[kennyp]

On BBO you convert the matchpoint scores to percentages before totalling the matchpoints. Then when you average out the percentage scores for each hand I think you treat them equally. This is OK if the boards have been played the same number of times but not when the boards have been played different times. The percentage scores are valid to evaluate how well a pair may have done on a given board but they are not valid to use when adding results up for a number of boards. You have to use the actual matchpoints. A board played 12 times will result in a maximum of 11 matchpoints while a board played 11 times has a maximum of 10 points. The maximum percentage in both cases is 100 but the matchpoint scores differ. This impacts the results when the scores are added together.

For example suppose two teams are discussing how they did in a recent bridge session and they focus on two tricky boards (say boards 1 and 2). Team AA got an absolute top on board 1 and an absolute bottom on 2. Team BB did exactly the reverse: a bottom on 1 and a top on two. So they would each get 100% and 0% which would average out to 50% and conclude that they tied on these two boards. But suppose board 1 had been played 12 times while board 2 had only been played 11 times (a common occurrence at most bridge clubs and certainly very
> common on BBO). ACBL scoring would give AA 11 points for board 1 and 0 for 2. BB would get 0 points for board 1 and only 10 for board 2. If you then calculated percentage scores AA would get 11/21*100 or 52.38% and BB 10/21*100 or 47.62%. When you score a larger number of boards the difference is not going to be as large as this but there is still going to be a difference.

A similar issue occurs with IMP scoring. If you average a score and treat it the same as other scores when adding them together you skew the results. For board played 12 times, if a NS pair beats all other NS pairs by 3 IMPs they would gain a total of 33 IMPs. If you take the average of this result it would be 33/11 = 3 IMPs. For another board played 11 times if the NS pair again wins by 3 IMPs versus all other pairs they would gain 30 IMPs and an average of 3 IMPs. If you add the averages the scores would be tied 3 to 3. But the real result is that one pair is ahead by 3 IMPs, 33 minus 30.

[gordontd]

You are right that percentages for boards that have been played different numbers of times should not just be added, but the larger the number of results the less difference it makes and it is because online boards are usually played a lot of times that it is reasonable to do this.

Where you are wrong though is in imagining that the solution is just to add matchpoints. The proper method is more complex and subtle than that and involves using the Neuberg Formula.

[mycroft]

Gordon is correct, of course. Having said that, simple version:

ACBL scoring will give

• AA 11 points for board 1 and 0 for board 2.
  
• BB 0 points for board 1 and 10 for board 2.
  
• Then, board 2's matchpoints will be factored to an 11 top (that's where the Neuberg Formula comes in; before computers we just multiplied by 11/10). AA's zero will end up around 0.06, and BB's 10 will end up around 10.94.
  
• So, AA will still win, but with about 11.06 matchpoints to 10.94 (and before Neuberg, they would be tied. What is "right" is an interesting question that takes into account the probability of the "missing" 12th pair on board 2 being Hamman/Zia, Mrs. Guggenheim/Unlucky Expert, or you and me).

For BBO, with 32 results on (most) boards, the difference between Neuberging and just using percentages is noise. Yes, for the odd boards that are played 4 times and then lost due to whatever, it can make a big difference if only one of those scores are 3NT+1 into 4S= (instead of somewhere between 2 and 6 of 32).

Neuberg also comes into play if boards are fouled (not relevant to BBO). It doesn't work well either when the factoring is strong (some boards played 12 times, some played 4, some played somewhere in between). But then again, it wasn't designed to - and nothing does, really.

[barmar]

mycroft is right, there's no perfect solution for dealing with boards played a different number of times in the same event. All the methods have flaws, and the errors are magnified as the number of comparisons decrease.

One of the biggest advantages of using percentages rather than raw matchpoints is that they're easily understandable by the players. I remember when I first started playing tournament bridge 20+ years ago, they would report player results just as the total matchpoints. In the case of national events that were scored across 4 or 5 sections, that would mean the total matchpoints would be somewhere around 800-1,000, and we'd have to figure out where reported results stood in comparison.

[mycroft]

mycroft, on 2015-March-27, 13:03, said:

For BBO, with 32 results on (most) boards, the difference between Neuberging

I *wrote* this, and I still seem to always read that as Nuerburgring.

I would expect there is less difference between the Nordschleife and noise...

[kennyp]

With due respect to whoever developed the Neuberg formula I think it is flawed. Any process designed to level the scores for boards played an uneven number of times should still respect some aspects of the original scores. The example given in the explanation of the Neuberg formula illustrates my concern. When played 10 times the person who got the bottom score gets zero matchpoints. But if you were expecting the board to be played 11 times that zero becomes 0.1. This doesn't make sense to me. A bottom is a bottom and should stay at zero. The original top score of 18 shouldn't become 20 so 19.9 seems OK and prorating the extra points to other pairs seems to work until you get to the bottom.

The issue for me is to try and adjust scores and total results fairly for a bridge club that normally has between 10 and 15 tables. We usually have 24 to 33 boards in play. Invariably the boards are not all played the same number of times. This may be due to the fact that some tables don't finish the final round or because some boards are simply missed. I think the ACBL approach of just adding the matchpoints and determining percentages after the addition makes the most sense. I recognize that the differences between the three approaches (calculating percentages and then averaging the percentages, applying the Neuberg formula adding the matchpoints and then taking percentages, or adding the raw matchpoints and then taking percentages) are quite small but I'd like to think that things are done properly and accurately, both at my club and certainly on BBO.

For IMP scoring you can apply the same principle that I support for matchpoints . You know the total number of times boards have been played and how many times the boards played by a given pair have been played so you can adjust the scores for each hand at each table accordingly, then multiply the actual results by the "adjustment factor." I have developed an Excel spreadsheet for the scoring and can determine the matchpoint results using each approach. For fun I also included IMP scores using cross IMPs and calculating IMPs on the average score,and net points.

Barmar mentioned the advantage of using percentages because they are better understood by players and I agree with that. My solution is to present the percentage scores for each hand and also for the final results. But the final results are not the average of the percentages but are determined by using the matchpoints in the background.

By the way, as a side issue, does anyone know if some clubs are changing to IMP scoring over matchpoints. With computerized scoring it seems to make sense to me.

[gordontd]

kennyp, on 2015-March-30, 10:56, said:

With due respect to whoever developed the Neuberg formula

That would be Gerard Neuberg.

kennyp, on 2015-March-30, 10:56, said:

I think it is flawed. Any process designed to level the scores for boards played an uneven number of times should still respect some aspects of the original scores. The example given in the explanation of the Neuberg formula illustrates my concern. When played 10 times the person who got the bottom score gets zero matchpoints. But if you were expecting the board to be played 11 times that zero becomes 0.1. This doesn't make sense to me. A bottom is a bottom and should stay at zero. The original top score of 18 shouldn't become 20 so 19.9 seems OK and prorating the extra points to other pairs seems to work until you get to the bottom.

So a bottom is always a bottom, but a top is not always a top? The point is that when a board has been played fewer times we can't know with certainty what would have happened if it had been played the same number of times. There is always some possibility that there might have been a worse score than the bottom, or a better score than the top.

kennyp, on 2015-March-30, 10:56, said:

The issue for me is to try and adjust scores and total results fairly for a bridge club that normally has between 10 and 15 tables. We usually have 24 to 33 boards in play. Invariably the boards are not all played the same number of times.

Much better would be to play movements where they are all played the same number of times. Then you would only have to worry about anomalies like fouled boards and artificial scores.

kennyp, on 2015-March-30, 10:56, said:

This may be due to the fact that some tables don't finish the final round or because some boards are simply missed. I think the ACBL approach of just adding the matchpoints and determining percentages after the addition makes the most sense.

Is that really their approach? Can anyone else confirm this?

kennyp, on 2015-March-30, 10:56, said:

By the way, as a side issue, does anyone know if some clubs are changing to IMP scoring over matchpoints. With computerized scoring it seems to make sense to me.

The only impact computer scoring has on this is a greater tendency to Cross-IMP rather than Butler score. The question of IMPs vs MPs is not one of scoring capability but one of tactics. You seem to assume that the only reason people play match-points is because they don't know how to score anything else!

[gordontd]

kennyp, on 2015-March-30, 10:56, said:

I think the ACBL approach of just adding the matchpoints and determining percentages after the addition makes the most sense.

I downloaded a copy of ACBLscore to see if that is in fact what it does and it is not. It uses Neuberg.

[barmar]

gordontd, on 2015-March-30, 15:45, said:

Much better would be to play movements where they are all played the same number of times. Then you would only have to worry about anomalies like fouled boards and artificial scores.

Of course, that's always desirable, but it isn't always feasible. Is it even possible when you have an odd number of pairs and have to have a sit-out?

[gordontd]

barmar, on 2015-March-31, 10:46, said:

Of course, that's always desirable, but it isn't always feasible. Is it even possible when you have an odd number of pairs and have to have a sit-out?

It's true there may be things that make it hard or impossible, but the original poster made it sound as though his club don't even try to minimise variance in numbers of times each board is played.

[mycroft]

1) Absolutely not. ACBLscore factors to a shared top, using Neuberg (and has for the last N years).
ACBL requires/d, for hand-scored games, that scores on board that were not played as often as others be factored up by N/M before addition. Also, that *always* you factor up, so if 3 boards got played 12 times and 27 got played 11 (sitout madness), 27 boards get factored up by 12/11. (note, this can be done (and usually was done) by addition of the low boards and factoring up the total, then adding it to the total of the boards played the larger number of times).

2) Why does Neuberg never give 100% of a top or 100% of a bottom? That gets to my handwavey comment earlier: if it was played 2 more times, it might have been played by the pair that could Relay Precision their way to the grand that nobody else could bid - and that should be reflected in the score (there's a chance your 6NT+1 on the non-simultaneous double may not have been a top). There's a chance that this hand could have been played by the EHAA pair, who gets caught by system for +200 into everyone else's game (or -800 into everyone else's game!) - so that zero you earned may not have been a zero (even if you scored -7600, who knows if the "unplay" would have done the same?)

3) So, long story short, the ACBL (and most other places):
- tots up the MPs
- factors up to "biggest top"
- adds up the MPs on each board
- converts to %age, which is (almost always) irrelevant and only for the benefit of the players (*).
Note that the last two steps could be flipped to "convert each board to %ile, then average the %iles) with only potential rounding errors.

(*) Even when scoring games with different tops (for instance, the NABC+ pairs events where there's two sections of 6x13 tables (top of 77) and one section of 5x13 plus a 21-table web (top of 85), the two small sections are factored to a top of 85 before doing the add-up.

The only time percentages matter are simultaneous games where the games are *not* scored across-the-field for overalls. The problem with that is that you are much more likely to win one of those in a 7-table Mitchell (and a 21-board game) at the worst club you can find than in a 15-table game anywhere, for exactly the reason you are mentioning; it is *much harder* to get a great score (or a really pathetic score) the bigger the top and the more boards you play. And Neuberg reflects that.

[barmar]

Why is this an issue on BBO? In BBO tournaments, all boards are played the same number of times. In tourneys with multiple sections, we matchpoint across all sections, so different section sizes don't result in matchpointing with different tops.

[mycroft]

I think we're discussing BBO main club results, where most boards are played the maximum 32 times, but some aren't for one reason or another. Since it's much easier to get a top (or a bottom) on a 3-top than a 31-top, those boards can have a significant effect on the running total (and a very fluctuating one, if you're one of the first few to play a board, as all the other results come in).

Of course, in BBO tournaments many boards are not played at one table and artificial scores awarded, for time or "half-table" reasons; similar issues apply. Also, if pairs are thrown out (or survivor'ed), the later rounds will be played fewer times than the first rounds. As you say, it's not really a big issue.

[barmar]

mycroft, on 2015-April-13, 15:16, said:

I think we're discussing BBO main club results, where most boards are played the maximum 32 times, but some aren't for one reason or another. Since it's much easier to get a top (or a bottom) on a 3-top than a 31-top, those boards can have a significant effect on the running total (and a very fluctuating one, if you're one of the first few to play a board, as all the other results come in).

In general, we're much less concerned about MBC than tournaments. MBC is free, you get what you pay for. No masterpoints or prizes are awarded, so results have less import. MBC is informal -- at many tables players are coming and going, there's no director, undoes are often allowed, etc. Running totals are constantly changing as boards get played more, and you can clear them any time.

The whole notion of trying to combine boards that are played 3 times with boards played 32 times is ridiculous, but we have to do something.

Just treat these results as approximate, since they're constantly changing anyway. It's kind of like looking at your results in a f2f tournament on the Bridgemate at the end of the session. It contains your score within the section, and doesn't include the results from tables that still haven't finished their last board. It's often a point or two different from the results across multiple sections, but good enough to know whether you did well or not -- 60% isn't likely to drop to 50% when all the results are added in.

[mycroft]

To be clear, Barry, *I* think you've done the best you could with the crazy situation you have in the MBC; I think Neuberging unfull boards to a "32 top" on the fly as new results came in would be even more confusing to the general MBC player than "yeah, your top could become a A- in 30 seconds, as we go from 4 to 18 results".

I think the OP feels a little disgruntled when his "clear top of 32 results" scores the same as his opponents' "clear top on 4 results", especially on the rare cases where the board is killed at 4 (or 25, or whatever). He has a valid gripe, but not as valid as the opposite "so how come our +2300 is worth less than his -1400 at unfavourable into -1470 just because it was played 2 fewer times? 'Nobody's' beating -2300, either."

TL;DR: I think we're violently agreeing. Thanks for everything you do, even in these odd corners where it's 'best possible result', not 'best result possible'.

[kontoleon]

So imagine that we play 8 board with the 1rst 100%,2nd 90%,3rd 80%,70,60,50,40,30% so average 65%. so now if count points and the 1rst one have 100 people so 100/100, 2nd 90 so 81/90. 3rd 110 so 88/110 and the rest 100 so total points is 519/800 slightly down from 65%. and if we reverce the 2nd 3rd board the % is come 521/800 slightly higher than 65%. (520/800 are 65%). with formula is better? to just add taken the averege of % or to have the total points/total theoritical points you can taken?

[barmar]

In the MBC, boards are retired after they're played 32 times. So you're not going to get such wide disparities in the number of times a board is played, except when a new board is being played at the first set of tables that receive it.