WBF VP scales revisited

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1 WBF VP scales revisited In my previous article On Victory Point Scales in Duplicate Bridge I was critical of the imperfections in the new WBF VP scales and suggested ways to solve those problems. The conclusion was that correcting the scales are difficult and that perhaps the WBF should be considering alternatives. Here I am going to question the validity of the new scales and consider the options and alternatives. In particular I would like to suggest that there is a definitive solution to the production of VP scales. The scoring panel s reply The comments by the WBF scoring panel on my previous article On Victory Point Scales in Duplicate Bridge indicates the panel did not correctly interpret some of my points. The most important was my suggestion to alter the blitz point to a lower value between 1 and 2 Standard deviations (SD). That was suggested in an attempt to overcome the imperfection in the continuous scale. My claim that the scales are not perfectly continuous is correct and this claim is supported by the WBF panels reply. As they say, for a scale to be perfectly continuous the concavity should always be negative. In fact in the WBF scales the concavity is either zero or negative. This was a compromise they made so that the arbitrary decisions of using 20VP scales and a 2SD blitz point could be adhered to. At this point I would like to commend the panel, and particularly Peter Buchen, for coming up with scales as good as they are. This is where my point of view deviates from the goals of the panel. The objectives of the panel were to produce scales that are continuous, so that each IMP earned by a team is considered in the VP scale and so that each additional IMP is worth less than the previous one. That is not fully achieved because of the compromises and therefore the scales are of questionable value. Changing the game The major conceptual problem I have with these scales is they do change the game. When you change a scoring method you change the game, whatever the game is. In the panel s reply they used the analogy of the game of cricket. In the original game of cricket ( Test cricket ) the number of overs (the number of balls delivered to the batsmen) is not of any practical consideration. The objective is to score more runs (read IMPs in bridge) than the opposition. The teams can take up to 5 days to complete the game. At the end of a test match the teams win, draw or lose.

2 Then a new form of the game called limited overs (each team faces exactly 300 deliveries) was invented. The objective is the same (score runs) but the batsmen can get out more quickly as they only have to bat for the 50 overs. They need to score faster, and the sixes and fours (in bridge that would slams and games) are more important than the ones and twos (part scores). This is a two session game each of about 3 hours, but in one day. More recently there was another form of game called 20 Overs. Similar to 50 overs but faster yet again, and played in one session. The scoring of sixes and fours is paramount and you only bother with the ones and twos if the other attempts fail. The batsmen gamble a lot more and the odds favor a very much more flamboyant style. All forms of the game of cricket are different enough to even considering using different players in the respective teams. The scoring method, that is the rules, have changed the games. At the end of each match the result is till converted to a win, draw or loss. The same applies to bridge. When you change the scoring method or rules, the game changes. The obvious one in teams is the use of board-a-match instead of IMP scoring. The players will use different strategies to achieve the goal of winning. In the new WBF scales the scoring method favors the small wins. In addition when a team is doing badly they can gamble a lot more to try to recoup IMPs without much fear of punishment. Consequently the continuous VP scales means when you are playing teams of roughly equal talent you should be more conservative and always consider very seriously about playing for overtricks in most contracts. When playing teams that are much stronger than yours, and expecting to beat you soundly, then it would be wise to play a flamboyant game and take more risks. Conversely when playing a weak team be careful if they have had a few risky moves pay off. It could be claimed that these ideas would also apply to the old scales, but certainly not to the same degree. The one thing that seems to have been overlooked is VP scales only apply to qualifying events. The qualifiers in the event are to play in a final where the result will be determined on IMPs alone. The standard teams strategies will apply there, where the bidding of tight games is rewarded and the contract is never risked for the quest of overtricks. Even when losing you should seek out swings but only when the odds favor that move. In the qualifying rounds you are asking the players to play a different game than that in the finals. We have seen that many players who do well in match point pairs do not do as well in IMP scored teams. I suggest that the teams that play a very conservative game will do better in the WBF VP scored teams than in the finals. I suggest the USA based teams fit this category very well. The reason for using a VP scale. VP scales were originally introduced so that the results of many teams matches could be compared directly. In the early days of the game there was no pre-duplicated

3 boards and the matches in a qualifying events were playing different deals. Each match would produce different types of results, some of them wildly swinging hands and others more conservative. Consider a very early European championships VP scale: IMPs Winner VPs Loser VPs Note the coarse granularity and less VPs involved than today. Here we have only 3 steps and 4 outcomes. Over the intervening years the granularity has been steadily getting finer with the latest being very fine, though, ironically, as pointed out by the panel, of the 2001 available scores only 121 are possible in a 16 board match. Note I frequently refer to the 16 board match which is the WBF standard event, though all the principles considered apply equally to other numbers of boards. When the scores from the two tables in a teams match are compared and a result determined we use a standard IMP scale to determine the net result on the board. This scale has 25 outcomes and 24 steps. The overtricks made in games compared with the result at the other table sometimes count and sometimes do not. Bid and make 3NT for 600 and the other table is one off in some contract (100) gets a net result of 700. An overtrick (net 730) earns no more IMPs but two overtricks (net 760) gets another IMP. I am sure there are many examples in this scale, but the bridge players and administrators see nothing wrong with this and it is accepted as part of the game. Difference in points IMPs

4 The results found with this less than perfect system are then to be converted to a VP scale that is continuous. Once we have added all the scores from all the boards in a match using this 25 step scale, we then are being asked to believe that it is fair to convert these scores to a 121 step scale. Where an overtrick originally did not count, we are now told that every IMP must count. In the old WBF scale for 16 boards there was only 10 steps to the maximum win and the results were simple integer values. No decimals are needed because we do not need all the extra steps. IMP Win Lose Note the maximum win occurs at 42 IMPs which is about half way between 1 and 2SD for 16 boards which are 30 and 60 respectively. The ultimate cut-off is about 2.5SD. This scale punishes the really bad losses and does not favor small wins. Also note the maximum win at 42 IMPs is actually 20VPs (25 5), in line with the new scales. I think the designers of this scale did a very good job. Moving the results from a 24 step IMP scale to a 10 Step VP scale seems about right. Scoring teams qualifying events The biggest change in teams events in the last 30 years is the introduction of preduplicated boards. Every team in the event plays exactly the same boards. This has been the case in pairs events since the introduction of the game of duplicate bridge. In a pairs event you play against only one pair as your immediate opponent. Your foes are the other pairs sitting in the same direction as you. Those foes can take away Match points on every board by getting a better score than you on that same board. In addition there are your allies who are playing opposite the foes and who are compared with your opponent. Teams are different. Every team plays in both directions. Your immediate opponents are also playing in both directions. It is clear at the end of a match, after you score-up, there is a winner and a loser, or maybe you have tied.

5 Once you know your score on the match the next most important question in the minds of the players is how did our foes perform in that same match?. This is a qualifying event so the relative positions and the teams scores are the most important issues. As in a pairs event, it is not until the scores are posted that the real results are known. Therefore not knowing what your exact VP score in a teams match is not that critical. The overall results are the most important. As mentioned above, the main reason for introducing VP scales was so the results of various teams matches could be compared in valid and realistic way. With duplicated boards it is valid to compare the results of teams matches directly. In any one round all teams have had the same opportunity to score well. That is not the case when comparing the results of other rounds. The boards from one round may be wild with many opportunities for slams and game, another they may be very flat and producing mostly part scores and in yet another the distributions may be extreme and very punishing with lots of opportunity for doubling and hence big scores. Each round is different. In fact the study by Henry Bethe shows the average score on a board is 5.2 IMPs. With a standard deviation of 4.8 it means 68% of the scores vary between 0.4 IMPs to 10 IMPs. That study was across 200,000 results, so within any one match of 16 boards the average could be anywhere but generally in that range. Depending on the size and quality of any field of teams, it could be possible that the VP results of one round does not include a maximum win (no teams gets 20 VPs) and in yet another round a high proportion of teams may get 20 VPs. The current method of awarding VP scores does not satisfy the requirement that the results of each round are comparable. One round in an event can be more important than another. In the panel s reply to my first paper they say: Ideally we should standardize the mean and variance of the results of all matches within a round before adding the scores. This would entail submitting the results and waiting for the computer to do the analysis before getting each team s score. No-one would really want to follow that path, so the use of a VP scale at least approximates the standardization process, and permits an instant result for the match. That is exactly the point I am making. The continuous WBF VP scales are a compromise. There may be an ideal solution, as identified by the panel, but to dismiss it on the grounds that we need a computer to calculate the result is not good enough. Once the results are in, the computer would produce the scores almost instantly. This is the same as in any pairs event. Of course once you have standardized scores they can be converted to a 20 point VP scale in the knowledge that all teams have been treated fairly. Another way to address this issue is to use a lower blitz point because the maximum win (20 VPs) would come into effect at an earlier point. The less volatile matches would not require the same action for a win. Again we see the old WBF VP scale being more effective than the new.

6 I examined the results of a major event in Australia (using the new WBF VP scale) and found of the 12 sessions we had: No. 20VP wins Sessions Conclusions In this paper I have shown that the new WBF VP scales are not satisfying the objectives of the WBF, namely the ever decreasing value of IMPs as the result moves away from the tied matches (negative concavity). The complexity of the scheme does not justify the results. The need for that negative concavity is of questionable value. The WBF VP scale is of a finer granulation than that of the standard IMP scale by a factor of 5 which defies logic. The objectives of all VP scales should be to produce a result that equalizes the value of all the matches in all sessions of bridge event. The new WBF VP scale makes small wins of disproportionate value and changes the game strategies. This scoring method, used in qualifying rounds, requires different strategies to those used in the finals. There are many possible alternate VP scales, with the most recent old VP scale being of particular merit. A new approach of making all matches of equal value, irrespective of the volatility of the boards in the session, must be of real interest to the players. The use of such a method, together with a simple linear scale with no decimals has particular merit. I am sure more research into this idea by the scoring panel and particularly Peter Buchen should produce a very reliable though far from simple scoring method. The irony is that the old WBF VP scale addresses all the contentious issues: It does not favor small wins It punishes big losses It discourages gambling for win Overtricks are not as valuable Encourages bidding tight games The lower blitz point makes all sessions of equal value Results are published in integer values The VP result is known to the teams at score-up time Has fewer step points than the IMP scale Above all it is simple I suggest we go forward to the past. Ian McKinnon, March 2014.

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