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Scoring in Bridge

Bridge is an excellent social game, in part because scoring is not highly correlated with the quality of play. This allows everybody to win some of the time, while skill prevails in the long run.

On the other hand, randomness in the scores is one of the reasons why it is difficult to convert the social game into a competitive sport. The longer the match, the more likely it is that the strongest competitors will win, but we don't have time for that. Culbertson and Lenz played 850 boards.

The various attempts to reduce the random effects take the form of a variety of ad hoc non-linear score corrections, matchpoints, IMPs and, most ad-hokey, VP's.

In a duplicate game a numerical score is recorded on a scale that is derived from quite a different game, namely rubber bridge, which few duplicate player take seriously. Since the relative magnitudes of these numbers are mostly devoid of meaning, they are immediately converted into other numbers; and since there are no arithmetical operations that can eliminate randomness from individual scores, converting meaningless numbers into meaningful scores, the form of this conversion is largely a question of taste, tradition and fake mathematics.

Nevertheless, a workable method was found, namely scoring by rank. This eliminates the meaningless size of the numerical differences and works on the premise that higher scores are better, which is true on average, i.e. in the long run. It also gives each board the same weight, which is undesirable, but you can't have a everything, e.g. a silk purse when you have a sow's ear.

For various reasons, mostly organizational and financial, most important championships are played as 'team games'. Of course, Bridge is not a team game by nature and the only function of the team-mates, who don't even have to know each other's identities, is to provide scores for comparison. The effect is duplicate bridge at two tables. You could still retain some of the advantages of rank scoring, whence you get 'board-a-match', which is rarely played and has its own set of advantages and disadvantages.

Instead of rank scoring, the weird rubber-bridge scores can be subjected to transformations that have the goal of reducing the likelihood that a few large scores make the rest meaningless. Since this can be done in a thousand ways, and since any theoretical justification is both difficult and tenuous, people have invented a variety of such schemes, each optimizing one thing or another.

The IMP scheme is, thank God, established and accepted as natural law, though nobody knows exactly why. The critical observer will ask how much sense it makes to add IMP's to each other and compare the sums. The answer is, as usual, that it makes some sense when you add lots of these numbers, vaguely appealing to the law of large numbers, and hoping that nobody asks: How many is 'lots'?

But IMPs still have quite a large range, so in a short match a single calamity can swamp the rest of the scores. So naturally we need to dampen the large scores by a second application of an ad hoc non-linear correction, whence the birth of 'Victory Points'. I don't know who invented these, and don't really want to know, since it is obvious that there is no objective criterion that might determine the optimal shape of the curve - it will be monotone and concave - but what else? Even concavity throughout can be questioned.

Since it isn't at all clear what makes one VP scale preferable to another, periodically somebody will set out to invent the best conceivable such curve. So now we have lots of different VP scales.

Two different scales will occasionally result in different rankings - after all, that is their purpose. When that happens, mature adults will understand that that is how the ball bounces; children will cry; and true competitors will blame the referee.

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