how does "step" contribute to SR in competitions??

Let me show it in point form, hopefully this would give a better understanding:

• In a particular competition, find out the ratio of Step/Move (abbreviated as "S/M") for all players;
• Find out S/M_max and S/M_min within those players;
• Penalize the player with S/M_min by 0 move; penalize the player with S/M_max by 1 move;
• Proportionally penalize the rest of the players according to their S/M relative to (S/M_max & S/M_min) between 0 & 1 move. Done!

To make it more interesting, here we take James Gdowik's results on 17 Jan 2001 as a real example. Six steps:

1. His scores are as follows:

Bricks I: 46222 (team of 2); Bricks II: 44779 (individual); Bricks III: 44139 (team of 2);
Millennium: 135; Pentominoes: 130/1582; The Wedge* A: 204; The Wedge B: 341; The Wedge Average: 272.5; Orzac: 95/221; Bubble Fun: 230/2031.

* The Wedge did not have step scores revealed.

2. For step-to-move conversion (see also "Advanced Topic" above; and "More Explanation" below):

In Pentominoes: S/M_max = 17.4; S/M_min = 6.6; James has 12.2; hence the conversion is to add (12.2-6.6) ÷ (17.4-6.6) = 0.515. Hence his move-score is 130.515;
In Orzac: S/M_max = 2.87; S/M_min = 1.99; James has 2.33; hence the conversion is to add (2.33-1.99) ÷ (2.87-1.99) = 0.383. Hence his move-score is 95.383;
In Bubble Fun: S/M_max = 11.4; S/M_min = 6.2; James has 8.8; hence the conversion is to add (8.8-6.2) ÷ (11.4-6.2) = 0.502. Hence his move-score is 230.502;

3. The Perfect scores of the games are as follows:

B1: 46238; B2: 44897; B3: 44626;
Bottles: 294.00; Millennium: 124.00; Pentominoes: 125.50; The Wedge: 145.50; Orzac: 84.73; Bubble Fun: 144.25.

4. By calculation, the scores different from the perfect in percent are (see also "More Explanation" below):

B1: (1788-1772) ÷ 1772 = 0.91%; with the adjusting factor of 5 it becomes 4.55% (which is obtained from "0.91% × 5");
B2: (3221-3103) ÷ 3103 = 3.80%;
B3: (3861-3374) ÷ 3374 = 14.43%;
Bottles: N/A; Millennium: (135-124) ÷ 124 = 8.87%; Pentominoes: (130.515-125.5) ÷ 125.5 = 4.00%;
The Wedge: (272.5-145.5) ÷ 145.5 = 87.29%; Orzac: (95.383-84.73) ÷ 84.73 = 12.57%; Bubble Fun: (230.502-144.25) ÷ 144.25 = 59.79%.

5. By calculation, James' SR sub-scores are (see also "More Explanation" below):

B1: 0.9989⁴⁵⁵ × 0.92 × weighting = 12.07;
B2: 0.9989³⁸⁰ × weighting = 12.51;
B3: 0.9989¹⁴⁴³ × 0.92 × weighting = 2.82;
C4: average of [0 (Bottles) + 0.9989⁸⁸⁷ (Millennium) + 0.9989⁴⁰⁰ (Pentominoes)] × weighting = 1.36;
C3: 0.9989⁸⁷²⁹ × weighting = 0.00;
C2: 0.9989¹²⁵⁷ × weighting = 3.26;
C1: 0.9989⁵⁹⁷⁹ × weighting = 0.02.

6. Hence his total score is 12.07 + 12.51 + 2.82 + 1.36 + 0.00 + 3.26 + 0.02 = 32.04 (Note: the actual rounding gives 32.04 too)

More Explanation on the above calculation (if you're still not sure):

• Step 2: the step-to-move conversion is needed to distingush score differences. Such as in Bubble Fun we have 3 players at 147 moves, but with different steps. With the method shown on the page we can obtain a non-integer value 0<x<1 which reflects on the performance on steps. It is then added to the move. You can think of this as a "step penalty" which add at most 1 move to your move-score (and at least 0 move).
• Step 4: score ranking is based on your score VS the perfect score. And the way to compare is to find out the extra moves needed VS perfect. e.g. in Bricks I if you have 46000 then you are 238 moves from perfect (which needs 1762 moves). The percentage is then 238÷1762×100%. Let this value be Z in the explanation below.
• Step 5: as the name "Penalty per 0.01%" suggests, penalty is calculated according to Z, per 0.01%. Say Z is 20% then the exponent is 2000. If Z is 12.9855% then the exponent is 1298 (the rest of the decimal points are truncated -- or rounded; doesn't matter ...).

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© Alan Chan