[pdmunro]

I copied the table below from http://www.microtopi...ridge/day4.html
It is an analysis, by bridgebrowser, of about 85 000 results from OKbridge
(i.e. approximately 2700 boards, each played about 32 times).

It shows the frequency and average IMPS for each possible contract.

Cntrct	Nmbr  Freq(%)	AvgIMPS 

PassOut	675   0.76   -0.25
1C ....	102   0.12    0.84
1D ....	171   0.19    0.70
1H ....	445   0.50    0.08
1S ... .884   1.00    0.37
1NT ..	5375   6.08    0.13

2C ...	1155   1.31   -0.49
2D ...	1858   2.10   -0.19
2H ...	3987   4.51    0.20
2S ...	4900   5.54    0.21
2NT ..	2612   2.95   -1.15

3C ...	2228   2.52   -0.60
3D ...	2615   2.96   -0.65
3H ...	3817   4.31   -0.49
3S ...	4140   4.68   -0.59
3NT .	16454  18.60    0.50

4C ...	1078   1.22   -0.77
4D ...	1054   1.19   -0.80
4H ..	10513  11.88    0.19
4S ..	12677  14.33    0.19
4NT ...	151   0.17   -1.61

5C ...	1736   1.96   -0.77
5D ...	2169   2.45   -0.63
5H ...	1503   1.70   -1.55
5S ...	1013   1.14   -1.83
5NT ....	23   0.03   -6.08

6C ....	554   0.63    0.88
6D ....	627   0.71   -0.49
6H ...	1238   1.40   -1.00
6S ...	1389   1.57   -0.24
6NT ...	855   0.97   -1.56

7C .....	45   0.05   -3.99
7D .....	70   0.08   -1.88
7H ....	118   0.13    1.85
7S ....	148   0.17    1.91
7NT ....	95   0.11    2.89

The author, Stephen Pickett, makes the points that

1) Not counting partscores that count as game when doubled, 51.8% of all contracts are Game (3NT,4H through 5NT), and a further 5.6% are slams (6C and up). Never let it be said that Bridge is boring!

2) The consistently profitable contracts are 1NT, 2H, 2S, 3NT, 4H and 4S.
________________________________________________________________

One question I have is: why do 3H and 3S score minus IMPS, on average?
Is it because declarers have overbid or underbid?
That is, do our bidding systems cause us to overbid to 3H-3S when we should be in 2H-2S?
Or, do our bidding systems cause us to underbid 3H-3S when we should be in 4H-4S?

I think it is an interesting table that provokes a number of questions. Any comments?

[Gerben47]

The problem with the "one under game" bids is that they are only right if they are exactly right.

If we play 3♠ and make 10 tricks game would have been better and if we make only 8 tricks we were too high.

Q: is passout plus for those sitting in 1st and 3rd or those sitting in 2nd and 4th?

[pbleighton]

I wonder if the numbers would change significantly in a stronger field?

Particularly, what about international and the final round of national events. Do the experts smooth out the results?

Peter

[hotShot]

Most contracts that should go down, are won by bad leads to the first trick.
So if you have a mixed field and save 9 tricks in ♥ or♠. At some other table opponents will find a "winning" lead or some other misdefence. So making or even playing +1 will not be good enough. Knowing this a lot of the 4M games are none.

Clearly if a board contains 4♠ and 3 ♠ results. The 4 ♠ results are listet under 4♠ in this table, while the 3♠ results are found behind 3♠.
As Gerben said 3M could be an overbid, too. So look at 2M as well. A plus score as expected.

4♠ + 0.19
3♠ - 0.59
2♠ +0.21

4♥ + 0.19
3♥ - 0.49
2♥ +0.20


If you add 4M and 2M IMP's it is almost what compensates 3M -IMPs.

[hotShot]

I don't think the table is interesting.

It tells us that:

If points and cards are about evenly distributed, the side playing on one level scores.
This is because you have 6.5 tricks and a good chance that defence makes a inferiour move.
At the 2 level, the risk is higher, so there are a few results down shrinking the benefit.
Close to game, those some who overbid get away with a big score. The others score less.

So where is the surprise? There is a lot of games and slams out there, but a lot of them are a free give away.
I made a simulation using a double-dummy solver. On 2000 Boards there are about 300 where you can make 11+ tricks. This is about 15%. 4.5% can make 6 or more, the tables 5.6% show that single dummy defence is harder.

[inquiry]

Well, the neat thing about that table is the frequency. There is obvioiusly little you can make from the rest of it. Consider pass out for example. This table show the average score for a passed out hand is minus 0.25 imps. But of course this is non-sense. If one side of the table passes the hand out and gets a minus 0.25 imps, then the other side gets a plus 0.25 imps. The passout score has to be a zero-score game, where the average is zero.

So why is the passout -0.25? It is because the way the averages are calcuated. Bridgebrowser shows the score relative to declerer. On a passout hand, declerer is first seat, so if the hand is passout out, the fellow in fourth seat who does the passing gets, on average +0.25 imps for his decision. No doubt because if he is weak, the other players may have made a mistake in not opening, so the balance of power is with 1st and 3rd chair. This answers Gerben's inquiry.

Next question is, is it even fair to consider just the final contract of, say 3H, out of context of the auction. Some auctions start 3H all pass. Some are a result of highly competitive auctions. Would vulnerabilty have an effect on the average score. What if you removed doubled and redoubled contracts from the mix? I don't feel like undertaking the exhaustive analysis printed above, but I did look at the 3H contract issue.

So I looked atBBO Data. I started out looking at all the IMP hands played in the main room during the week of May 9th and a very few from May 10th 2004 (I created a smaller database, primarily one day, to deal with). There were 15262 auctions in this (since this is main room, divide by 16 for number of hands). There were 627 3H contracts, for a frequency of 4.1% (close to published value of 4.31 on much larger data set), and average imp score of -0.57 (a little worse than the published -0.49), but similar to the value for 3S (which was -0.59).

This data, however was lumped in at both vul, and all the doubled and redoulbed contracts include. LEt's see what happens to various contracts...

3H when not vul = averaged -0.86 (includes x and xx contracts)
3H no double or redouble when not vul = average -0.65
3Hx or 3Hxx not vul averaged -2.32


3H when vul = average -0.18 (includes x and xx)
3H no double or redbl vul = -0.53
3HX and 3Hxx vul = +1.63

This data is not valid yet. There was no redoubled vulnerable 3H contracts, and only one 3Hxx not vul contract, and that one went for huge number, pushing the x and xx not vul average down. But I think an approach like this would help if you wanted to look at such numbers.

Further of the 627 3H contracts, 9 of them began with a 3H openig bid (averaging plus 0.77 imps), and another 9 of the hands overcalled three hearts, here average a very poor -2.29 imps/hand (the single redouble hand WAS NOT in this group).

Five of the hands were jumps to 3H in response to a takeout double, for an average of minus 4.92...

This is too small a dataset to make too much of a decision, but this is how it should be approached.

Ben

[helene_t]

The bad results from 2♣ and 4NT may be related to bidding misunderstandings. A pick-up pd may pass New Minor Forcing and Blackwood. The bad results from 3♣ until 4♦ (except 3NT) may also to some extend be related to pick-partners passing forcing bids.

[inquiry]

helene_t, on Feb 22 2005, 12:10 PM, said:

The bad results from 2♣ and 4NT may be related to bidding misunderstandings. A pick-up pd may pass New Minor Forcing and Blackwood. The bad results from 3♣ until 4♦ (except 3NT) may also to some extend be related to pick-partners passing forcing bids.

We have all heard the worse contract to play is 2NT, but these statistics suggest that the very worse on is 5NT.... :-)

Ben

[mikestar]

I believe it was Jeff Rubens who said that 2N-1 was a misdemeanor, 4N-1 was a felony , and 5N-1 was a hanging offense.

[keylime]

I have heard pros saying that if their clients rested in 5NT, they had to pay a fine, whether or not they made it or not.

I'm trying to remember which pairing Hamman mentioned in his book "At the Table" that was scolded for playing 2NT making three constantly...

2NT GOTTA be more of a felony than 5NT - higher rate of occurance.

[dogsbreath]

Hi
i hate 2nt .. as y all know it rarely makes exactly 8 tricks. What i hate even more is these data showing 'x' result over x-thousand boards .. what is the statistical background to this data? .. the variables involved are complex .. level of declarer-play, good/bad opening leads .. i find it impossible to attach ANY credibility to an anaylsis like this of x-thousand random declarers and random opening leads
..am i missing something?
Rgds Dog