WBF VP scale changes

[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]

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.

Edited September 16, 2012 by aguahombre

[Jboling]

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) > (V - 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 or from V to V[0] ?

 

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

[Jboling]

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. :unsure:

[woefuwabit]

I made a simple js app to generate the scales for any number of boards:

http://woefulwabbit.com/wbf-vp/

 

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 http://i.imgur.com/g3QcD.gif which comes round to ~.289 which seems to agree with your estimation.

[Jboling]

If I'm not wrong the standard deviation can be calculated as http://i.imgur.com/g3QcD.gif 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]

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]

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]

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]

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? :P

[Fluffy]

Since this has been resurrected I will throw a random idea.

 

IMO a team that wins 13-2 IMPs should score better than a team that wins 113-102, not by much but by some ammount nevertheless. giving 95% VPs to IMP difference and 5% to IMP ratio could be more accurate to me.

[pigpenz]

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

J Lall probably came up with it when he turned 25

[mycroft]

Since this has been resurrected I will throw a random idea.

 

IMO a team that wins 13-2 IMPs should score better than a team that wins 113-102, not by much but by some amount nevertheless. giving 95% VPs to IMP difference and 5% to IMP ratio could be more accurate to me.

Not sure I agree with this. I certainly don't in the ACBL, where almost never are people playing the same boards. Yes, VPs are badly biased based on "swinginess", too, but adding a penalty to the swing set is even more random.

 

But in the real world, where everybody's playing the same hands, that does tend to disfavour the "oddball system" players. I play K/S in a "2/1, strong NT" world. As a result, we "wrongside" 80% of the contracts where opener has a balanced 12-17. We win some, we lose some, we draw (+/- an overtrick) a lot. But we're going to be punished for playing a system that will, on average, score about 5IMPs more a 7-board set than playing "standard" - if we win. If we lose, the opponents will be punished.

 

Precision does similarly. Anybody playing a highly aggressive preempting style, or a 10-12 NT, or T-Walsh in a "standard" world has the same problem. We play it because it's better, or suits us better, or is deliberately high-variance in a world where we'll probably lose if we don't roll the dice; but now high-variance systems punish the winners - even if they're not the ones playing it.

 

And the other question is "should the team that lost 112-102 get more VPs than the one who lost 12-2?" If not, then we're either rewarding the losers for playing high-variance (or against high-variance) or each match is being scored on a different scale. I don't really have a problem with the latter - say "25 VPs on IMP difference, and 5 VPs on how many IMPs you let out, based on a fixed IMPs/board metric", but thousands would. And, it brings back the "you're going to be punished for playing a swingy set against the wild bidders, as opposed to the next team who gets the wild bidders on the boring flat partscores - because you won 44-30, and the next team won +5, push, push, -1, push, +6, push".

[Trinidad]

Since this has been resurrected I will throw a random idea.

 

IMO a team that wins 13-2 IMPs should score better than a team that wins 113-102, not by much but by some ammount nevertheless. giving 95% VPs to IMP difference and 5% to IMP ratio could be more accurate to me.

There is no fundamental reason why 113-102 is better or worse than 13-2. If the basketball score is simply due to a large number of boards then the VP scale takes care of that already: A 13-2 score in a 4 board match leads to 15.38-4.62 VP. A score of 113-102 in a 64 board match will score 11.62-8.38. (If my calculations are correct.)

 

Rik

[RunemPard]

There is no fundamental reason why 113-102 is better or worse than 13-2. If the basketball score is simply due to a large number of boards then the VP scale takes care of that already: A 13-2 score in a 4 board match leads to 15.38-4.62 VP. A score of 113-102 in a 64 board match will score 11.62-8.38. (If my calculations are correct.)

 

Rik

 

 

It seems pretty obvious that he is talking about both teams playing the same # of boards to me.