Scoring skewered movements

ONE point for every pair you tie with, TWO points for every pair you beat.

This is basis of all match point scoring – it doesn’t change.

Incomplete movements can produce short boards. The number of match points available from the board is going to be less than that from a complete board. The mps must be increased to normalise the board and make it equal in weight to a complete board. A short board should be scored as though it had been played the same number of times as a complete board and so be scored-out-of the same mps total as a complete board.

Short boards are initially scored as-is and then the awarded match points are adjusted or normalised using the formula:

                                    MP x SF + (SF-1) = Normalised Score

(MP are the as-is scores, SF is the scaling factor)

Normalising works as follows, consider a short board with three results:

NSScore          NSMatchPoints

150                  3

150                  3

80                    0

There are 2 results of plus 150 and 1 result of plus 80

If the board were to be played 30 times your best guess is

30/3 x2 = 20 results of 150 and 30/3 x1=10 results of 80

THE SAME LOGIC IS USED FOR 4X

If the board were to be played 4 times your best guess is

4/3 x 2 results of 150 and 4/3 x 1 results of 80

i.e. 2+2/3 of 150 and 1+1/3 of 80

 Apply the rule::

One MP for each pair you tie with and Two MPs for each pair you beat so….

If your score is 150 you tie with 1+2/3 other pairs (don’t forget to subtract the 1 that is you) and you beat 1+1/3 pairs:

1.66x1+1.33x2 = 4.33, as specified above in the table for normalising or scaling a 3 MPs score

If you have a score of 80 you tie with 1/3 pairs (don’t forget to subtract the 1 that is you) and you beat 0 pairs:

0.33x1+0.0x2 = 0.33, as specified above in the table for normalising or scaling 0 MPs score

The formula at the top is obtained using the same logic with a little simple algebra:

E= number of pairs (on your side) with an equal contract score* (includes you)

L= number of pairs (on your side) with a contract score less than the E score.

λ = scale factor

* remember EW pluses are treated as NS minuses and vice versa

One MP for each pair you tie with and Two MPs for each pair you beat

as-is MP score             =          (E-1)×1 + (L)×2  = [(E-1) + 2L]

normalised score           =          (E×λ -1)×1 + (L×λ)×2  =(Eλ -1) + 2Lλ

=          (Eλ – λ + λ -1)   + 2Lλ

=          (Eλ – λ) + (λ -1) + 2Lλ

=          (E –1) ×λ  + (λ -1) + 2Lλ

=          (E –1)λ  +  2Lλ   + (λ -1)

=          [(E -1)  + 2L]  ×λ + (λ -1)

=          MP ×SF  + (SF-1)

A three result board has a maximum of 4mp and total of 6mp for each  NS and EW pair set

A four result board has a maximum of 6mp and total of 12mp for each  NS and EW pair set and a par of 3mps

The three result board after normalising has a total of 9mps but then by adding in PAR results of 3mps for NS & EW PHANTOM PAIRS the board the total is 12mps just like four board. Indeed the board IS now  scored out of 12 but only 3 results appear.  Also the Normalised UP scores for NS and EW add up (across) to 6 just like the four board.

Note: There is a slight ambiguity with the phrase ‘scored-out-of’. It can apply to whole board or just the board’s  NS or EW pair sets totals  each equal to  half the value for the board or just  the top value.

So simply score as-is,  multiply by a scale factor say 4/3 and add the offset (4/3-1)= 1/3 and treat the board as scored-out-of 12.

Using a scale factor of 5/3 you can scale up or normalise a  3 result board to 5 results and so on. Or you can scale up 3 to 4 and then scale the 4 to 5 to get the same answer as scaling 3 5 direct.

You can never secure a real TOP on a normalised short board because there is always a chance that had the board been played one more time the best score becomes a second. Similarly you can’t get a real BOTTOM either. But for scoring purposes (calculating the overall percentages) the board is deemed to offer a real  TOP equal to a complete board.

The score  table is a reconciliation of all board results (normalised if appropriate) in columns with the mp  scores aligned by row to  correspond to each  pair , the row total being that pair’s score. These rows totals are converted to a percentage of the maximum possible score - (boards played) x  (value of a TOP). The max is usually the same for all pairs, but  if the movement has a sit-out and ends before completion, some deprived pairs will have played fewer boards. A proportional max possible score is determined for each pair (no boards played by the pair) x (TOP value).

The percentage is  then simply   100 x Score Total / Max Score Possible

An alternative but less popular method is to  replace gaps(the missing results) in the reconciliation table with PARs - (half real TOPS), but only where a set of boards would have been played had the movement been completed: This allows the same max possible score value to be used for all pair percentages. The GAP PAR method should  assist slightly any  deprived weaker pairs  and diminish slightly any deprived stronger pairs.

The choice between the proportional scoring above and using gap pars is one of attitude about the leading pairs. A leading place achieved by a deprived strong pair despite the slight disadvantage of included PARs, must be considered a just and worthy reward as opposed to a placement arising from numerical conjuring. Occasionally a strongish pair, having a bad bridge day, may benefit from having a PAR score assigned rather than the proportional equivalent of a pair average score,  but that pair wouldn’t then be on track for a leading place anyway. 

Click HERE for a follow up page on accommodating a set score award(60:60) by director