Scouting Report?

[kenrexford]

An interesting idea has been in the back of my mind for a while, one that would be useful and fun but very labor-intensive and difficult to accomplish.

 

In many sports, statisticians keep records of every little thing having to do with the game. Football (American) is a good example. Pass completions, pass completions within 10 yards, pass completions in the red zone, 3rd down conversion rates, fourth down conversion rates, and the like. Also, teams review film from opposing teams for play calling, weaknesses, strengths, and the like.

 

It seems that it would be useful for competition and fun for spectators to have similar stats at bridge, at least for the top competitors in major events. Does anyone know of any "secret black book" with this info? I've never heard of one, but I'd be interested.

 

Actually creating one from scratch is a difficult idea. First, you'd need a list of items to include. Second, you'd need a very talented reviewer to give accurate assessments in many cases.

 

I have informally, without recording anything, reviewed entire matches to determine themes explaining wins or losses, and it was interesting. I would love to see full stats developed and maintained for some of the top players/partnerships.

[hrothgar]

I suspect that this is way too much trouble.

 

This type of approach works well for baseball because there are relatively well established statistical measures that can be used to judge player performance. Occasionally, something new comes to the forefront: For example, the book "Moneyball" documents the rise of a new set of performance measures and their impact on salary structures and trading strategies. However, my impression is that none of the underlying statistics is particularly difficult to calculate.

 

I don't think that this (necessarily) holds true for Bridge. I think that evaluating performance is MUCH more subject and, accordingly, requires much more work. Case in point: Suppose that the your partnership scored poorly on a given board: In some cases, its very easily to assign blame: Declarer might have taken a radically inferior line. However, in many cases, the fault for the result might not lie with any clear mistake that "you" perpetrated, but rather some brilliance on the part of the opponents. it takes time and effort to differentiate between these types of cases.

 

I've seen some efforts at detailed performance analysis of the type that you suggest. The Dallas Aces (famously) analyzed their hands after practices and matches and assigned "charges" for bad results. In a similar fashion, if you go back to old issues of the OLD issues of the Bridge World you'll see some attempts by the Editors to judge the performance of different members of US Bermuda Bowl teams. If you lok at these records, I think that you'll concur with my assessment that a lot of time and effort is required to produce meaningful results.

 

If you're seriously interested in this topic, you mgiht want to take a look at this page on the OzOne web site. http://www.australianbridge.com/analysis_results.php I know that the group is attempting to develop an system that can be used to evaluate performance.

[inquiry]

lol.. a scouting report doesn't have to be accurate...all one has to do is propose that in their esteemed opinion, something is a stregnth or weakness of a pair. Let's say pair XYZ can be pushed around by preempts more than other pairs, or whatever. Then the rest of can argue and say no way.

 

Take college football and recruiting going on right now. You think Scout and Rivals webpages would rate players the same. They do not. Oh a few they both rate high, but there are many huge differences. Then everyone can argue and pontificate on who is better, pointing to who ever and what ever criteria thay want to use.

[kenrexford]

My God did I just start sweating! I just thought of what could happen, here.

 

BCS!

 

Each week, we'd have some mysterious group decide which partnership/team is rank how high and then schedule a face-to-face between them for the world championship. It would be just about as dumb as the BCS polls. I hope that never happens in bridge!

 

Uh.

 

Um.

 

BCS=WBC?

[winkle]

Take a look at: http://www.cag.csail.mit.edu/~walt/lindeals/ . It contains

statistics from selected team matches in world class play. The statistics

categories are made up by me, and they are organized according to pairs. I

don't have time to explain what all the statistics mean. Below is a brief

summary.

 

The "Pair Report Card" will tell you for each pair, the average imps/board it

won or lost on different types of deals. Each deal is categorized based on the

final contracts reached at both tables. Example: if two pairs in the same

direction reach the same game contract, the deal is classified as "Game: pure

play". If one pair lands in 2S and the other one lands in 3S, the deal is

classified as "Part score: level." If one pair is declaring a part score while

his counterpart is defending a part score, the deal is "Part score: vs part."

If one pair is in game while his counterpart is not in game, the deal is "Game:

non-game." For each deal we also distinguish between the declaring and the

defending side.

 

The "Pair Category Rankings" sort the above data by imps/board.

 

The "Pair Summary" collects some very primitive data on individual pairs, which

includes: how often they declare, how often they declare in game, how often they

make the games they bid, etc.

 

The "Pair Summary for All Events, Sorted by Criteria" sort the aforementioned

data by category.

 

In general it is tricky to interpret draw valid conclusions from this data,

especially for the first set of tables. One problem is most pairs have very few

samples. The data itself is from Nikos Sarantakos' "The Vugraph Project," which

may contain bugs. The collection of data available is somewhat arbitrary.

However, there may be enough data to draw some conclusions for the Italians and

the Nickell team.

 

Some observations:

 

- How aggressive are individual pairs? Two ways you can measure that are: (1)

how often they declare, (2) how often they declare in game. If you look at

that, you'll see:

 

   - Notable pairs who like to defend: Balicki/Zmudzinski (consistent with

reputation), Fantoni/Nunes.

 

   - Duboin/Bocchi bid an insane number of games and make an insane number of

them.

 

   - Levin/Weinstein are generally conservative, but boy, they sure make what

they bid.

 

- Most experts bid games between 25% to 35% of the time. The 10% spread is

quite wide and is interesting in and of itself.

 

- Some pairs that distinguish themselves in slam decisions: Martel/Stansby,

Meckstroth/Rodwell, Lauria/Versace, Hamman/Soloway.

 

Some more specific observations about Nickell and the Italians:

 

- What are their strengths relative to their peers?

 

   - The Italians as a team absolutely crush their opponents when both tables are

in the same game contract. Don't let anyone tell you card play is not

important in world class play! If you look at the individual pairs, you'll

see that Duboin-Bocchi have extremely impressive declaring stats (even in

part scores) while Lauria-Versace have extremely impressive defending stats.

But keep in mind that in this study one cannot tell whether a swing in the

play is due to superior declarer play or superior defense.

 

   - Both Meckwell and Lauria-Versace are very well rounded and don't have any

obvious weaknesses.

 

- What are their Achilles' heels relative to their peers?

 

   - This is the most striking observation of all. In spite of all their

successes, both Duboin/Bocchi and Fantoni/Nunes are awful (relative to their

world class peers, mind you) in slam bidding decisions. On boards where

either those Italians or their counterparts are declaring in slam (but not

both), Duboin/Bocchi lose 0.93 imps per board, while Fantoni/Nunes lose 2.12

imps per board. Just think how much better the Italians would be if they

fix this.

[cherdano]

- What are their Achilles' heels relative to their peers?

 

   - This is the most striking observation of all. In spite of all their

successes, both Duboin/Bocchi and Fantoni/Nunes are awful (relative to their

world class peers, mind you) in slam bidding decisions. On boards where

either those Italians or their counterparts are declaring in slam (but not

both), Duboin/Bocchi lose 0.93 imps per board, while Fantoni/Nunes lose 2.12

imps per board. Just think how much better the Italians would be if they

fix this.

Except that your number are not even close to being statistically significant.

 

In 40 slam vs non-slam deals, you get 40 swings of at least 10 IMPs either way. If you assume two equally good pairs bidding these against each other, you have to expect a total swing of sqrt(40)*10 either way, i.e. roughly 60 IMPs. Only if you had one pair losing/winning more than 120 IMPs on 40 slam deals could you tell with some statistic certainty that they are better or worse than the average of their opponents.

 

You would need a much larger number of deals to get statistically significant numbers for specific questions like this, unfortunately.

 

Arend

[hotShot]

I think this is a very interesting subject. Very useful to find out areas where improvement seems most effective.

Does your partnership e.g. bid enough games?

Obviously if your partnership makes 100% of the games bid, your not bidding enough, if you make less than 40% you obviously bid to many.

But what is the best ratio and what is the ratio of the best?

 

I always find it useful to look at MP and Butler score of a board.

If the MP score is bad but the IMP score is small, you missed a trick and should work on declarer play or defense. if you MP score is bad and the IMP score is bad too, your bidding might be the problem.

 

@ winkle

These are some interesting parameters. Thank you for this constructive post.

 

@Arend

The number of deals may be small, but this just means that you need to use e.g. Poisson-methods to calculate the std deviation. It will be bigger and you will need to be more careful interpreting the data.

[helene_t]

I think it's a good idea. Some statistics that could be computed:

- % optimal (according to Deep Finese) leads

- % makeable contracts (after the lead) defeated

- # phantom sacrifices

- # "stolen" partscores

- # doubled contracts made

 

Of course, those statistics are potentially subject to over-interpretation but that's true for most statistics.

[hrothgar]

This is the most striking observation of all.  In spite of all their successes, both Duboin/Bocchi and Fantoni/Nunes are awful (relative to their world class peers, mind you) in slam bidding decisions.  On boards where either those Italians or their counterparts are declaring in slam (but not both), Duboin/Bocchi lose 0.93 imps per board, while Fantoni/Nunes lose 2.12 imps per board.  Just think how much better the Italians would be if they fix this.

Silly comment:

 

Did you ever consider that there is nothing to fix? Its entirely possible the the poor slam decisions that you identify by D+B and F+N are a necessary trade off for other (positive) features in the system.

 

My original training was in classical micro-economics. One of the basic concepts used in economics is "Pareto Optimality" which Wikipedia defines as follows: "Given a set of alternative allocations and a set of individuals, a movement from one allocation to another that can make at least one individual better off, without making any other individual worse off, is called a Pareto improvement or Pareto optimization. An allocation of resources is Pareto efficient or Pareto optimal when no further Pareto improvements can be made."

 

I think that its possible to conceptualize bidding systems in a similar manner. When you design a bidding system there are a lot of different tradeoff that you make. One of the most fundamental is accuracy of your constructive bidding compared to the preemptive effect of the system. There are (obviously) a lot of other trade-offs. I firmly beleive that there are a lot of really crappy bidding systems out there. (In this case, when I use the expression "crappy" I'm suggesting that its possible to make significant improvements to one part of the system without any real cost anywhere else).

 

Equally significant, I also believe that most of the top players use relatively efficient bidding systems. I find it hard to believe that F+N wouldn't have corrected such a glaring flaw in their system. (After all, F+N are going to be much more intimately aware of their results than any outsider). Instead, I expect that their poor performance in the slam zone is a necessary tradeoff for some other equally significant benefit elsewhere in the system.

[kenrexford]

I think you are being unnecessarily defensive, Hrothgar.

 

Scouting reports would, of course, be interpreted by people by their own criteria for their own reasons, often errantly. However, if you know that X Pair has made a systemic decision, for whatever reason, that results in timid slam decisions (on average going low on tight calls), then you might know better what to do against them on tight calls yourself.

 

A real-world scenario. In a teams event, I was playing against a friend's team. The eight players bounced around between teams, so everyone knew everyone. In my seat on the other team was a friend I knew to be a conspiracy theorist. I also knew that he had a strong opinion of my predispositions. I also expected that these would combine to have him do what he thought I would do, rather than for him to do what he thought he should do, and he might get wrong what he thought I would do in a specific way -- aggressiveness.

 

So, on a slam decision hand, my gut told me to not bid the slam. However, I looked down the row and thought. My friend also would think the slam was a poor choice. However, he would be blinded by thinking that I would bid the slam, even though I really would not. Not wanting a swing on the hand, therefore, I bid the slam. Later, I found out that he bid the slam "because Rexford would bid the slam." The slam failed, we both went down, but because each was protecting against the other -- him against his perception of me and me against his perception of me -- there was no swing on the board.

 

So, if Pair X is known for one view or another on tight calls, equity may justify a tweak of your style to cater to theirs if you want to avoid a swing, if maintaining equity when you are up is more critical than purely correct theory. If you are up by 10 going into the last few boards, winning by 20 instead is relatively meaningless, but losing by 1...

 

I also think you are sounding a bit zealous. No one understands the will of God. It may seem off at times, but He has some master plan that we are unaware of and must trust. No one understands the slam decisions of Pair X. They may seem off at times, but They have some master plan that we are unaware of and must trust. It might be that Pair X has a master plan, and perhaps more study by us mortals might lead us to greater understanding and appreciation, but sometimes a bad decision is just a bad decision.

 

If all systems, and all decision-making, are equally sound if created/taken by the top pairs of the world, then the World Championships is reduced to watching to see if fate favors one team over another or to see if someone trips. I believe that the top players think that system and decision-making are huge, or they would not spend the time creating hundreds of pages of system notes. Each thinks they have a better grip on theory than the others, I'm sure. The Championships let them test their prowess at judgment and their theory of system against each other.

[hrothgar]

I believe that the top players think that system and decision-making are huge, or they would not spend the time creating hundreds of pages of system notes. Each thinks they have a better grip on theory than the others, I'm sure. The Championships let them test their prowess at judgment and their theory of system against each other.

>If all systems, and all decision-making, are equally sound if created/taken

>by the top pairs of the world, then the World Championships is reduced to

>watching to see if fate favors one team over another or to see if someone trips.

 

In all seriousness, this (pretty much) summarizes my impressions about the Bermuda Bowl and other similar events.

 

1. I think that top players - the ones who have a real chance at winning the event - are pretty well matched in terms of their skill at declarer play and defense. There are obviously) some gradiations. No one would dispute that Michael Rosenberg is an incredible talented card player. Even so, the number of hands where he gets to exercise the extra edge are few and far between. Personally, I think that endurance is probably much more significant than talent. In many cases it appears that the level of play drops measurably over the course of long events. Players get worn down. As they do, they start to "trip" up.

 

2. There's an awful lot of luck involved in these events. As I've commented numerous times in the past, different hand types favor different bidding systems. If a given set of deals has an abnormally high number of 16+ HCP hands its going to hurt pairs playing strong club based systems. If a set of deals has a lot of 9 - 12 HCP hands its probably going to help the strong club pairs. People might not want to believe that this sort of luck is a factor in events, but it does occur.

 

3. Here's my last point, and probably my most important: This is incredibly complicated stuff. I already alluded to the amount of time and effort that folks like the Dallas Aces, the Bridge World, and BJ Becker spent analyzing hands trying to assign charges for different bad results. I'm not saying that this can't be done. Hell, if you enjoy this sort of thing go ahead and do it. However, I don't consider this a very cost effective way to improve one's score.

 

Moving on to the larger meta-questions about trying to evaluate different bidding systems from on high: Back when I lived in academia my course of studies focused on Game Theory and mathematical modelling. The complexity of modelling bridge bidding systems is orders of magnitude more complex than anything I saw in Economics. Anyone who wants to study bridge bidding in a rigourous manner needs to deal with some incredibly thorny issues. Here's what I consider the two ugliest issues that need to be addressed

 

A. How does the "bidding game" impact the "declarer play / defense" game. There is enormous amounts of feedback between the amount of information that gets divulged during an auction and the subsequent play of the hand.

 

B. Do bidding systems exhibit transitivity?

 

If "Precision" is better than 2/1 Game Force

 

and

 

2/1 Game Force is better than Acol

 

can we necessarily assume that

 

Precision is better than Acol?

 

(Personally, I dont think that bidding systems are transitive. Accordingly, the equilibirum for the system is going to be a mixed population of different bidding systems rather than some kind of monoculture. Worse yet, its entirely possible that you have a cyclical equilibirum)

 

Last, but not least, there are all sorts of issues associated with regulatory regimes and their impact on bidding system design. You have all sorts of weird external constraints that are warping your statistical results.

 

In short, it doesn't seem like a fruitful area to study.

[the hog]

A real-world scenario. In a teams event, I was playing against a friend's team. The eight players bounced around between teams, so everyone knew everyone. In my seat on the other team was a friend I knew to be a conspiracy theorist. I also knew that he had a strong opinion of my predispositions. I also expected that these would combine to have him do what he thought I would do, rather than for him to do what he thought he should do, and he might get wrong what he thought I would do in a specific way -- aggressiveness.

 

Ken, I enjoy reading your posts - I really do, but wtf are you talking about here?

[kenrexford]

A real-world scenario. In a teams event, I was playing against a friend's team. The eight players bounced around between teams, so everyone knew everyone. In my seat on the other team was a friend I knew to be a conspiracy theorist. I also knew that he had a strong opinion of my predispositions. I also expected that these would combine to have him do what he thought I would do, rather than for him to do what he thought he should do, and he might get wrong what he thought I would do in a specific way -- aggressiveness.

 

Ken, I enjoy reading your posts - I really do, but wtf are you talking about here?

The point, albeit perhaps buried in personal nostalgia, was that a scouting report (here, my "scouting" of my friend) is a useful tool in assessing action at the table. If you know, for instance, that Pair X will default to 3NT instead of 4♠ when the decision is close, you might zig when they zig if the match is close or zag when they zig if you are behind. In other words, 51-49 decisions might be made less on math and more on scouting expectations and needs of the match.

[bid_em_up]

2. There's an awful lot of luck involved in these events. As I've commented numerous times in the past, different hand types favor different bidding systems. If a given set of deals has an abnormally high number of 16+ HCP hands its going to hurt pairs playing strong club based systems. If a set of deals has a lot of 9 - 12 HCP hands its probably going to help the strong club pairs. People might not want to believe that this sort of luck is a factor in events, but it does occur.

I think you said this backwards (even if unintentionally). I would expect an abnormally high number of hands of 16+ hcp to HELP the strong clubbers, while the 9-12 hands will hurt them.

 

Not the other way around (as it appears you stated).

 

Likewise, an disproportionally high number of opening bids by the opponents (preemptive or otherwise) will tend to reduce the overall effectiveness of the strong clubbers as well, imo.

[hrothgar]

2.  There's an awful lot of luck involved in these events.  As I've commented numerous times in the past, different hand types favor different bidding systems.  If a given set of deals has an abnormally high number of 16+ HCP hands its going to hurt pairs playing strong club based systems.  If a set of deals has a lot of 9 - 12 HCP hands its probably going to help the strong club pairs.  People might not want to believe that this sort of luck is a factor in events, but it does occur.

I think you said this backwards (even if unintentionally). I would expect an abnormally high number of hands of 16+ hcp to HELP the strong clubbers, while the 9-12 hands will hurt them.

 

Not the other way around (as it appears you stated).

 

Likewise, an disproportionally high number of opening bids by the opponents (preemptive or otherwise) will tend to reduce the overall effectiveness of the strong clubbers as well, imo.

I don't know many good strong club players who relish the thought of lots of 1♣ during a session. Indeed, most seem to DREAD the thought. Strong club openings inevitatable draw overcalls and the strong club pair is (typically) at a significant disadvantage compared to the field who was able to start clarifying shape early on.

 

In contrast, the strong club pair has a significant advantage on 9 - 12 HCP hands where they are able to start with a descriptive and limited opening bid. The strong club pair is also better positioned on that set of hands where they chose to pass since their pass is also much more descriptive.

[Finch]

2.  There's an awful lot of luck involved in these events.  As I've commented numerous times in the past, different hand types favor different bidding systems.  If a given set of deals has an abnormally high number of 16+ HCP hands its going to hurt pairs playing strong club based systems.  If a set of deals has a lot of 9 - 12 HCP hands its probably going to help the strong club pairs.  People might not want to believe that this sort of luck is a factor in events, but it does occur.

I think you said this backwards (even if unintentionally). I would expect an abnormally high number of hands of 16+ hcp to HELP the strong clubbers, while the 9-12 hands will hurt them.

 

Not the other way around (as it appears you stated).

 

Likewise, an disproportionally high number of opening bids by the opponents (preemptive or otherwise) will tend to reduce the overall effectiveness of the strong clubbers as well, imo.

Nope, I agree with hrothgar. Overall, strong club systems gain most when they can make their limited openings, particularly limited natural openings (the 1D opener can also be a bit of a pain).

 

There are occasional big gains when they can have a long complex relay auction to the best high-level contract, but these are (I believe) rarer than the times that opposition pre-emption over the strong club hurts their auction.

[mycroft]

...although I would be tempted to limit it to 16-20 HCP hands. Once Standard bidders are getting into 2NT and 2C territory, the vulnerability to preemption of 1C is balanced by the self-preemption of the "Slamkiller" 2NT (and 2C...2NT) and the vulnerability to preemption of strong 2C.

 

When you get to describe your hand with the opening bid, you are in better shape. With a hand with spades, a bid showing spades will do better on average than a bid showing amorphous strength. It's just that a bid showing spades and a narrowly defined strength will do better on average than a bid showing spades and amorphous strength.

[Finch]

This topic started on general statistics and moved onto a 'scouting report'. Ken started talking about something rather different: the advantage of playing against players you know well.

 

I will always play better when I know my opponents well, because you know all the little bits and pieces - do they make aggressive opening leads, how bent are their 1NT openings, how often do they psyche, how conservative are their opening bids, how scientific are their auctions, how manic are they in the slam zone, what is their 3rd in hand approach, how much do they need to double a 1NT opening, should I believe their penalty doubles of a pre-empt....

 

Overall this doesn't actually improve my results, because the majority of the opponents I know well, know me just as well and it balances.

 

But certainly one advantage of a decent coach/npc is they should study prospective opponents' style. Even between sets of a match, if we are changing opponents our team will pass on anything they have learnt (how accurately do they signal, for example).

[kenrexford]

This topic started on general statistics and moved onto a 'scouting report'. Ken started talking about something rather different: the advantage of playing against players you know well.

The title of this post was "Scouting Report." I'm not sure how it "moved" from something else into this, unless we are talking theoretical physics here.

 

The idea behind a scouting report is not to gets stats for the back of bridge cards (not playing cards, but like baseball cards). Rather, it is to get to know your opposition better.

 

Thus, the whole idea is to sxout out the unknown such that you gain an "advantage" from playing against someone whom you now "know well."

 

The anecdote about the friends match was to point out how I sort-of had a "scouting report" available to me of my friend, and how this gained. Had I instead not known this person at all, but watched his bidding and play, reviewed his bizarre committee actions, and gained access to his beliefs about me, then I'd have the same information. A scouting report.

[mike777]

;) Geez I worry enough about just bidding and playing sanely out of my own hand let alone worry about the opponents but.... :D

[bid_em_up]

The anecdote about the friends match was to point out how I sort-of had a "scouting report" available to me of my friend, and how this gained. Had I instead not known this person at all, but watched his bidding and play, reviewed his bizarre committee actions, and gained access to his beliefs about me, then I'd have the same information. A scouting report.

It did not gain. It tied.

 

Had you just played bridge and not bid the slam (as you stated that your gut feeling was the slam would fail), then you would have gained.

 

<_<

[kenrexford]

The anecdote about the friends match was to point out how I sort-of had a "scouting report" available to me of my friend, and how this gained.  Had I instead not known this person at all, but watched his bidding and play, reviewed his bizarre committee actions, and gained access to his beliefs about me, then I'd have the same information.  A scouting report.

It did not gain. It tied.

 

Had you just played bridge and not bid the slam (as you stated that your gut feeling was the slam would fail), then you would have gained.

 

<_<

Sure, on THAT hand I would have "gained."

 

However, here was the problem. We won the match (and the event) by a slight margin, and I anticipated that we would win that way anyway.

 

Had I not bid the, say, 30% slam, the results would have been that 70% of the time we'd win by a large margin and 30% of the time we would lose. I hedged and ensured the win.

[cherdano]

By the way, since I made a negative comment above, I should maybe add that some of the statistics linked to by winkle above are indeed quite impressive. Lauria-Versace gain one imp on average in a deal where they are defending the same game contract as opponents at the other table. Since this is a sample of 205 deals, it's absolutely statistically significant, and quite an impressive figure in my opinion. (Of course, the fact that they usually have competent declarers as teammates will help that figure, it would be more useful to have a CrossIMP score for this in a large field.)

[Finch]

Your point shows why it's so hard to do this analysis for pairs rather than teams.

Lauria / Versace are great players... but I promise you my imps/board would look pretty good if I could score up with Bocchi & Duboin or Fantoni & Nunes!

[Finch]

- What are their Achilles' heels relative to their peers?

 

    - This is the most striking observation of all.  In spite of all their

    successes, both Duboin/Bocchi and Fantoni/Nunes are awful (relative to their

    world class peers, mind you) in slam bidding decisions.  On boards where

    either those Italians or their counterparts are declaring in slam (but not

    both), Duboin/Bocchi lose 0.93 imps per board, while Fantoni/Nunes lose 2.12

    imps per board.  Just think how much better the Italians would be if they

    fix this.

Except that your number are not even close to being statistically significant.

 

In 40 slam vs non-slam deals, you get 40 swings of at least 10 IMPs either way. If you assume two equally good pairs bidding these against each other, you have to expect a total swing of sqrt(40)*10 either way, i.e. roughly 60 IMPs. Only if you had one pair losing/winning more than 120 IMPs on 40 slam deals could you tell with some statistic certainty that they are better or worse than the average of their opponents.

 

You would need a much larger number of deals to get statistically significant numbers for specific questions like this, unfortunately.

 

Arend

I'm not sure that this isn't significant, because on the majority of "slam vs non-slam" deals it's not random whether you bid slam or not. If (and it's a big if) one pair have worse judgement in the slam zone, then they will bid the wrong ones: this total swing you expect it not random, it's a reflection on their bidding ability.

 

Let's say that

i) All potential slam hands are 100% or 60% each equally likely and each with nothing to the play.

ii) Pair A, who are too conservative, bid all the 100% slams, but not the 60% ones

iii) Pair B bid all of them

iv) The swing for slam off/game making or both making is 10 imps either way

 

In 40 potential slam deals under these conditions, you expect

20 flat boards (excluded from winkle's analysis)

12 10 imp swings to pair B

8 10 imp swings to pair A

 

or a total expected swing of only 1 imp per board

 

In fact, if you then add in the condition that F&N are more likely to make 12 tricks than their opponents on average, and more likely to take 2 tricks in defence on average, it makes things look even worse (particularly if they are over-aggressive rather than conservative in the bidding).