[ArtK78]

fromageGB, on 2014-February-18, 14:31, said:

I'm happy with generated fractions because I look at it in a different way. I don't think one top is worth as much as another. If you played in a 4 player movement, and score 6 UK mps, by beating the other 3 pairs, then that's a top. But if you played a board against 5000 pairs and beat all 4999 of them, isn't this a more convincing victory?

I don't know what the Neuberg formula would make of this scenario, but it would probably agree with me. (Or I with it!)

Your example is a bit extreme. In almost all instances, the difference in the number of comparisons will be very small. In a club game, it is unlikely to be more than one (except in the case of fouled boards). Online, there can be a larger difference in the number of comparisons, and the Neuberg formula is not used.

Maybe you would think differently if you lost a major event (or failed to advance to the next stage of a major event) by .01 matchpoint because of the Neuberg formula.

By the way, in worldwide bridge competitions which do not have fixed matchpoint results, gaining a world-wide top is typically the result of getting some huge number. There is very little practical difference between getting a top on a 5001 comparison board and getting a top minus .01 matchpoints when top on a board is 5000 (or 10000 European style). When the top on a board is much lower - say, 12 or less (24 or less European style), the chance that .01 matchpoints will break a tie is much higher, as the chance of a tie is much higher.

I have witnessed tie breaks between pairs for the final qualifying position in a 4-session pair event with the top 3 qualifying for the National finals (District North American Pairs - two sessions qualifying, two sessions final). It would be difficult to explain how the Neuberg formula broke a tie by arbitrarily awarding an extra .01 matchpoints to a pair that otherwise would have gotten a zero, or .01 less matchpoints to a pair that would have otherwise gotten a top. Of course, the tie-breaking procedures in use are also difficult to justify. Quite frankly, I don't know what they are. I believe that the first tie break is on a board a match style comparison if the pairs played in the same direction, but I am not sure about that.

[barmar]

In normal club games or f2f tournaments, I think it's unlikely that Neuberg would result in just .01 difference from normal matchpoints. Factoring between 11 and 12 tops (or 22 and 24 in British style) will result in multiples of something like .08.

Where you get smaller fractions that break ties are when you have multi-day events with carryover. The carryover typically contains fractional matchpoints, and if you also had to use Neuberg for some boards, the final results can be close by tiny fractions.