This discussion taken from https://www.keepandshare.com/doc/578083/scoring-pdf-may-17-2008-10-19-pm-75k?dn=y&dnad=y
Scoring at Duplicate Bridge
The principal feature of Duplicate Bridge is the ability to draw comparisons of scores across several tables on an individual hand by hand basis where the same hand is played ("duplicated") at different tables so that (supposedly) if you perform better or worse than your counterpart at another table then this is not down to luck of the deal.
The players in duplicate are assigned a label to designate their relative location at the table, referred to by the cardinal points of the compass, North, East, South and West. North and South are partners, East and West the opposing partners.
There are several formats of Duplicate Bridge, each with its own scoring idiosyncrasies (with consequential effect on optimal strategy). This document considers the following formats in the listed order:
1) "Aggregate" or "Total Points" scoring 2) "Chicago" scoring 3) "International Match Points" ("IMP") scoring 4) "Victory Points" ("VP") 5) "Butler scored" pairs 6) "Match Pointed" pairs scoring ("MP") 7) "Point-a-board" sometimes referred to as "Board-a-match" ("PaB" or "BaM")
The ordering of the list is deliberate. Scoring a duplicate event can be a process of several stages or conversion processes, and some of the stages involved in the laterlisted formats require an initial process of scoring up under the earlier-listed formats.
For example, all scoring methods require in the first instance that a hand be scored up on Aggregate scoring principles. In an Aggregate scored event that is the end of the process, but in all other formats that aggregate score then undergoes further conversion.
We should just take this opportunity to stress that despite the apparent similarities between the names of the 3rd and 6th listed methods (IMP v MP) there are no similarities in the method of scoring, as will become apparent below.
Onward, then, to a description of each method.
1) "Aggregate" or "Total Points" scoring
The hand is scored exactly as if in Rubber Bridge with the following exceptions:
There is no "line" dividing the score between "above the line" and "below the line". the score is amalgamated into a single total.
No hand starts with a partscore already credited toward game.
The vulnerability of each side, and the position of dealer, are both predetermined by the board number. Every combination of dealer and vulnerability is catered for in a cycle of 16 hands which then repeats according to the table shown in Appendix 2 to this document.
The reason for this is that it is undesirable for the result on one hand to be dependent on the result achieved on a preceding hand. In Rubber bridge the strategy of a hand depends on the vulnerability and the existing partscore, both of which are the cumulative result of previous deals. In duplicate we strive to ensure that each table starts with the same "history", to ensure that in theory the same strategy is dictated and to make a cross-table comparison of actions meaningful.
In order to recognise within Duplicate the strategic value of winning a partsore or of bidding and making a game contract, you are awarded an immediate bonus. This is necessary because just as the past history of previous deals has no impact on your current deal, so the result of the current deal is "forgotten" when considering the strategy and ultimate score of the next. The immediate bonus is 50 for succeeding in a partscore contract, 300 for succeeding in a contract that qualifies for game, when initially non-vulnerable at the start of that deal, and 500 for succeeding in a contract that qualifies for game when already vulnerable according to the initial conditions.
This is considered as a fair true market value of the expected long term benefit. The 300 bonus for a non-vulnerable game bid and made coincides with the 300 bonus awarded in Rubber bridge for having achieved a vulnerable state in an unfinished rubber. You might have expected the bonus for having a partscore also to be the same, and indeed at one point they were: before the powers that be last revised the laws of Rubber bridge in 1993 the bonus for a partscore in an unfinished rubber was also 50, ie the same as the 50 point bonus for making a partscore in Duplicate. It is difficult to see what the justification was for changing it to 100. Unfinished rubbers are not so frequent that you would expect any attention to be focused on this issue, and even if it were, it is hard to see how you could arrive at a meaningful long term expectation of the value. Indeed it seems obvious that a partscore when vulnerable at Rubber would have a greater strategic value than at an earlier state in the rubber. The change was probably motivated more by politics than by merit. The authorities that govern Rubber bridge laws are not the same authorities that govern Duplicate bridge laws. Periodically both sets of laws change, not usually at the same time, and there may be some antagonism between the parties.
The bonus awarded for making a vulnerable game (equivalent to the Rubber bonus) is a full 500. This is the same as the Rubber bridge bonus for winning a 3-game rubber.
Intuitively, you would think that if the vulnerability of a particular hand were pre-set such that the side which bids and makes game was already vulnerable but the opposing side was not, then you should qualify for the higher equivalent rubber bonus of 700 for a 2-game rubber. However this would overly complicate the scoring, and providing a variety of just two game bonuses provides enough variety to afford the application of skill.
If you bid and make a slam contract, you get the game bonus (300 or 500 according to vulnerability) in addition to the slam bonus (500, 750, 1000 or 1500), as clearly any slam bid and made would also be sufficient to qualify for game. By the same token, in a rubber bridge game, if you bid and make a slam when vulnerable you score the rubber bonus as well as the slam bonus.
Note that although in duplicate there is no concept of a "line" dividing bid-and-made trick scores from other scores, doubled overtricks still score the same as the rubber bridge equivalent (ie suit-independent). Likewise, you still think in terms of a notional "line" in order to calculate whether the contract qualifies for a game bonus. A contract of 1 Spade doubled making 8 tricks does not qualify for a game bonus, while a contract of 2 Spades doubled making the same 8 tricks does so qualify, because the former example only scores 60 (30 doubled) below the line (and 100 or 200 above the line for the overtrick depending on vulnerability, +50 for making a doubled contract), for a grand total of 210 non-vul or 310 vul, while in the second example, although there were no overtricks, the score below the line is 120 which breaks the 100 barrier, on top of which you therefore get the 50 bonus for making a doubled contract, plus either 300 or 500 for the game bonus depending on vulnerability, and a grand total of 470 or 670.
In almost all duplicate events there is no recognition of the "honours" bonus (for holding 4 or 5 of the top trumps in one hand or all 4 aces in Notrumps). Indeed I am only aware of one duplicate event that recognises or recognised honours, being the Hubert Phillips Bowl (a knock-out mixed teams event in the UK based on total aggregate score). Even that event may by now have changed its format to disallow the honours bonus. I am not aware of any event at all that is not a pure aggregate scored event which makes use of the honours bonus.
There are very few events that just use the pure aggregate score. The Hubert Phillips is one, as mentioned above, and the Total Points Tournaments on Bridge Base Online is another.
The Total Points Tournament on Bridge Base Online is an oddity among "duplicate" events, in that there are no cross-table comparisons despite that the scoring is computed on aggregate duplicate principles.
Having determined your aggregate score on the hand, in those events where there is a cross-table comparison, you simply nett off your result against the corresponding score(s) achieved by those sitting in the same seat who played the same hand.
So, in all of the following alternative scoring formats, the first process is always to compute the result of the hand using the aggregate scoring principles as above
(without the honours bonus). We now deal with the further conversion processes based on the alternative remaining scoring formats.
2) "Chicago" scoring
This is effectively Aggregate scoring adopted by players in a social game where there are no cross-table comparisons but where the players are used to, and prefer, the Aggregate scoring method of Duplicate bridge to the original Rubber bridge scoring system. You simply adopt the Aggregate scoring rules as above. In some variations the vulnerability recycles after just 4 deals rather than the complete 16. That is certainly easier to remember, but it does mean that (eg) it is only ever (and is always) West who is dealer when both sides are vulnerable.
3) "International Match Points" ("IMP") scoring
IMP scoring requires that you first determine your net aggregate score, compared with the results achieved at another table, and then convert that net aggregate to an IMP score using the table provided in appendix 3 to this document.
Thus, the maximum IMP score that you can achieve on a deal is 24, when there is a difference of 4000 (or more) aggregate points between your result and that achieved by your counterpart at the other table. At the other extreme, a net aggregate difference of up to 10 points results in zero IMPs. Your counterpart scores the same IMP score as you do, but with opposite sign. If you win 4 IMPs then your counterpart loses 4 IMPs (or scores -4 IMPs).
The purpose of the IMP conversion is to reduce the influence of large aggregate differences over an entire match and so reward consistency. It will be observed that the scale is approximately logarithmic, rather than scalar. In other words, if you score a large aggregate swing, then the margin required to gain an additional IMP is much larger than would be the case if starting with a smaller aggregate difference. For example, if you score a positive aggregate result of 320 on two deals, each deal is worth 8 IMPs according to the above scale, so over the two deals you would score 16 IMPs. However if you scored the same aggregate difference on just one deal, ie a single gain of 640, the IMP score for that would be just 12.
An IMP result requires a minimum of two table comparisons, and this is common in a head-to-head teams match. There may however be a large number of table comparisons, as in an event comprising solely of pairs (contrasted with teams of 4 or 8 etc). Where there are a large number of table comparisons, you would normally calculate the average IMP score for a hand, by totalling up the IMP score of every comparison and then dividing by the number of comparisons. This can be an important exercise if not every hand in an event is played the same number of times, and you would want each hand to carry the appropriate "weight" in your overall score for the event.
This averaging accounts for the fact that in (say) an IMP scored pairs event on Bridge Base Online, your IMP score for a hand may not be shown as a whole number.
For most purposes, the conversion from aggregate to IMP does not have a dramatic effect on strategy.
4) "Victory Points" ("VP")
Victory Points are awarded in an event where several matches between teams contribute toward the overall ranking, and it is not a knockout event. The purpose of the VP scale is to ensure that each individual match assumes equal importance.
There are several recommended VP scales, mainly depending on the number of hands being played in a match. Typically there are 20 VPs "up for grabs" in a single match, which are shared out between the opposing sides. The hands within the match are individually scored on an IMP scale (as described in the preceding section in this document), and the net IMP score of all the hands within an individual match are added together are then converted to a number of Victory Points. A landslide victory for one side would net that side all 20 of the available VPs for that match, the losing side getting none of them. If the overall IMP score is nil either way (maybe plus or minus one IMP), the VPs are shared 10-10. Between those extremes the VPs are awarded accordingly. The cut-off that qualifies for zero VPs varies according to the scale in use, but the scale within that extreme tends to be pretty much a straight line.
There are some events in which a MASSIVE landslide qualifies the losing side for negative VPs. Typically the most extreme result would be 20 VPs to the winning side, with -5 VPs to the losing side. Initially there are the normal 20 VPs at stake, and the winning side can normally aspire to beating the opponents 20-0. However if the winning side achieve sufficient overkill, the losing side get docked VPs WITHOUT the winning side getting any further credit.
The rationale for this variation is that most points (whether measured as aggregate points or converted to IMPs) change hands as a result more by reason of errors on the part of the losing side, than because of skill on the part of the winning side. There are of course exceptions, and indeed luck can play a part. But as a generality, the rationale is valid.
If the losing side lose by a huge margin, the overwhelming likelihood is that the magnitude of the result has more to do with the incompetence of the losing side than with the expertise of the winning side. It is considered undesirable to give undue reward to the winning side where that credit accrues more as a result of the luck of the draw (concerning choice of opponents) than as a result of skill at the table.
There is an additional factor: if you believe that you are heading for a 20-0 loss, and there is no penalty for overkill, there would be no incentive to playing a sensible game. By taking wild actions you stand to gain VPs if the wild actions work, but lose nothing if they fail. Such an environment is not regarded as good for the game, particularly given that there will usually be other matches taking part in the event of which neither participant has a say in the proceedings at your team's tables.
We desire an environment in which there is no incentive either to give up or otherwise to randomise the game. And yet we do not wish to reward unduly a team that has done nothing to deserve the extra credit that the score-line indicates. This is the justification for those regimes that award negative VPs to the losing side for excessive losses after a 20-0 (or whatever-0) loss has already accrued.
The space devoted to this issue in this document is perhaps unrepresentative of the magnitude of the problem addressed. Events in which negative VPs are a possibility are exceptional, and tend to be restricted to high-level events the entrants of which would be unlikely to be reading this document.
5) "Butler scored" pairs
These are very similar to other IMP score pairs events.
To recap, in a "simple" IMP scored pairs event, each table comparison is IMP'd, and the totals averaged over the number of comparisons.
In a "Butler" event, a "par" result for each result is determined, not by using any double-dummy software, but by using the actual results achieved at the table. In determining the "datum" or "par" score, extreme scores are discarded as being "wild" and the remaining results (aggregate scored) are averaged. The number of extreme scores per board that are discarded depends upon the number of times that the hand is played, but it is typically only one or two (an equal number from both ends). Each individual result is then compared with that datum or average score (and now this includes any extreme scores that were originally discarded for the purposes of determining the datum) and that aggregate difference is then convered into IMPs.
Butler scored IMP events distort the result contrasted with a true cross-IMP scoring that bypasses all of this palava. The only reason that this method ever achieved popularity dates back to the days before personal computers became commonplace.
The prospect of manually cross-IMP-ing every table of a pairs event is daunting if doing the entire thing manually. By a computer, of course, the calculations can be done in a twinkling. Without a computer, it is considerably easier (but even then by no means trivial) to calculate a datum or par, then IMP each result by reference to that datum. This exercise does however distort the logarithmic scale that the IMP table was designed to accommodate.
Nowadays, of course, everyone has a computer, so Butler scoring is consigned to the dustbin of history.
6) "Match Pointed" pairs scoring ("MP")
This format is applied in pairs events (not teams) in which several pairs play each hand. As always you start by calculating and recording the aggregate score at your table. After the hand has been played by all tables, you are awarded a number of Match Points according to your positional ranking with respect to the other pairs.
In the UK (and some other jurisdictions) you get 2 Match Points for every pair that you beat, 1 Match Point for every pair whose score is identical with yours, and 0 Match Points for every pair who score better than you (in your direction). In the US (and some other jurisdictions) you get 1 Match Point for a win, half a Match Point for a draw, and 0 Match Points for a loss. It really doesn't matter which method you adopt: the scale is retained and the overall rankings achieved would be the same in either case. You could just as easily assign 735.7 points for a win, 367.85 for a draw and 0 for a loss. You would be mad, but you could do it.
These Match Points are then expressed as a percentage of the total number of Match Points available (ie on the assumption that you beat every other pair). In some movements some of the hands are played a different number of times than others, and in that case you should not convert individual hands to percentages as to do so would suggest that each hand carries equal weight, while in fact a "top" (ie winning all the Match Points on the hand) should carry more weight on hands that are played more times. Anyway, the winner is the pair who amasses the most Match Points.
So, where the size of the margin between scores is relevant in other forms of scoring, that margin is entirely irrelevant in MP events, except to the extent that you might expect to beat more pairs if you beat a particular pair by a large margin than by a small margin. Otherwise, the mere existence of the margin (of whatever size) is sufficient to determine the result. It is frequency of gain, not amount of gain, that is relevant. If by taking a certain course of action you have a 60% chance of gaining an aggregate 10 point margin over the rest of the field, but on the other 40% of the time you stand to lose hundreds, then it remains a good bet to go for the 60% shot. It is not hard to imagine how this can affect the dictated strategy compared with other methods of scoring. It is not necessarily either a less skilful game nor more skilful for that, but it is certainly a totally different game.
To take an extreme example, suppose that you played in an event in which each hand is played the same number of times (once at each table). On each hand you can make 10 tricks in either Spades or Notrumps, except for on one hand where you can again make 10 tricks in Spades but on this occasion only 8 tricks in Notrumps. At every other table your competitors bid and make 4S exactly on every hand. At your table you decide to bid 3NT on every hand, failing by one trick on one hand but making an overtrick on every other hand. In a Match Pointed event you would take first place. On all but one hand you outscore every other pair in aggregate score. Even a margin of 10 aggregate points is sufficient to qualify you for the Match Points. Each hand ranks equally in importance, so your one loss is swamped by the other gains. If you replicated that result in an IMP event you would take last place. Each 10 point aggregate gain is insignificant, in fact translating to 0 IMPs (as you can see from the above scale you need to score 20 aggregate points to get 1 IMP). However that one hand where you went down costs you 10 IMPs if not vulnerable (420 + 50 = 470
aggregate difference = 10 IMPs) or 12 IMPs if vulnerable (620 + 100 = 720 aggregate difference = 12 IMPs).
MP events achieved popularity mainly because it takes a lot less effort to score up an event under the MP method if having to do it manually, without the benefit of a computer, than alternatives.
Whatever the reason for their popularity, their advocates also point out a perceived benefit that every hand assumes broadly the same proportionate importance, as you can never hope to gain more than 100% of the Match Points on any particular hand (or less than 0%), a range which remains constant on every hand (a slight variation is possible if some hands are played more frequently than others, but even then you never in practice achieve much variation in the number of times that a hand is played).
An IMP-scored hand also has upper and lower limits (+/- 24 IMPs), but the difference is that it is not necessary (indeed very seldom) for 24 IMPs to be scored on a hand, whereas the total number of Match Points must be shared out.
Whilst their statement (that each hand ranks equally in importance) is correct, the conclusion that this is better for the game is not axiomatic. Certainly it may be the case, but it does not automatically follow, just because it has an elegant "feel". If anything, it is more logical that more difficult hands (within the constraints of the scoring system) should be awarded greater weight. The only problem with that is that there is no reliable way at the outset to determine the "difficulty rating" of a hand. It is also arguably a skill worthy of reward to be able to identify which hands have the most scope for a variation in result.
7) "Point-a-board" sometimes referred to as "Board-a-match" ("PaB" or "BaM")
This is an attempt at simulating Match Point principles in a teams format. There are several competing teams. You play a fairly low number of hands against each team. You are awarded 2 Victory Points for each hand on which you achieve a net positive aggregate score within your match (just a 2 table comparison), regardless of the margin, but sometimes there is a pool of additional VPs at stake for the overall margin of IMPs won or lost over the set.
This is quite a rare format but extremely challenging. The Pachabo is an example of a UK event scored under these principles.
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