mycroft, on 2014-February-17, 13:46, said:
The reason the 22/20 factoring method (which is what was used pre-computers to do formulas) is flawed is that who knows if the "phantom" 12th pair to play it has the system to find 2210 on that hand that everybody else in the room got 1460 on - or conversely, if the defence is good enough/declarer is bad enough to go -800 on the hand that everyone else is either -500 or -620 on? There's a non-zero chance of this.
Take it down farther. Assume all boards are played 12 times, so top is 22; but one board had to be replaced halfway through because of fouling, and it was played 6 times (as was the unfouled board). Now top on the board is 10; now we have to multiply the scores by 22/10. Seriously, is there not a chance that the top (and there are two of them, one for each fouling state) isn't going to get beat if it were played another 6 times? So, shouldn't your "top" reflect that chance?
With all due respect, factoring up the score on the board by multiplication to bring the top on the board up to the top on the rest of the boards is not flawed. It is mathematically accurate and absolutely appropriate.
The board was played with a field consisting of one less comparisons than the field the other boards were played in. There is no "phantom" pair, and any speculation about what the score would be if there were another comparison is just that - speculation. There is no need to account for it, and any method that does so is just making a guess with no substantiation.
The fact that anyone came up with some sort of computational algorithm that results in a low score of .01 and a top score of .01 less than the typical top is mere hocus pocus. There is no rationality to it. I accept that fact that the powers that be have chosen to use this scoring system when there are boards with different numbers of comparisons. I don't have to agree with it, and I don't have to like it.
I note that in match point pair games on BBO, each board is scored using the number of comparisons on the board and the scores are converted to percentages of the top score on that board. That eliminates the need for any other computational algorithms to compute matchpoint scores on different tops - each board is scored with a top of 100% to two decimal places. That works, and it is accurate to two decimal places.
As for fouled boards, Barmar correctly reports the procedure for dealing with fouled boards using manual scoring. And I agree with that method for the same reasons that I agree with the pure factoring up method. There is some other method used with computer scored fouled boards, and I have no idea what the rationale is. I know that, "in the old days," there was a different method for dealing with fouled boards at sectional and higher rated tournaments, even when scoring was done manually.
By the way, when factoring was done "in the old days" it was always factoring up - never factoring down. This was due to the fact that making the scores larger increased the chance of breaking ties due to fractional matchpoints resulting from the factoring. As agua noted, the old rule was that score differentials of less than .25 matchpoints were considered to be tied results. The .25 rule sometimes created really peculiar results. For example, suppose three pairs scored 145.60 MPs, 145.40 MPs and 145.20 MPs, and suppose these were the 2nd, 3rd and 4th best scores. Using the .25 rule, the top pair tied for 2/3, the middle pair tied for 2/3/4, and the bottom pair tied for 3/4.