# Can one show that a majority of bridge hands could have been successfully defended?

In noting the importance of defense in overall bridge scores, a bridge teacher opined that half or more contracts were either defeated or could have been.

I was wondering if available records of the results in pairs or duplicate tournaments could prove or disprove this statement. Specifically, I was wondering about the proportion of "contested contracts" that some declarers made, and some defenders defeated.

For our purposes, a "contested contract" in a pairs tournament will be one where the declarer made it in one room, and the defense defeated in the other room. A declarer's contract will be one that both declarers made, and a defender's contract will be one that both defenders defeated.

A "contested contract" in a duplicate tournament will be one that declarers and defenders made and defeated in non- lopsided proportions. A declarer's contract will be one that most declarers made, and a defender's contract will be one that most defenders defeated.

Are there percentage breakdowns of contested, versus declarers' and defenders' contracts from tournaments? And do they show that the percentages of defeated plus contested (and presumably defeatable) contracts is greater than 50 per cent? Or are declarers supposed to make more than 50 per cent of their contracts because bidding systems are constructed that way?

-
A tough theoretical question- if you wish this is useful source- Vugraph project from which you might do your own analysis sarantakos.com/bridge/vugraph.html – user2617804 Nov 12 '13 at 4:12
'The number of contracts that were or could have been defeated' is about as useful a statistic as 'the number of days when it rained or might have done'. – TimLymington Nov 12 '13 at 23:35

What level of play are we talking - world class or novice or somewhere in between.

Any player who is making or defeating an inappropriately large, or small, percentage of contracts weighted by point value is inefficient by definition, and thus is a poor player.

Good players make and defeat the right number of contracts, weighted by point value (for the scoring type - match-points, rubber, IMPS or board-a-match), because that is the definition of competent play. Given the close competition of most world championship finals, those players are all efficient, and thus actually good players.

Update:
It's widely accepted that defense in Bridge is more challenging than offense. Is that not semantically equivalent to stating that, double-dummy, most contracts could be defeated (by perfect defense). Only a naïve or extremely weak declarer is not going to bid aggressively, on the premise of taking proper advantage of the greater difficulty of defending.

-
If I understand you correctly, there is a theoretical frequency distribution, to which actual frequencies ought to converge, based on scoring rules. And players' abilities can be measured by how their performance stacks up against the theoretical frequencies. – Tom Au Nov 14 '13 at 0:23
@TomAu: Yes; it is called the scoring table. The nature of bridge is that there is hidden information, and players must make informed decisions based on their best estimate of that hidden information. Better players will set an above average number of contracts declared by weaker players, and make an above average number of contracts against those same weaker players. This will both skew and counter-skew the statistics, back to roughly the same as for equal quality opponents. ... – Forget I was ever here Nov 14 '13 at 5:24
To maximize advantage, both weaker and stronger players will adjust their bidding tendencies, with stronger players becoming more aggressive and weaker players less so. Any that do not make such adjustments, or over-adjust make themselves weaker by definition to accomplish the balance. @TomAu: Really, this is very elementary Game Theory; you should look up some references. – Forget I was ever here Nov 14 '13 at 5:27