Yesterday's combined game illustrates well the effect of using fixed strata when the mix of pairs is unbalanced. Here is the Recap for North-South, with 4 A's, 2 B's, and 6 C's:

Pair    Pct   Score      Section Rank      MPs     
A     B     C  
01   63.19  136.50  A   1                1.20(A)  Jim Somma - Ann Pullman
09   60.65  131.00  A   2                0.84(A)  Mary Ann Dufresne - Marion Ell
07   58.80  127.00  B   3     1          0.64(B)  Mary Ellen Vanzler - Millie Da
10   57.87  125.00  A   4                0.42(A)  Gerry Panos - Darlene Drietz
04   56.25  121.50  A   5                0.24(A)  Lois Fortunato - Donald Bowen
08   52.78  114.00  C         2     1    0.48(C)  Alice Jones - Aruna Raghavan
02   46.76  101.00  C         3     2    0.34(C)  Jan Foster - Patricia McCullou
12   45.83   99.00  C                             Chris Ekris - Nancy Gooch
06   45.60   98.50  C                             Tom Brousseau - Margaret Zieli
05   41.90   90.50  C                             Ron Watson - Nora Watson
11   39.35   85.00  B                             Michael Miller - Bob Mooney 
03   31.02   67.00  C                             Diane Linindoll - Christie Ben

Note that 7 of the 12 pairs won MPs. Note also that Alice and Aruna's award was higher than Gerry and Darlene's, and that Jan and Patricia's award was more than Lois and Donald's.

Had the strats been recalculated, here is my estimate of what it might have been with 4 A's, 4 B's and 4 C's. I don't have all the MPs available to be sure and I don't know the MPs the C's would have gotten. Also, I'm not sure 8 pairs would have scratched -- ACBL policy tries to pay about 60% of the field -- 8 would be 67%.

Pair    Pct   Score      Section Rank      MPs     
A     B     C  
01   63.19  136.50  A   1                1.20(A)  Jim Somma - Ann Pullman
09   60.65  131.00  A   2                0.84(A)  Mary Ann Dufresne - Marion Ell
07   58.80  127.00  B   3     1          0.64(B)  Mary Ellen Vanzler - Millie Da
10   57.87  125.00  A   4                0.42(A)  Gerry Panos - Darlene Drietz
04   56.25  121.50  A                             Lois Fortunato - Donald Bowen
08   52.78  114.00  B         2          0.48(B)  Alice Jones - Aruna Raghavan
02   46.76  101.00  B         3          0.34(B)  Jan Foster - Patricia McCullou
12   45.83   99.00  C               1    0.??(C)  Chris Ekris - Nancy Gooch
06   45.60   98.50  C               2    0.??(C)  Tom Brousseau - Margaret Zieli
05   41.90   90.50  C                             Ron Watson - Nora Watson
11   39.35   85.00  B                             Michael Miller - Bob Mooney 
03   31.02   67.00  C                             Diane Linindoll - Christie Ben

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Anonymous   |2011-12-29 13:58:09 You need at least 5 pairs in C in a Mitchell movement in order to award points in C. Stratas must be assigned before the game starts per ACBL policy. The club policy is to be sure there are at least 5 pairs in the C strata in a Mitchell movement and the required 3 pairs in the C strata in a Howell movement, (although this can be problematic in the Tues. and Wed. games). Where the game can be stratified along standard strata points, it is done that way, using 300, 500, or 750 for the top in C; 1500, or 2000 for the top in B and Open in A. When the game has to stratified using other limits, the director tries to provide stratas that create a least disparity, i.e. if the next two pairs are within a few points of each other and the third pair is far above, the director usuallly adds two pairs. the exception is when the 6th pair would be over a normal break point such as 300, 500 or 750. Once the C level is established, the director tries to stratify the A and B pairs as fairly as possible. Since the C pairs count for B awards, there is no minimum for the number of pairs needed in B to award points. Likewise for A. It is cause for revocation of a club's sanction if the club does what Pat is suggesting and awards points according to results. We did this at one time but were notified by ACBL that we had to stop. All directors at NCBC know how to stratify games within the rules of ACBL and they do a good job. Each game is stratified as soon are the players names are in the computer. There are no fixed stratas.

Pat Clark   |2011-12-29 14:33:31 I never suggested stratifying by results! While the game is being set up, the MPs of all the players is known. Strats can (and should) be set at that time to balance the field. The field is required to be balanced by direction and by section. If it is not required to be balanced overall, I would be surprised. But I know it is legal to do what I have suggested. Quoting from the ACBL's club director's handbook: "You can use any strat limits you feel are best for your clientele." The results shown were for North/South. There was a similar number of C pairs sitting East/West, so the total would have been 8.

Anonymous  - Calling All Math Scholars   |2011-12-29 15:04:14 The way the strats are now determined in the open games seem to indicate that the players with MPs at the bottom of the B classification have the least chance to earn MPs. Would any math scholar care to do an analysis of this?

Pat Clark  - Bracketing Effect   |2011-12-30 07:53:54 Any time you have a bracketing effect, the players at the bottom of a bracket will have more difficulty in beating people at the top of the bracket. Ideally, this should apply equally to A, B, and C. But if the brackets are not equally divided, like 1/3, 1/3, 1/3, the effect is magnified. In addition, the way ACBL scores stratified events is more complex than I have indicated and is slightly erroneous, mathematically. The way it actually works favors A players a little and B players a little less. This is offset by allowing B's and C's to score in a higher bracket. It's not exactly correct, but is a reasonable compromise. An alternative mechanism can be imagined, such as is done in Golf or Bowling, where lower ranking players are given a handicap. I'm not familiar with Golf's handicaps, but in Bowling, the handicap is some percentage, like 67%, of the difference between your average and the highest average. Note that to be mathematically "fair," it would have to be 100% of the difference. But if you do that, then you might as well flip a coin. As far as I know, ACBL does not sanction any handicapped events. There is the possibility of "flighted" events, not much used anymore, where the Brackets are truly separate games. You need a lot of pairs to have 3 good games. But that does not alleviate the Bracketing Effect.

Paul Lauer  - Handicap game/stratification   |2011-12-30 10:10:36 Pat A club may run santioned handicapped games-it's easy with a small game (6-8 tables) and the same participants every session - I've played in such a game often. I for one am not interested in such a game in our club and do notbelieve it would address your concerns. Also, the Wed. game you exampled was stratified in an effort to cater to the 299ers - I for one believe we as a club should make every effort to keep them involved. Your example really does not make a clear point --do you think more points would be awarded to c players if strata was changed - also to place the named C players in B strata the two sections would demand irregular numerical allocations between sections. What a nightmare, as if seating players is not enough of a problem now. The system may not be great but it is the best we have at this time. Directors do all know how to stratify games and I often confer with other directors to see if my stratification seems acceptable. I'm willing to change as long as it is a board mandate-but until then I will do what I think is as fair as possible as I am sure the other directors do.

Pat Clark  - I guess I don't write clearly   |2011-12-30 10:24:37 I don't support or suggest a handicapped game. I was merely making a mathematical point about bracketing versus handicapping. The attempt to cater to C players backfired. By not having 1/3, 1/3, 1/3, you actually reduce their chance of being awarded MPs. To answer your question, Yes, I believe more points would be awarded to C players if strata were changed. The "nightmare" you suggest is a phantom. I thought so too until I considered just what would happen. Pairs would be seated according to an "assumed" strat. Then, while the game is being set up, and after the game has started, the actual strats to be used for scoring are determined. I believe that almost never would this result in an imbalance between directions or sections. There is no absolute way around it, however, if we continue to seat ourselves. Perhaps we wait to get an assigned seat, after considering all the balancing requirements and those needing a stationary seat. That may not be as bad as we all assume -- it happens on Thursday night quite often, especially the stationary seat part.

Pat Clark  - Minutes of 7/9 2010 Quote   |2011-12-31 08:54:58 The Board has addressed this before. The following outlines how the stats are to be determined, and when. Then the last sentence seems to say, in effect, "never mind -- the director can do whatever he wants." "A motion was made by Jim Logan as follows: In a Mitchell movement, the C strata will have a minimum of 5 pairs. The rest of the players will be divided as evenly as possible in the A or B strata. In a Howell movement, the C strata will have a minimum of 3 pairs. The rest of the players will be divided as evenly as possible in the A or B strata. Motion was seconded by Annabelle Hills. The vote was unanimous. Our club will no longer have set stratifications limits. Stratification for each NCBC game will be at the discretion of the director after all names have been entered in the computer."

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