[inquiry]

Pearson points (rule of 15) says to open in 4th seat, add you hcp to your number of spades. IF this total 15, you should open. If the total is less than 15 you should pass.

In another thread, Frances has said that:

Quote

My experimental evidence is that on a marginal hand it's never right to pass a board out at matchpoints in 4th seat. I don't know exactly why, but whenever I pass a hand like that (or a strong HCP-fewer Pearson point hand) I get a bad matchpiont result.

I can't give a logical justification for this, because I think it 'ought' to be correct to pass in 4th seat on this pile of rubbish. But I'll open it anyway.

In fact, I have looked at Pearson points for some time using BridgeBrowser and have not found them to be relevant (supporting Frances’ observation above). But to answer the question do they matter, (or at least is 15 the magic number to open on) I have performed the following experiment. I used the largest online database for bridgebrowser (with more than 23 million hand plays). This is from a non-BBO site, but I choose it for two reasons. 1) Typically they have many comparisons on the same hand (often more than 50 tableS), and 2) they have as many matchpoint hands as imp hands.

I set the criteria for the dealer and next three hands as having 4 to 12 hcp, and that they must all pass (thus no forcing pass systems, and no flake accidently passing a 15 hcp hand). The fourth hand, I varied the hcp and number of spades. HCP went from 11 to 14, spades went from 0 to 3. The fourth seat hand (for these studies) never had a six card suit, and was five-five only the times I tested with a spade void (so either 0445 or 0355). Then I determined the result the player in the fourth seat would get for passing.

Let’s start with 14 hcp (and thus spade void).

Passing out the hand with these 14 Pearson points occurred to rarely to be of significance (only 4 times out of 23 million hands and out of 751 that matched the search criteria – but passing there was still a huge loser), So I looked a passing out with spade void with 13, 12, and 11 hcp (and pearson points), In each case, Passing out was a loser despite having as few as 11 pearson points. With 13 hcp and spade void, passing earned -5.09 +/- 0.72, and 34.87% (+/1 8.3%). But again, so few people passed with 13 hcp and void to be not significant. So with 12 hcp, passing was worth -1.47 (+/- 0.81) and 40.31% (+/- 3.97), only with 11 hcp and a void did we see some trend where passing was better, and even then only at matchpoints. With 11 hcp and spade void, pass earned -0.46 (+/- 0.35) at imps (did better bidding), but 50.21% (+/- 3.89%) at matchpoints. Both these numbers are not significantly different from “average”. So with 5530 and 5440 and 11 hcp, other factors beside hcp should be used in determining you opening bid (rebids? Quality of suits?).

Now lets turn our attention to hands with 13 hcp and a singleton ♠ (14 pearson points). I divided this search up into 1444 and 1(543) hand patterns. Passing with both of these 14 pearson point hands were statistically worse than taking action. With 1444 pass was worth on average -1.46 (+/- 0.38) and 28.19 (+/- 2.85). With 5431 pattern, the results were even more in the favor of bidding. The passers earned (on average) -1.94 (+/- 0.19) and 29.28% (+/- 1.14).

So with 13 points or more, ignoring pearson points seems to be clearly the winning strategy. What happens as we weaken the hand further with regards to hcp? How about 12 hcp and 2 spades (along with no six card suit)? Passing the hand out earned -1.05 imps (+/- 0.03) and 42.95 (+/- 0.32). This 12 hcp and 2 spades totaled 14 Pearson, so how about 11 hcp and 3 spades? Here we divided the hands into unbalanced (5431) and balanced (4333 and 4432) with 3 spades in each case. With unbalanced, passing again was bad, earning -0.98 imps (+/- 0.08) and 44.53% (+/- 0.68). So far the data has been consistently that opening with 14 Pearson points is better than passing. But with 4333/4432 we got a split decision. Passing at imps continued to give (on average) a poor result of -1.09 imps (+/- 0.01), but gave a better matchpoint result 52.74 (+/- 0.04).

So with the possible exception of 11 hcp and 3 spades, bidding in fourth seat with “only” 14 pearson points and “typical” distributions (0 to 3 spades, no six card suit) appears to be statistically the best strategy.

What about with 13 pearson points? I showed above that with a void, bidding with 13 and even 12 hcp was a winner. What about with other hand patterns and fewer hcp than studied above?

With a singleton spade and 12 hcp (13 pearson points), passing with 5431 patterns earned -0.94 imps ((+/- 0.13) and 38.88% (+/- 0.33); while it was a little safer to pass with 4441 pattern, getting only -0.18 (+/- 0.19) at imps, but 43.62 (+/- 1.92). Note, this matches Frances feeling that at matchpoints you want to bid with these non-descript hands, but here at imps, the number is not statistically significant from average. Since the 12 hcp hand with 5431 (12 Pearson points) was so overwhelmingly in favor of bidding over passing, I looked at 11 hcp hands with same pattern. Here again, the passers did worse than “average”, earning -0.55 imps (+/- 0.07) and 46.9% (+/- 0.82).

So there is nothing magical about 15 Pearson points, and in fact, with 14 and normal hands, it was better to bid than to pass, and indeed, opening with even 13 and 12 pearson points worked out (generally) for the best. Thus, perhaps the role for Pearson points is if you should open light with 10 or 11 hcp in 4th seat. We have the data above for opening hands with 5440 short in spades and 11 hcp was essential average. What if the short suit was not spades? Would that change the results? While passing with 5440 or 5530 short in spades and 11 hcp earned essentially “average” (not significantly different from average), passing with same hcp and distribution but holding five spades was horrible .. -1.57 imps (+/- 0.35) and 38.93 (+/- 2.11).

So if holding five spades and 11 hcp it is better to reopen while holding a void in spades and same distribution in other suits it is roughly a toss up, what does that say about the decision to reopen when holding four spades and some average distribution. This would lend itself to an extensive study (the value of a third, fourth, fifth spade) in pass out position but keeping the hand “pattern” the same. If such a study found that extra spades increases the likelihood they opponents have to outbid you by going to the next level, such a finding might support a real significant meaning to pearson points, After all, reopening with 11 hcp and 5 spades is better than reopening with 11 hcp and a spade void (as shown above), so there is a grain of truth to pearson points somewhere.

This data probably may reveal the “truth” behind pearson points. If you have an opening hand, even a marginal opening hand, the number of spades is just one indicator on whether you should open it in fourth seat. Good distribution counts more, and the data suggest that all 12 hcp, regardless of spades, should be opened. Distributional hands with 11 hcp should be opened. Perhaps if you are trying to decide to open with 10 or 11 hcp (and with 11 hcp, with balanced distribution), looking towards spades might should factor into the final decision, but clearly it should not be the over-arching factor.

[hrothgar]

I'll add the obvious comment: This type of data mining really doesn't prove very much.

Case in point, consider the following hypothetical:

Players who know about Pearson points and apply the theory of Pearson points have more experience than players who don't. Because these players declare/defend better we expect these players to achieve higher scores.

[han]

Although I agree with what Justin and Richard have said, this experiment does suggest the conclusion that Ben draws: with marginal hands the number of spades does matter, but perhaps not as much as Pearson points suggest.

It is tempting to conclude that opening somewhat aggressively in fourth seat is a good idea. However, as I have pointed out before, if you frequently open light in 4th seat then this may influence your results when you do have a sound opening. Thus, to draw a reliable conclusion one would need to check how the pairs that open light in 4th seat do on sound openings to, something that I believe is not really possible using bridgebrowser at this point.

Also any serious bridge player already knows that there is more to a hand than HCP and number of spades. I can't imagine that anybody being surprised by the conclusion that shape is as least as important as the number of HCP.

[han]

This is not because I thought that they defend so badly I will have an edge.

Yeah yeah, fake modesty. We know better.

[EricK]

Justin, as usual, makes a very valid point. If you have a very marginal opening hand, then other players at the table will also have near opening strength. If you are playing against a pair who open light, or against a pair whose third hand openings are light, then there is an increased chance that the second best hand at the table will be your partner's in second seat. This seems likely to swing the odds towards bidding.

When were Pearson Points first formulated? Was it at a time when opening bids were in general stronger so that the above argument no longer works. In that case,if there was another near opening strength hand at the table it was 2:1 against it being your partner's hand, so bidding with short spades becomes more dangerous as the opponents are now more likely to win the part score battle.

[inquiry]

Jlall, on Apr 26 2006, 12:53 PM, said:

I think you misunderstand pearson points. They are only used for marginal opening hands. 13 with a void does not qualify. Any normal opener should be opened, it is just hands like a balanced 12 with a doubleton spades, or 11 with 4 spades, or 10 with 5 spades, etc. Hands that are clear openers are opened regardless as you may well have a game.

If a beginner runs across the "rule of 15" he will find something like this:

excerpt from Fifth Chair organisation. [url=" date= said:

http://www.fifthchai...%20and%2020.pdf[/url]']Rule of 15 - in 4th seat, count your high cards, add to them irrespective of where high cards are - the number of spades in your hand. If you reach 15 open the hand. Helps to decide whether to open in 4th seat. The Encyclopedia of Bridge gives the rule of fifteen but gives no attribution. It is attributed to (the late, I believe) Don Pearson of California. The sum of hcp and spades is known in some circles as "Pearson points". Rule of 15 is in Max Hardy's books.. "Points, Schmoints" by Marty Bergen has Rules of 15 & 20, with good explanations.

The bridgeguys go as far as state on their webpage that:

The Rule of Fifteen can be used effectively, on but should be adhered to. If Fourth Seat has less than 15, after adding the high card points and the number of Spades, then Fourth Seat should pass., said:

The Rule of Fifteen can be used effectively, but should be adhered to. If Fourth Seat has less than 15, after adding the high card points and the number of Spades, then Fourth Seat should pass.

NOTE, this is their words "less than 15" don't open. And how about this from the ever improving bridgehands.com

]Typically used by the player in the fourth (passout) seat, the player counts traditional High Card Points and adds 1 point for each Spade.  If the cumulative value is 15 or greater, the player should open the hand for bidding.  Some like the thought of competing vigorously enough to use the Rule of 15 in the third seat as well.[/quote]The Bridge world even gets into the arguement, albeit more accurately than the above (making Frances view look better and better... btw).. where they say, [quote name= said:

Pearson Points. high-card points plus spade length. [Sometimes used in a guideline for whether or not to open the bidding in fourth position, especially at matchpoints: Open when you have at least 14 Pearson points.]

And a thousand times I have heard people say, "why did you open that hand, you didn't have 15 pearson points" or something similar, and BBO teachers are teaching Pearson points.

Now having shown how "Pearson points" are presented by "respectable" online sites (bridgeworld, bridgeguys, bridgehand.com, 5th chair), I will turn around and agree with you. I don't use pearson points as a general rule. Anyone who fails to open an opening hand becasue they have too few spades is making a big mistake. In fact, most 11 hcp hands with 5431 distribution is an opening bid for me (for instance) as I use ZAR points and that distibution has 13 of the needed 26 in distibutional points and I will always open them. The fallicy is that people are taught (not me, I never learn) to "OPEN with 15 Pearson points in 4th seat and to pass with 14 (or in Bridgeworld's case, open with 14).

richard said, on among other things, said:

I'll add the obvious comment: This type of data mining really doesn't prove very much.

Case in point, consider the following hypothetical:

Players who know about Pearson points and apply the theory of Pearson points have more experience than players who don't. Because these players declare/defend better we expect these players to achieve higher scores.

Let's handle Richard's hypothetical first. "Players who know about PP will be more experienced ( better)." In that case Richard, all the 14 PP hand data I showed above, the better players will be passing and getting "poor results" because in each case, it was the passed out hands where the DEALER side got the best of the result. These represented thousands of hands out of a pool of millions. We can assume at some tables the bidding didn't go p-p-p to the 4th chair. But that is real world. The bidding coming to you may or maynot be the bidding at the other tables. But we presented with a choice of passing or bidding, in these cases bidding worked out better. There was other facts that the data showed, The side that played the contract at or below 2♠ in almost everycase earned above average. The side that played the contract at 2NT or higher did worse than average. Where the big win was for bidding, was that the 4th seat side played more of the hands by far than the side that had passed twice already. Now such a statement might not apply if you were searching for the results of an opening bid where 2♥ opening showed 4-4 in the majors. Perhaps the majority of people playing such a convention are nutcases and always earn horrible results, or maybe they are bridge genius and do better with the cards they hold than I do with the same cards. But here, all we judge is to open or to pass out the hand. A very simple bridge judgement question indeed.

Also, for what it is worth, this data was mined from a database of OKBridge hands. The frequent assumption is that the average standard of bridge on OKBridge is better than BBO, but the truth is it doesn't really matter for two reasons. The first, is the good and the bad players can be in any of the four seats, and all this randomizes out. This is also true of card play as the study of millions of hands played almost average out the number of tricks winnable by double dummy (some defenders throw away tricks, some declarers throw away tricks, look at a large sample they average out).

IF you search on an opening bid using bridgebrowser, any opening bid other than say something wacky like 7NT which gets out os wack by angry people or people being cute, once you look at 10,000 hands or so (for that opening bid), the average will generally be 0 imps, and 50.00 percent matchpoints. This is because there is still potential in the hands. If you start looking at certain "restraints" on an opening bid, different trends come to light. For instance, opening 2♥ with 6♥ and 5 hcp vul versus nonvul doesn't normalize at 0 imps. This is what happens to these fourth seat opening bids. First off, three passes and foiurth seat beiing weakish 11-12, is fairly rare these days. Someone generally opens something, freeling 2 bid, weak 2, light third seat.

So back to richards comment about "this type of data mining doesn't prove much"... what this data shows is that out of the more than 200,000 (out of 23.4 million) auctions that I examined that went pass-pass-pass where the 4th seat held 14 Peason points, passing was a statistically a losing proposition. Some of these SD's are very low, but primiarily because the "n" is very high. But this data clearly shows what BridgeWorld says, that if you have 14 pearson points BID, and this can be extended to 13 and even less pearson points if the hand is unbalanced. We could ask one of the statisticians to speculate on the meaning of the differences, but the data shows that over thousands and thousands of hands, passing these is loser in the long run. Just as Frances stated her experience was, just I have felt. and now as I found buried on Bridgeworld, just as BW says (with 14 bid!! they could ahve added with 13 bid too most of the time).

This is one great thing about BridgeBrowser data. The only requirement is to select the parameters you want to search and then see what happens. IF you used the same patterns for a first seat bid (as opposed to a 4th seat bid) you get completely different results. For instance, I searched on 5431, 11 hcp, 3 spades (14 pearson's) that I searched for above, but in the first seat.

What you get is about what you expect, the hand is 3(541) with 3 spades and 11 hcp. The two choices are third seat (After three passes) or first seat, and we are just comparing the results of "pass".

In First SEAT, pass earned... -0.15 imps (+/- 0.06) and 50.58% (+/- 0.36)
In third SEAT, pass earned... -0.98 imps (+/- 0.08) and 44.53% (+/- 0.68)

So it seems opening light in fourth chair (not passing) is a better idea than opening light in first chair, but that is the point. And it is the point justin makes in his lastest post.. against people who open light in third seat, the fact that they didn't open light means partner will have slighlty more than his "share" of missing hcp (on average). BridgeBrowser can be used to test for this as well. I set the parameters to 4 to 12 hcp for 1, 2 and 3rd seat (as in original seach), and 4th chair to 11 hcp and setting the bidding up with 3 passes to 4th chair. Mathematically the missing 29 hcp will be divided 9.67 between the three seats (not 4th chair). But we all know people get "cute" in the clown seat an open light on few hcp. So the expected hcp in 3rd seat will be less than this average. In fact, the data shoiwed just this. To keep it short, I examine 34,396 hands where the auction went pass-pass-pass and the 4th seat had 11 hcp.

1st = 9.89 pts
2nd = 9.82 pts
3rd = 9.29 pts
4th = 11 hcp (fixed)

There was a marked difference in the number of hands with 12 hcp from RHO and partner as well. RHO had 12 hcp only 1050 of the nearly 35K hands, while partner had 12 hcp more than twice as often. Partner was also held 11 hcp 178% as often as RHO held 11 hcp. What isn;t clear is if this 1/2 point is significant. But this is the type of stuff that is both easy and fairly reliable with bridgebrowser.

[mike777]

I would find it interesting to see how passing hands in 4th seat with no voids, no 5-5 or greater extreme dist. and a max of 14 Pearson points works out.

That would mean passing on:
x....AKxxx...AQxx...xxx

[inquiry]

mike777, on Apr 26 2006, 04:02 PM, said:

I would find it interesting to see how passing hands in 4th seat with no voids, no 5-5 or greater extreme dist. and a max of 14 Pearson points works out.

That would mean passing on:
x....AKxxx...AQxx...xxx

That was covered in the original post in this thread, the only 5-5 I considered was with a void in spades (could be 0(454) or 0(553) as I disallowed six card suits.

[barmar]

When I learned the Rule of 15, the justification given for counting the spade suit is that the fewer spades you have, the more likely the opponents are to have that suit, so they're likely to be able to outbid you. If everyone else has passed and you have a marginal opening hand, the points are likely to be evenly distributed, and the assumption seems to be that the bidding won't get past the 2 level. Thus, whichever side has the spade suit will win the auction, and may be expected to make their contract.

The Law of Total Tricks says that with both sides having 8-card fits, it's usually right to bid 3 over 2. If they can make 2, you'll go down only 1, for a win (it's rare that they can double you).

However, if you had the opportunity to pass the hand out, the logic of taking the push because of the LOTT doesn't seem to apply. You could have avoided either minus score.

Maybe the assumption that 4th seat's spade shortness implies that the opponents usually have a spade fit is wrong. Or maybe the assumption that the opponents can make their 2♠ contract is wrong. It seems like BridgeBrowser should be able to tell us where the logic is failing.

[han]

Ben said:

Quote

Let's handle Richard's hypothetical first. "Players who know about PP will be more experienced ( better)." In that case Richard, all the 14 PP hand data I showed above, the better players will be passing and getting "poor results" because in each case, it was the passed out hands where the DEALER side got the best of the result.

Richards main point as I interpreted it was that a player who opens light in fourth seat with suitable hands may be on average a better card player than the player who still counts up to 13 HCP. I don't know if that is true, but it seems a valid arguement, and as far as I can see nothing in your post argues that this is not the case.

Ben said:

Quote

But this data clearly shows what BridgeWorld says, that if you have 14 pearson points BID, and this can be extended to 13 and even less pearson points if the hand is unbalanced.

I naively hoped that people would be more careful about using the words "clearly shows". The statistical test results you have don't show anything like that, but it maybe true that they suggest something.

[hotShot]

Ben the result of your query is basicly that if you hold 11 HCP in 4th seat, your side almost has a 21 to 19 HCP advantage. You need to score positive when you have more HCP, esp. at MP.
At 1 or 2 level 7card suits are often good enough to make the contract.

[inquiry]

hotShot, on Apr 26 2006, 04:35 PM, said:

Ben the result of your query is basicly that if you hold 11 HCP in 4th seat, your side almost has a 21 to 19 HCP advantage. You need to score positive when you have more HCP, esp. at MP.
At 1 or 2 level 7card suits are often good enough to make the contract.

Well that final little test was just proof of principle that after third hand passes he TENDS to have a weaker hand than after 2nd or 4th hand passes. The larger search (first post in thread), 4th seat had from 11 to 14 hcp. I guess the best search is unrestricted fourth seat and see how pts for 1st, 2nd and 3rd seat stack up if you wanted to askthe question how does third seat pass compare with first or second. That could be a very long search.

[hotShot]

inquiry, on Apr 26 2006, 07:26 PM, said:

Good distribution counts more, and the data suggest that all 12 hcp, regardless of spades, should be opened. Distributional hands with 11 hcp should be opened. Perhaps if you are trying to decide to open with 10 or 11 hcp (and with 11 hcp, with balanced distribution), looking towards spades might should factor into the final decision, but clearly it should not be the over-arching factor.

Indipendent of the seat you are in, if you are holding 11 HCP, the other 3 will have an average of 9 2/3 HCP.
So what difference does it make what seat you are in?
If you are in 1st seat you will find that the HCP's of the other players are much wider spread. The standard deviation would clearly show that. If you look at the average suits length , you will find that even when the averages are similar, extreme suit length will be rare if the bidding has been p - p - p.
If you are in forth seat, obviously nobody in seats 1-3 had 12 HCP, a weak 2 or some distributional opening. If nobody of the other 3 has more than 11 HCP, there can be nobody with less than 7 HCP. If opps open with 11 HCP in 3rd seat, nobody in seat 1-3 will have less than 8 HCP. When opening in first seat, the other players lower limit of HCP is 0.
Indipendent of the seat you're in:

Your HCP [space] HCP average other seats [space] [space] average combined HCP of your side
 9 [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space]10 1/3 [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space]19 1/3
10 [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] 10 [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space]20 
11 [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] 9 2/3 [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space]20 2/3
12 [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] 9 1/3 [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space]21 1/3 
13 [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] 9 [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space] [space]22 

Each player that passed in front of you, narrows the possible range around this average, cutting of weaker (more of the weaker!) and stronger hands. Additionally
If you have to decide about a 4th seat opening, you can expect to hold 20(+) HCP on your side most of the time, if you hold 10+ HCP.
The side with the majoraty of points needs to score positive, passing produces "0" which is not positive (enough).
What about a fit?
After 3 passes, the other players distribution should be sort of balanced. Possible extremes are 5332 or 4441. So bidding a 4 or 5 card suit will often produce at least a 7 card fit. Low level contract are often won, by the playing side. With little information available for the opening lead, this trick is often a gift to the declarer.

So any 5(4) card suit with 11 HCP in 4th seat, will on average lead to a 7+ card fit and will on average produce a positive result (>0).

Of cause opening the auction gives opps a chance to enter the auction too, and some times they will force you one level up or to get the defending side. If they can score positive, bad luck.
Opening ♠, preempts the 1 level (opps can't have a 1NT overcall) and reduces the likelihood of opps to enter the auction. But i don't think today this is important enough to justify the use of Pearson points.

[sfbp]

I have looked in vain for the article that I wrote on this.

However there's a reference to it in one of my more obscure web pages, and yes I confirm Ben's observations by a somewhat different (perhaps more thorough) route.

Quote

b. Playing 1 of a suit seems to be profitable most of the time, the exception being 1C at matchpoints. A related assertion which we have made is that you should always open in 4th seat holding more than your fair share (10) of HCP, and that Pearson points are simply incorrect.

from http://www.microtopi...ridge/day4.html

What I did was to pull all the boards that were passed out at least once (ie there is some perception that one should not open) and excluding accidents I think rather like Ben did. With this subset of boards, I then looked at all the possible actions in fourth seat as a function of HCP and spades.

Same conclusion, essentially

Stephen

[sfbp]

Hotshot got it in one.

BRBR shows essentially this: if you have more points than average it pays to act. The exception is 4432 or 4333 11 counts because you may get punished. The bidding structure I use makes sure that I open all 11 counts with 5 cards in any seat.

When it comes to 4th seat openings, essentially you are guessing that most of the time the first three players have 10 points or less. So if you have 11, you should open, giving your side 21 points versus 19.

Stephen

[inquiry]

I am not sure stephen's approach was more complete than mine, but it was different. HE held the hcp by the 4th seat the same, and varied the number of spades. So, for example, he compared 11 hcp with 4 spades, to 11 hcp with 3, to 11 hcp with 2, etc. So he varied pearson points based on spade legnth and determined the "advantage" or "disadvantage" of passing versus bidding.

I in effect held person points constant, but varied the HCP and showed that for 14 pearson points bidding was a clear winner, and often for 13 and 12 too. What I didn;t do was look at 5 spades and 10 hcp etc (I stopped at 11). Using different data sets and different analytical approaches, he and I reached the same conclusions including that opening in fouirth seat with 11 hcp and 3334 is not different on average from passing.

[inquiry]

Ok, so I decided to do a 15 pearson point test. For this, I choose 10 hcp, and five spades (something I haven't done) and then compare that with 10 hcp and 0 and 10 hcp and 1 spade. So the hands swing from 15 to 10/11 pearson points.

Again, I only show what happens if you pass (your "average" outcome).

10 hcp, and 5 spades (15 pearson)
2091 passed out hands, average -0.25 imps (+/- 0.05) and
2052 passed out matchpoint hands, averaging 49.15% (+/-0.39%)

10 hcp and 1 spade (11 pearson)
961 passed out hands, averaging 0.23 +/- 0.07 and 792 hands 47.53% +/- 0.49

10 hcp and 0 spades, (10 pearon)
187 passed out hands, avergint 0.27 +/- 0.25 and 129 hands 40.4% +/- 1.33

Obviously passing with 15 to 10 pearson points here are all abou the same, In fact, pass worked out "worse" at matchpoints with fewer pearson points than with more. This caused me to consider the model I am using. Is it ligitamate to only evaluate how well or poorly passing did (which is the question being asked), or do we need to evaluate how well (on average) each of the people who didn't pass did too? This is doable, but requires exporting data to excel. The point being, maybe after three passes, bidding is worse than passing on average (something I didn't examine), I just compared what passing "scored" on average.

[sfbp]

Ben I have saved for you in the place where you normally upload files for HB a file called ALLPASS.BRD (actually its zipped as ALLPASS.ZIP). You should be able to download to laptop and use as search using the maroon button,, on the 23million+ dataset

Good luck!

Stephen