Par           2S by NS +1 = 140 to NS
    Forced by     2H by EW +0 = 110 to EW

    Par           3S  by NS +0 = 140 to NS
    Forced by     3Hx by EW -1 = 100 to NS

    Par           4Hx by EW -1 = 100 to NS
    Sacrifice vs. 3S  by NS +0 = 140 to NS

    Par            4S  by NS +0 = 420 to NS
    Least bad sac  5Hx by EW -2 = 500 to NS

Notes on Double Dummy Analysis Report

The Double Dummy Comparison Report consists of three parts,

Blame Points

Blame Points attempt to show which pair was at fault when a team lost points on a deal.

Bid and Play Potential Points Lost

Bid and Play Potential Points Lost shows all cases where a pair could have bid or played more accurately, even if they did not lose points on a hand.

Bidding "Mistakes"

Bidding "Mistakes" attempts to show at what points during the bidding a pair made a bid that lowered its expected par result.

In all cases, double dummy par is used as a comparison point.
Some terms used are:

PAR

This is the double dummy par as described above.

EXB

Expected Result after Bidding. At each table, we can take the final contract that was reached, and figure out the expected double dummy result if that contract was played with perfect offense and defense.

EXL

Expected Result after Lead. At each table, we figure out the expected double dummy result given the opening lead. (again assuming the rest of the hand is played with perfect offense and defense).

ADJPAR

Adjusted par is used to determine blame points, see below. It is computed separately for each two-table comparison. Each pair's par starts out as double dummy par but after the bidding and again after the opening lead, each pair's par can be adjusted in the following way:

• If the opponents at your table make a bid or lead whose expected result is less than par, that means your own new expected result is greater than par, so your par is adjusted upwards to this new expected result.
• If both of the pairs sitting your direction have expected results that are less than par, then your new par gets adjusted down to become the least bad of these expected results.
• Otherwise, your par remains unchanged

See under blame points for the usefulness of adjusted par.

NS1, NS2

These are the actual results at each table.

SWING BLAME

This is the number of IMPS or MPs lost by not achieving adjusted par. We compare the actual result (in IMPs or MPs) to what the result would have been if your pair had made adjusted par and the other table had kept their result. For example, par on a hand is 6S making 6 not vulnerable. Table 1 stops at 4S and makes 6. Table 2 gets to 6 spades but goes down. The actual IMPS result is -11 (480 vs. -50). But if the pair at table 2 had made the makeable 6S, the IMPS result would have been +10 (480 vs. 980). Thus the swing blame in this case is 21 IMPS. Note that you can get some "swing blame" even if your team wins a board (meaning you could have won by more if you had achieved adjusted par).

Blame Points

When a team loses IMPS or MPs on a hand, it is the fault of one or both of the pairs on the losing team. The Blame Points section tries to allocate the blame for the loss between the two losing pairs. Note: when there are more than two tables, the procedure outlined below is done for each pair of tables, then totalled to get the total blame for that hand.

In IMPs, the total blame equals the total IMPs lost on that two-table comparison. In MPs, the blame is the MPs lost on that two-table comparison, which by the nature of MPs is either 0 or 1. Blame points are allocated by comparing a pair's actual result with it's adjusted par result as follows:

• If only one pair shows a deficit with respect to its adjusted par, that pair gets all the blame.
• If both losing pairs show a deficit with respect to their adjusted par, the blame is divided among the two losing pairs, proporationally to how much swing blame each pair incurred. (In this case when both losing pairs do worse than adjusted par, we average a pair's normal swing blame with the swing blame they would have incurred had their teammates made their adjusted par).

After totalling the blame points that each pair made, we compare that total to the average total for pairs that held those same hands and we show your departure from that average (in percent plus or minus). We compare this way rather than comparing absolute blame points because, on many hands, the opportunities for mistakes are usually more in one direction than in the other.

Blame Points Examples

The following IMPs examples show three hands where the NS2-EW1 team lost 13 IMPs on a hand, but on each hand the blame points are allocated differently. For simplicity, the following examples ignore any adjustment coming from the EXL (expected result after lead) but the logic for that adjustment would be similar.

• Example 1: Par is 4S by N making 4 (+620). At table 1, NS1 bids 4 and makes ie, they get the par result. At table 2, NS2 misplays, going down 1 (-100). Since NS2 was the only member of the losing team to not make adjusted par, all the blame goes to NS2. So the scores vs. adjusted par would be: (Here DIFF indicates RESULT-ADJPAR).

                                                            IMPS
                      PAR   EXB ADJPAR RESULT  DIFF  BLAME  LOST
  NS1                +620  +620  +620  +620       0     0     0
  NS2                +620  +620  +620  -100    -720   -13   -13
  EW1                -620  -620  -620  -620       0     0   -13
  EW2                -620  -620  -620  +100    +720     0     0
  
  

  In normal team scoring, EW1 being a temporary teammate of NS2, shares in the disaster. (and NS1 being a temporary teammate of EW2, shares in the benefit). In Blame Points scoring, the burden for the 13-IMPs loss falls only on NS2 who failed to make a contract that should have been made. Everyone else gets average.

• Example 2: Now suppose on that same hand NS had been able to make 9 tricks at NT and also only 9 tricks at spades. Par would then be +600 (3NT making 3). Again, both our NS pairs bid to 4 spades (expected result -100). And again, NS1 makes 4S and NS2 does not. In this case we would have

                                                            IMPS
                      PAR   EXB ADJPAR RESULT  DIFF  BLAME  LOST
  NS1                +600  -100  -100  +620    +720     0     0
  NS2                +600  -100  -100  -100       0     0   -13
  EW1                -600  +100  +100  -620    -720   -13   -13
  EW2                -600  +100  +100  +100       0     0     0
  
  Note: Par for NS1 and NS2 both adjusted down (both misbid)
  
  

  In this case, of the losing pairs (NS2 & EW1), only EW1 had a deficit from adjpar so EW1 gets all the blame points. (the Normal IMPS scoring is the same as before). It makes sense that now the burden for 13-IMP loss suffered by the EW1-NS2 team falls on EW1, because they were supposed to set 4 Spades, but instead they let NS1 make it. Note that if we had been using original par rather than adjusted par, NS2 would have had a deficit of -700 and would have incurred some of the blame (for misbidding), when really they didn't bid any worse than the other NS pair.
• Example 3: Assume the same hand as above (par = +600 to NS), but now NS2 actually bids 3NT (expected result +600) but then they manage to misplay it and go down a trick. (and at table 1, assume NS1 still bids and makes 4 spades which should have gone down). So we would have:

                                                                  IMPS
                      PAR   EXB ADJPAR RESULT  DIFF  SWING BLAME  LOST
  NS1                +600  -100  +600  +620     +20     0    0     0
  NS2                +600  +600  +600  -100    -700   -12   -6.5  -13
  EW1                -600  +100  +100  -620    -720   -13   -6.5  -13
  EW2                -600  -600  -600  +100    +700     0    0     0
  
  Note: No NS adjustment needed from EXB
  
  

  Now of the losing team pairs (NS2 and EW1), both were responsible for large swing blames (-12 and -13 respectively). It makes sense that both should share in the blame since NS2 went down in a contract that should have made, and EW1 allowed a contract to make that should have gone down. Looking at it another way, together they managed to convert what should have been a 13 IMP swing their way to a 13 IMP swing the other way. Again if we had just used original par, NS2 would have had most of the blame.

Bid and Play Potential Points Lost

This part of the report attempts to show a pair where they might have bid, led, or played better, including hands where their team did not lose any points.

BIDABS

Set if the expected result from bidding (EXB) is less than original PAR.

BIDREL

Set if the expected result from bidding (EXB) is less than that pair's par as it was adjusted after the bidding step. In other words, bidding discrepancies that are common to all tables are subtracted out. BIDREL is perhaps a more fair indicator of bidding errors since some PAR results are unreasonable to bid. Still, it may be worth inspecting the BIDABS errors to improve your bidding further.

For bidding discrepancies, the symbol < indicates an underbid, > an overbid.

LEAD

Set if the expected result after the lead (EXL) is less than the expected result after bidding (EXB). In other words, the lead was not one that maximized the defensive tricks. The actual leader (N,S,E or W) is shown.

PLAY

Set if the actual final result is less than the expected result after the lead (EXL) If the pair was on offense, the declarer is shown (N,S,E or W). Otherwise a "D" is shown to indicate they were playing defense.

Note that not all discrepancies are "punished". A pair can overbid but still make the contract. For example, pair A overbids to 3NT when only 2NT can be made on the hand. Pair B then misdefends and allows 3NT to be made. Therefore, at this table we would have (assume vulnerable)

             NS1   EW1 
PAR         +120  -120   (2NT bid and made)
EXB         -100  +100   (3NT should go one down)
ACTUAL      +600  -600   (3NT bid and made) 
BIDABS      -220         (unpunished)   
PLAY              -700

so pair A potentially lost 220 points (the difference between +120 and -100) by overbidding (potentially because they would have lost it against perfect defense), but then in the play, pair B lost 700 points (the difference between +600 and -100) by underdefending.

As usual, when comparing to double dummy, use your own judgement to decide whether to worry about any particular hand.

Bidding "Mistakes"

The PAR result described above is computed before the bidding has started. With perfect bidding, this should also be the expected par result when the bidding is completed (called EXB above). However, sometimes the bidding is not perfect.

In this section, we go thru each hand at each table, and compute a new par after each bid is made. (To keep things simple, we only show NS par (EW par is just the opposite). If the bid has lowered par for a pair, we mark the bid with a "?", and add a comment showing what the new par is and what a better bid would have been. At the end of the comment, the figure in parentheses shows the offending pair and by how much their bid lowered their par.

Note that by the definition of par, there is no way a pair can by their own action "raise" par during the bidding, only lower it. Of course, you can benefit from your opponent's misbidding, for when they lower their par, they raise yours.

Note that this section doesn't take into account the final result from the play. It only concerns itself with the bidding. So, for example, a bid that looks like an overbid in double dummy might have worked out by actually making at the table.

Note: The following examples are from the Dec 9, 2004 game. On this hand, NS can make 9 tricks in hearts, EW can make 8 tricks in clubs and 6 tricks in NT.

Example 1:

Board 24, Table 2:  parNS=  140 (3H   by NS) GB vs DJ, None Vul
W    N    E    S    
P    P    1C   1H   
1N   2H   3C   3H   
P    P    P    

Here the bidding was perfect. NS got to the par contract, and EW never "stuck their neck out" by making a dangerous bid that would have allowed NS to collect more than it's par 140. (3CX would have only gone -100). Note that there are no comments.

Example 2:

Board 24, Table 1:  parNS=  140 (3H   by NS) PN vs TG, None Vul
W    N    E    S    
P    P    1C   1H   
1N   2H   3C   3H   
3N?                 parNS=  300 (4CX  by E );  Better was P        (TG   -160)
     P    4C   P    
5C?                 parNS=  500 (5CX  by E );  Better was P        (TG   -200)
     P    P    X    
P    P    P    

This is the same hand as above from the other table, with not quite as good bidding on EW's part. You can see that with the West bid of 3N, they were already in trouble. 3NX would have gone for -500 to EW, but par at that point was "only" reduced to -300 because EW could recover from 3NX by bidding 4C and getting doubled there (-300). Note that E did indeed recover to 4C which was the par bid at that point. The 5C bid by W then made things worse again and reduced the par to -500. Since South did properly double 5C, 500 for NS became the final par.

Example 3:

Assume on the same hand above that S had not doubled the final 5C bid. Then one would have seen

5C?                 parNS=  500 (5CX  by E );  Better was P        (TG   -200)
     P    P    P?   parNS=  150 (5C   by E );  Better was X        (PN   -350)    

In other words, EW would lose 350 points by not doubling.

Example 4:

In this example, imagine the same bidding as in Example 1, but imagine that double dummy had computed that EW could take only 7 tricks in clubs. Now the 3C bid by E would be dangerous (going for -300 when doubled). And if S continued with 3H, that would also be marked with a comment because he let EW "escape".

Board 24, Table 2:  parNS=  140 (3H   by NS) GB vs DJ, None Vul
W    N    E    S    
P    P    1C   1H   
1N   2H   3C?       parNS=  300 (3CX  by E );  Better was P        (DJ   -160)
               3H?  parNS=  140 (3H   by S );  Better was X        (GB   -160)
P    P    P    

Note that the final par was unchanged from the original par. Howver, NS did miss an opportunity to punish EW.