[MickyB]

I've just discovered that the abomination of a VP-scale that has been used by the WBF [See my previous rant on the subject] is to be replaced.

From the EBU newsletter for AC members and TDs -

"A Scoring Committee was set up by the WBF President in January of this year. The committee was chaired by Ernesto d’Orsi of Brazil and co-chaired by Max Bavin (UK).

Other Committee members are Henry Bethe (USA) Bart Bramley (USA), Peter Buchen (Aus) and Maurizio de Sacco (IT).

After deep and long analysis, the committee proposed — and the WBF Executive Committee accepted — the following:

1. The adoption of a 20-point victory point scale with the following features:

The scales are continuous and given to two decimal places
Subject to a cap, each IMP margin translates to a specific VP award
Each additional IMP in the winner’s margin is worth no more than the previous one
Relative to the current WBF scales, the “blitz” margins in the new scale will be approximately equivalent to the 25-2 in the old scales. There is no reduction of VPs for the loser when the margin exceeds the blitz margin.

2. It is recommended that the new scales be used in the next World Bridge Championship (including Youth tournaments) and be available to all NBOs by the end of 2012.

3. Also, the Committee will prepare new “discrete” scales (whole numbers) to be used by NBOs if they wish to during the transition from the old to the new VP scales.

4. On the World Bridge Federation website (www.worldbridge.org), the Committee will publish the “continuous” and “discrete” scales for the most-used number of boards per match and will publish them together with instructions on how to determine VP scales for other sizes of matches. Also on the website, using the actual algorithm, users will be able to enter the number of boards and the preferred scale type to read, print or download the result.

5. Future work by the Committee will include consideration of aggregate score, the IMP scale and match-point scoring, although not necessarily with a view to suggest changes."

Committee member Henry Bethe posted on Google groups to say that it is the existing USBF scales that are being used - see the last two pages of this document.

Does anyone have details of the discrete scales, or know the formula for the continuous scale? Thanks.

[woefuwabit]

Does anyone know the formula used by the USBF scale?

[aguahombre]

woefuwabit, on 2012-September-16, 10:17, said:

Does anyone know the formula used by the USBF scale?

14 board RR scale=20-0 at 57 IMPS, graduated down by fractions.

10-10 for zero
10.33 for one,
19.91 for 56,
etc.

That is the only one I have found, so far.

Edit: since my description is more "layman" than Micky's, I don't know how it compares to the abomination he found in WBF conditions.

This post has been edited by aguahombre: 2012-September-16, 11:51

[Jboling]

woefuwabit, on 2012-September-16, 10:17, said:

Does anyone know the formula used by the USBF scale?

I have actually tried to reverse engineer it, I do not think that there is any simple underlying function, they have probably just constructed the tables by hand. The imp-limit for 20-0 seems to be 15 multplied by the square root of the number of deals. Using this (for normalization of the imp-ranges) and a third order polynomial I could get down to an maximal error of about 0.02, but no significant improvement if I used higher order polynomials. Which was an disappointment, an error below 0.005 would have resulted in a simple formula for perfect generation of the tables, which also could have been used for generation of conversion tables for any other number of deals as well.

[HenryB]

The function is

VP(Winner) = 10+10*((1-Tau^(3M/B))/(1-Tau^3)) with a maximum of 20
VP(loser) = 20 - VP(winner)

where
Tau = (5^.5 - 1)/2 which is the "golden mean" and approximately 0.618...
M is the margin
B = 15*(number of boards^.5)

Both values are rounded to 2 decimals and truncated

Occasionally because of the rounding the rule V(i+1) - V(i) <= V(i) - V(i-1) will be violated. In that case the value of V(i) is increased by .01. Usually this will eliminate all violations; sometimes it takes as many as four iterations of this procedure to eliminate all of them.

A VP score of 15-5 will be achieved when M = B/3 (five times the square root of the number of boards)
A margin of 2B/3 will get a VP score of 18.09
A margin of B or greater will get a VP score of 20

[woefuwabit]

Thanks Henry, glad to hear it from the inventor himeslf

[woefuwabit]

Are the scales in the USBF COC accurate?
Comparing my results to the scales in there gives me some off-by-1 errors. I'm truncating V values to 2 decimals and running the diff check iterations.

Source here:

package test;

public class VPScale {
	public static void main(String args[]) {
		int boards = 10;
		double B = 15 * Math.sqrt(boards);
		int V[] = new int[(int)B + 2];
		for (int i = 0; i < V.length; i++) V[i] = Math.min(2000, convert(i, B));
		
		int d, iterations = -1;
		do {
			iterations++;
			d = 0;
			for (int i = 1; i < V.length - 1; i++) {
				if ((V[i+1] - V[i]) > (V[i] - V[i-1])) {
					V[i]++;
					d++;
				}
			}
		} while(d > 0);
		
		for (int i = 0; i < V.length; i++) System.out.println(i + " " + V[i] /*+ " " + (i > 0 ? V[i] - V[i-1] : 0)*/);
		System.out.println(iterations + " iterations");
	}
	
	private static double TAU = (Math.sqrt(5) - 1) / 2;
	private static double DENOM = 1 - TAU * TAU * TAU;
	
	public static int convert(int M, double B) {
		return (int)(1000.0 + 1000.0 * (1.0 - Math.pow(TAU, 3.0*M/B)) / DENOM);
	}
	
	public static int convert(int margin, int boards) {
		return convert(margin, 15 * Math.sqrt(boards));
	}
}

Result for 10 boards:
0 1000
1 1039
2 1077
3 1114
4 1150
5 1184
6 1218
7 1251
8 1282
9 1313
10 1343
11 1372
12 1400
13 1427
14 1454
15 1479
16 1504
17 1528
18 1552
19 1574
20 1596
21 1618
22 1638
23 1658
24 1678
25 1697
26 1715
27 1733
28 1750
29 1767
30 1783
31 1799
32 1814
33 1829
34 1843
35 1857
36 1871
37 1884
38 1897
39 1909
40 1921
41 1933
42 1944
43 1955
44 1966
45 1976
46 1986
47 1995
48 2000

[HenryB]

I can think of a couple of reasons why you might get a table that differs by .01 VP at some values.

The procedure to determine values is to round first, then truncate. More specifically, truncate to three decimals, then round to two decimals with .005 rounding up.

The "adjustment" algorithm for the USBF scales was then "eyeball" rather than computer. The WBF scales will use the mechanism shown in my previous post.

[Jboling]

I did also try Henrys formula, and did niether get the same as USBF nor the same as woefuwabit. Below mine and USBF (in that order):
0 0 0
1 1039 1039
2 1077 1077
3 1114 1114
4 1150 1150
5 1185 1185
6 1218 1218
7 1251 1251
8 1283 1283
9 1314 1314
10 1343 1344
11 1372 1373
12 1400 1401
13 1428 1428
14 1454 1454
15 1480 1480
16 1505 1505
17 1529 1529
18 1552 1552
19 1575 1575
20 1597 1597
21 1618 1618
22 1639 1639
23 1659 1659
24 1678 1678
25 1697 1697
26 1716 1716
27 1734 1734
28 1751 1751
29 1768 1768
30 1784 1784
31 1800 1800
32 1815 1815
33 1830 1830
34 1844 1844
35 1858 1858
36 1871 1872
37 1884 1885
38 1897 1898
39 1910 1910
40 1922 1922
41 1933 1933
42 1944 1944
43 1955 1955
44 1966 1966
45 1976 1976
46 1986 1986
47 1996 1996
48 2000 2000

I think the difference compared with woefubit comes from that the type cast (int) does not round, I think it truncates.

By the way I did the calculations using floating point, and first forgot that you then have to add a factor that takes into account the finite precision of floating point numbers in the comparison. For example
((V[i+1] - V[i]) > (V[i] - V[i-1]+0.005))

[woefuwabit]

Yes sorry, I misread "rounded to 2 decimals and truncated".

Fixed the code to

        public static int convert(int M, double B) {
                return (int)(1000.5 + 1000.0 * (1.0 - Math.pow(TAU, 3.0*M/B)) / DENOM);
        }

and I get the exact same result as Jboling.

Henry: Not sure if it makes a difference, but did you specify if the violation scan should be from V[0] to V[B] or from V[B] to V[0] ?

P.S.: Next up, updating the IMP scale to be continuous too?

[Jboling]

woefuwabit, on 2012-September-18, 20:50, said:

P.S.: Next up, updating the IMP scale to be continuous too?

Good point, I did some calculations regarding this too, I estimated that the standard deviations for the errors due to round off to whole numbers are about equal (~0.3VP per match) for the IMP and the VP conversion.

[Bad_Wolf]

Very cute. However the mathematician in me wishes that the score approached 20 asymptotically.

[woefuwabit]

I made a simple js app to generate the scales for any number of boards:
http://woefulwabbit.com/wbf-vp/

Jboling, on 2012-September-19, 00:33, said:

Good point, I did some calculations regarding this too, I estimated that the standard deviations for the errors due to round off to whole numbers are about equal (~0.3VP per match) for the IMP and the VP conversion.

If I'm not wrong the standard deviation can be calculated as which comes round to ~.289 which seems to agree with your estimation.

[Jboling]

woefuwabit, on 2012-November-05, 07:17, said:

If I'm not wrong the standard deviation can be calculated as which comes round to ~.289 which seems to agree with your estimation.

Yes this was the number I used as the standard deviation of VP round-off. This assumes that all results are possible and equally likely, which neither are true, but it is an ok approximation. The standard deviation for rounding off imps is then also about the same, but when you express that in VPs it is not a constant, it depends on the actual imp-difference. You can most conveniently observe it using the new imp-to-vp table for 12 deals matches, when you have a standard deviation of 1 expressed in IMPs. This means that we have a maximal standard deviation of 0.36 VPs at imp-difference 0, and below 0.3VPs at imp-differences greater than 8. So on average we should have about the same standard deviation.

[Fluffy]

This will reduce those random tie breaks by around 99%. I wouldn't care about 0.01 more or less as long as the table is published at the start of the tournament.

[Rossoneri]

Has this been officially ratified?

Some hilarity: Was playing a tournament over the weekend using this new scale and my team ended up in a position where we might have lost a position by 0.001 VP due to a 10% carry over from a previous stage if we had beaten our last round opponents by 7 IMPs. We won the match by 8 IMPs.

[gordontd]

Rossoneri, on 2012-December-19, 22:30, said:

Has this been officially ratified?

Some hilarity: Was playing a tournament over the weekend using this new scale and my team ended up in a position where we might have lost a position by 0.001 VP due to a 10% carry over from a previous stage if we had beaten our last round opponents by 7 IMPs. We won the match by 8 IMPs.

I thought it was only coming in in the new year, though I've heard of another event that has used it. So you were allowing a third decimal place because of the carry forward? Had it all happened as it might, just think that it would have saved everyone from a tie-break.

[jallerton]

Fluffy, on 2012-November-06, 08:35, said:

This will reduce those random tie breaks by around 99%. I wouldn't care about 0.01 more or less as long as the table is published at the start of the tournament.

It will also reduce the number ot teams who know their exact VP score by around 99%.

[Bbradley62]

jallerton, on 2012-December-21, 17:04, said:

It will also reduce the number of teams who know their exact VP score by around 99%.

It's not like we actually want people to understand the rules of the game they are playing.

[Rossoneri]

gordontd, on 2012-December-20, 01:13, said:

I thought it was only coming in in the new year, though I've heard of another event that has used it. So you were allowing a third decimal place because of the carry forward? Had it all happened as it might, just think that it would have saved everyone from a tie-break.

Using U-25 players as guinea pigs of course, what other useful purpose do they serve?