[inquiry]

There is a lot of disagreement over rather to open 1NT or 1M with 5332 hand patterns. Some always open 1NT, some 1M, some pick and choose, using different criteria.

I performed a very simple BRidgeBRowser Study to see 1) the frequency of 1NT versus 1M opening bid, and 2) If the results favor one method over the other

For this study, I limited the DEALER to 15-16 hcp, 5332 hand pattern, and either five spades or five hearts. The five card major had to be headed by QJ or better (Kxxxx is considered "better"). This last requirement is to avoid anyone treating xxxxx or Jxxxx or Qxxxx as a four card suit.

I also used the two largest online BRidgeBRowser DATABASES (23 million and 16 million hands) and the two largest BBO DATABASE (~6 million hands each on average), meaning I examined 52 million potential auctions. There were a total of 171,195 deals where the dealler matched the precise requirements in this study and opened either 1M or 1NT (1C, pass, and other bids not considered).

I have averaged the results at imps and mp, and normalized the frequency for these bids. Also the large BBO databases are from the main room, so that MP results are under-represented, accounting for onlly about 1.5% of the hands... in okb, mp was 50.15% of played hands).

First an obsrevation. OKB players open 1NT nearly twice as often as BBO players with this hand pattern, draw whatever conclusion you will about that observation (1NT instead of 1H was opened 29.2 % of the time in OKB, but only 16.0 % of the time in BBO. A similar trend was observed with 1NT versus 1S opening bid (15.3% on BBO, 23.5% on OKB). However, while BBO players opened 1NT with 5H or 5S at about the same rate, OKB players choose to open 1NT much more frequenty with hearts than with spades (the total number of hands matching the requriement for spades and for spades in OKB was essentially identical (61,078 for hearts, 60,939 for spades).

It should be also noted, that at imps, where the BBO sample was large the imps for 1M opening was much closer to 0 than for OKB 1M opening. I have a theory about this. Using bridgebrowser, the "normal" opening bid (where pretty much everyone agrees) generally averages to 0.0 imp. In fact, if you just look at all hands (no selection on shape, hcp, etc) you will find that the average is always 0.00 imps (or a few 100th's off that). With a smaller frequency of divergent bids, the average will always move back towards 0.00. So with fewer choosing to open 1NT, there is a greater chance that 1M opening will lead to "average" result over thousands of hands. The same move back towards "average" can be observed for the 1S opening bid at OKB, where a smaller percentage chose 1NT compared to 1NT.

For the record, here are the statistics...

1) Overall (lumping OKB and BBO data together)
Opening 1♥
-0.145 imps, 48.89%MP, versus for 1NT +0.386 imp and 54.07%

Opening 1♠
-0.106 imps, 49.28% MP, versus for 1NT +0.382 imp and 53.26%

2) OKB versus BBO averages

1H versus 1NT (imps)
OKB -0.209 versus +0.415
BBO -0.050 versus +0.266

1H versus 1NT (MP)
OKB 48.9% versus 53.5%
BBO 47.7% versus 56.5%

1S versus 1NT (imps)
OKB -0.14 versus +0.38
BBO -0.05 versus +0.40

1S versus 1NT (MP)
OKB 49.3% versus 52.9%
BBO 49.3% versus 56.5%

This also doesn't predict rather opening 1NT or 1M in second or third seat will offer different results. For a prelimianry test, I examined hands where third hand matched the requirments for this study, and the dealer and 2nd chair had passed before it was time for the third chair to open. After Pass-Pass-1H compared to Pass-Pass-1NT the results from one OKB database (only one looked at) were similar to first chair opening (1H was -0.34 imps and 49.14 %MP, while 1NT opening was 0.56 imps, and 52.29% MP)

To showthe consitency of this data, lets compare the results for 1S for the two large OKB databases (23 million and 16 million hands).

1S opening was -0.14 imps in both databases (25741 matching hands in large data base opened 1S, 18425 opened 1S in the "smaller" one).

1NT opening (as opposed to 1S) was 52.85 (7036 openings) and 52.96 (3936 openings) in these two database when holding 5 spades

The question becomes, what other metrics can be applied to see if some other feature is useful. Things like vul conditions, suit quality, total controls, stregth of the doubleton (regardless of suit it is in), etc. and the rebids after opening 1H or 1S (how does a 2NT rebid fair -- on average -- compared to a raise a rebid of openned suit, etc). Bear in mind that as you add limits, for instance, opener to a doubleton in the other major, the number of matching hands will decrease dramatically (forcing doubleton in other major, will reduce hands by 2/3 rds, and requiring doubleton in other major with Qx or better will reduce it further). It is possibile require opener to have 15-16 and this pattern regardless of seat, but the search on line takes a lot longer if you can not restrict to a specific seat. On the other hand, you will find nearly 4 times as many hand from such a search.

Anyway, a little food for thought....

1) Why is OKB 1NT higher frequency than BBO 1NT with this pattern?
2) What factors might explain the better results with 1NT versus 1M, possible explainations,
---> opening 1NT occurs more frequenty among strong players than weak players, so these results reflect the pool of abilities (on average) that choose these methods
---> opening 1NT allows more precise bidding (less over bidding, less underbidding) by limiting openers hand than opening 1M and then finding a suitable rebid
----> other?
3) would a study of 3NT contract versus 4M where opener has a 5-3 major fit that is missed show that on such hands, opening 1NT was a detriment but show larger gains on other hands where 5-3 fit does not exist?
4) After looking at 52 million potential hands, there is still not enough data to suggest the difference between these results are real. More hands need to be examined (there is more than 200 million hands in BRidgeBRowser database). But remember, of the 52 million hands, we threw out all but those that matched the requirements in the dealer seat, so this reduces the number studied from 52 million by a factor of 4. The advantage of looking at dealer is there is no spurious results due to bids in other seats before the hand being studied has a chance to bid. For instance, if you force pass-pass-to opener, tables where pass-pass does not occur can affect the outcome (the imps or the MP).

[hrothgar]

inquiry, on Aug 8 2006, 06:58 PM, said:

4) After looking at 52 million potential hands, there is still not enough data to suggest the difference between these results are real. More hands need to be examined (there is more than 200 million hands in BRidgeBRowser database). But remember, of the 52 million hands, we threw out all but those that matched the requirements in the dealer seat, so this reduces the number studied from 52 million by a factor of 4. The advantage of looking at dealer is there is no spurious results due to bids in other seats before the hand being studied has a chance to bid. For instance, if you force pass-pass-to opener, tables where pass-pass does not occur can affect the outcome (the imps or the MP).

From the looks of things, you've based your study on a sample of 171,195 hands.

This is a very large sample. Most folks doing social science research would give their eyeteeth for this many data points. I respectfully suggest that if you can't reach an accurate conclusion based on this type of sample size, it probably means that your asking the wrong question...

If you do plan to examine a larger sample, I suggest that you familiarize yourself with a concept known as "asymptotic normality". This is a pretentious way of saying that there are diminishing returns from increasing the size of your sample. If you double your sample size from 5 observations to 10, you should expect an enormous improvement in accuracy. If you double the size of the sample once again, from 10 to 20, you'll still get a lot of bang for your buck... However, once your sample size is in the hundreds of thousands increasing the sample size probably isn't going to have an significant impact on the accuracy of your study...

[mike777]

Thanks for the info.

Would be interested in seeing the results from opening strong (14-16 or 15-17)1nt on 5332 hands with xx in the doubleton compared to 5332 hands with at least jx in the doubleton.

[inquiry]

hrothgar, on Aug 8 2006, 11:37 AM, said:

inquiry, on Aug 8 2006, 06:58 PM, said:

4) After looking at 52 million potential hands, there is still not enough data to suggest the difference between these results are real. More hands need to be examined (there is more than 200 million hands in BRidgeBRowser database). But remember, of the 52 million hands, we threw out all but those that matched the requirements in the dealer seat, so this reduces the number studied from 52 million by a factor of 4. The advantage of looking at dealer is there is no spurious results due to bids in other seats before the hand being studied has a chance to bid. For instance, if you force pass-pass-to opener, tables where pass-pass does not occur can affect the outcome (the imps or the MP).

From the looks of things, you've based your study on a sample of 171,195 hands.

This is a very large sample. Most folks doing social science research would give their eyeteeth for this many data points. I respectfully suggest that if you can't reach an accurate conclusion based on this type of sample size, it probably means that your asking the wrong question...

If you do plan to examine a larger sample, I suggest that you familiarize yourself with a concept known as "asymptotic normality". This is a pretentious way of saying that there are diminishing returns from increasing the size of your sample. If you double your sample size from 5 observations to 10, you should expect an enormous improvement in accuracy. If you double the size of the sample once again, from 10 to 20, you'll still get a lot of bang for your buck... However, once your sample size is in the hundreds of thousands increasing the sample size probably isn't going to have an significant impact on the accuracy of your study...

Oh, I think the study is quite adequate as it is...for what it measured.

the 170K "hands" are not unique deals of course. The BBO hands are main room, so presumably the total hands there divided by something close to 16 willl give you the total (ignorie 1H or 1D transfer oopenings and 1C precision type). The OKB hands are from larger events, often more than 50. But since the auction diverge I don't worry too much about it.

Even lookng at the very small BBO samples, the results are reproducible. But as we alll know, not all 5332 hands with 15-16 hcp are created equal. It is what other features might be useful to look at that interest me.

[inquiry]

For those familar with DATABASEs, BRidgeBRowser has some indexs you can search on very quickly, other searches have to be by bruite force. An indexed search on 23 million records, even on line, is very quick. For instance, the search by position (dealer, 2nd seat, etc) is indexed to hcp, team hcp, shape, suit legnth (any of the four suits) and quality. I found all the hands fitting the requirements for the first seach in this thread in about 5 minutes or less (per database search).

To do brute force searching, well that is several order of magnitudes slower. For istance, I took the small BBO database, and searched jsut fro any hand that has 15-16 hcp, five card major, 5332 distribution (no regard to seat, just has to open). This takes hours (of course, can do it in background). The reason being this is not an index'ed search. The next generation of BRidgeBRowser will allow you to store intermediate searches, so I hope to be able to do four fast searches based upon each seat postition, combind them, then do the brute force just on that subset. Other values are also indexed, like players names. Thus, finding all hands played by inquiry or even all hand which inquiry defended, or all ahnds inquiry played against pclayton, is extremely quick.

Anyway, I looked at every opening bid in one of the bbo databases (main room from Sept 25 to Jan 1, 2005) that had 5H, 5332 distribituon and 15-16 hcp. There were 29079 of these. The average result for opening 1H was -0.06 imps, and 47.95% (only 352 of these 29 thousand hands were played at matchpoints in the main room). These numbers remain consistant with the just the dealer alone solution.

I looked at some of the responders bids. I thought 1H-2H would lead to good results (something not possible perhaps after 1NT opening bid). Turns out, 1H-2H was very bad. There were 5131 1H-P-2H auctions. The average result was -0.32 imps. The only worse auctions as far as average result were 1H-P-2S (that average -0.75), and 1H-P-3S (which averaged -3.32), and 1H-4bids (other than 4H and 4NT) which were bad as well.

I have been running this test for several hours now, not sure when I will get the 1NT opening bid results completed. It is calcuating them now...

[1eyedjack]

Reminds me of the time I programmed my (then new) Texas Instruments TI59 calculator to work out all of the positive integers that were equal to the 4th power of their constituent digits. Brute force iteration one integer at a time, left it running for days, having to restart it every time it found one. Ah! the good ol' days. (Sorry - been on the vino)

[keylime]

I'd be interested to see how 1M-2M-4M compares to 1NT-3NT on the hands. The eternal debate continues.

[inquiry]

1eyedjack, on Aug 8 2006, 02:19 PM, said:

Reminds me of the time I programmed my (then new) Texas Instruments TI59 calculator to work out all of the positive integers that were equal to the 4th power of their constituent digits. Brute force iteration one integer at a time, left it running for days, having to restart it every time it found one. Ah! the good ol' days. (Sorry - been on the vino)

Well actually, doing BRidgeBRowser by brute force is horrible choice. That is why the need for intermediate saving of hands and then brute force the much smaller subset is important. I will sy this.. 1NT- Pass-Pass leads to very good result when compared to opening 1H... according to the data.... other auctions still coming in....

[1eyedjack]

keylime, on Aug 8 2006, 08:23 PM, said:

I'd be interested to see how 1M-2M-4M compares to 1NT-3NT on the hands. The eternal debate continues.

There is no excuse for ending in the wrong game in an uncontested auction, whichever opener you choose (of those under debate in this thread). If a disparity emerges from a statistical analysis it would only confirm a prevalence of inferior methods.

[inquiry]

keylime, on Aug 8 2006, 02:23 PM, said:

I'd be interested to see how 1M-2M-4M compares to 1NT-3NT on the hands. The eternal debate continues.

So you want to compare auctions taht went 1H-2H-4H to auctions that went 1NT-3NT, but they have to be the same hands, right? That is, we dont want all 1N-3N hands becasue on many of them the auction would not have gone 1H-2H had 1H been opened.

This is a non-trivial request as I sit here. I can find all 1N-3N hand easy enough, and 1H-2H-4H too. I can even find all 1N-3N hands where responder holds 3H (or heaven forbid, 4H;s). But I am not sure how restrict the second search to hands where the auction was 1H-2H-4H... we could decide on 3H, relatively balanced (to expalin 3NT bid), no 4 card spade suit (snce no stayman), and some point count range. Say constructive 8 to 10 or 7 to 9 or 7 to 10. And then compare the results of 1H-2H-4H auctions to 1N-3N auctions. Is that clear? Wouild that satisfy you?

In a quick test of this requirement (1st seat opener, so speed not an issue), 1H-2H where the 2H bidder has 2 or 3 Spades, 8 to 10 hcp, three to four hearts, and no singleton (five card minor ok), the average result for 2H was -0.44, but 51.87% (only 19 hands for MO, 190 for imps). 4H averaged -0.3 (a subset of the 2H biddign hands, (126 of them) and 63.68% (only 9 hands). The 1NT-3NT auctions that meet these requirements were quite poor. -0.54 imps, and 38.89% MP. There were only 2 matchpont hands, so we can safely ignroe all the mp rresults, However, it should be noted that 1NT-2NT (followed by either pass or raise to 3NT) was quite good. So good in fact that that the 3NT contracts on the whole avraged +0.58 and 59.26% (3 hands totall... so one more the bunch).

[hrothgar]

1eyedjack, on Aug 8 2006, 10:36 PM, said:

keylime, on Aug 8 2006, 08:23 PM, said:

I'd be interested to see how 1M-2M-4M compares to 1NT-3NT on the hands. The eternal debate continues.

There is no excuse for ending in the wrong game in an uncontested auction, whichever opener you choose (of those under debate in this thread). If a disparity emerges from a statistical analysis it would only confirm a prevalence of inferior methods.

Wow...

I wish I had the luxury of guarunteeing that I'd face an uncontested auction before I chose my first bid.

[HeartA]

keylime, on Aug 8 2006, 02:23 PM, said:

I'd be interested to see how 1M-2M-4M compares to 1NT-3NT on the hands. The eternal debate continues.

In my opinion, it is included in the hands Ben has studied. For the subset of 5-3 (opener has 5) major fit, 1M opener might be better.

Good job, Ben!!

[jtfanclub]

1eyedjack, on Aug 8 2006, 02:36 PM, said:

There is no excuse for ending in the wrong game in an uncontested auction, whichever opener you choose (of those under debate in this thread). If a disparity emerges from a statistical analysis it would only confirm a prevalence of inferior methods.

5332 across 4432, 8 card major suit fit, 25-28 hcp total, what IS the better contract, 3NT or 4 of the major? If I open the 5332 1 of a major we're almost sure to get to 4 in it, while if I open it 1NT we're almost sure to get to 3NT.

Enquiring minds want to know.

[1eyedjack]

jtfanclub, on Aug 8 2006, 10:05 PM, said:

1eyedjack, on Aug 8 2006, 02:36 PM, said:

There is no excuse for ending in the wrong game in an uncontested auction, whichever opener you choose (of those under debate in this thread).  If a disparity emerges from a statistical analysis it would only confirm a prevalence of inferior methods.

5332 across 4432, 8 card major suit fit, 25-28 hcp total, what IS the better contract, 3NT or 4 of the major? If I open the 5332 1 of a major we're almost sure to get to 4 in it, while if I open it 1NT we're almost sure to get to 3NT.

Enquiring minds want to know.

I expect I am missing the point, but IF there is a significant benefit of one game contract over the other, and IF one opener gets you to an inferior contract "almost surely" then that "almost certain" result arises out of inferior continuations to the particular opener. There is plenty of room between the opener and the game contract o adjust your responses to eliminate that disparity, if the will is there.

I repeat, in my opinion the benefit of one opener over the other is NOT in their respective success rates at finding the correct game in an uncontested auction. It will arise primarily because of greater accuracy in the partscore bidding and greater accuracy in contested auctions (or preempting against contested auctions).

[1eyedjack]

hrothgar, on Aug 8 2006, 09:33 PM, said:

1eyedjack, on Aug 8 2006, 10:36 PM, said:

keylime, on Aug 8 2006, 08:23 PM, said:

I'd be interested to see how 1M-2M-4M compares to 1NT-3NT on the hands. The eternal debate continues.

There is no excuse for ending in the wrong game in an uncontested auction, whichever opener you choose (of those under debate in this thread). If a disparity emerges from a statistical analysis it would only confirm a prevalence of inferior methods.

Wow...

I wish I had the luxury of guarunteeing that I'd face an uncontested auction before I chose my first bid.

Neither keylime nor I were guaranteeing an uncontested auction. We were only considering whether, OF the uncontested auctions when the combined values are sufficient for game, the choice of opener is significant to the result.

Personally, I am with you. The contested auction is likely to be the deciding issue.

[jtfanclub]

1eyedjack, on Aug 8 2006, 04:53 PM, said:

I expect I am missing the point, but IF there is a significant benefit of one game contract over the other, and IF one opener gets you to an inferior contract "almost surely" then that "almost certain" result arises out of inferior continuations to the particular opener. There is plenty of room between the opener and the game contract o adjust your responses to eliminate that disparity, if the will is there.

I repeat, in my opinion the benefit of one opener over the other is NOT in their respective success rates at finding the correct game in an uncontested auction. It will arise primarily because of greater accuracy in the partscore bidding and greater accuracy in contested auctions (or preempting against contested auctions).

My point was information given to the opponents.

If I open 1NT with 3532, and partner bids 3NT with 2344, we have told the opponents next to nothing. If I open 1♥ with 3532, partner makes a bid that shows a 10 count with 3 card support with 2344, and I take it to game, we have again told the opponents very little. On the other hand, getting to 4♥ after the 1NT opener or 3NT after the 1♥ opener is going to involve revealing a great deal of information to the opponents, not to mention giving them lots of chances for lead directing doubles and suchlike.

So, I think you're right in the 'two handed' game, but not the 'four handed', as my mentor used to say. I think the logical thing to do is to open it in such a way that you can not just get to the right contract, but the right contract exchanging as little information as possible.

[inquiry]

I ran out of time before completing the brute force study even of a small database. So I have designed the following search criteria.

1) Primary hand (seat position) has 15-16 hcp, 5332 dist, 5 H QJxxx or better
2) His partner has three hearts, and either 4333, 4432, 5332, 5431, 6321, or 6331 distribution.

In each case, the primary hand gets to open. Then I checked for first, second, third and 4th seat begin the primary hand. This allows an index searched that is much quicker than the brute force. I ran this against the 23 million database hand (earlier study placed no restriction on the responder hand, here, the only restriction is three card heart fit, and not terribly wild distribution.

Position 1 .
1H -0.13 imps (5402 hand), 48.88 MP (7391 hands)
1N +0.29 imps (2747 hands), 53.47 MP (2432 hands)

Final contracts of
4H averaged -0.30 (2105 contracts) and 44.52 MP (2409)
3NT averaged +0.21 (1254) and 56.73 (1136)

Seat 2.
1H -0.29 imps (4327 hands), 48.94 MP (6292)
1N +0.48 imps (2248), 54.03 MP (2111)

Final contracts of
4H averaged 0.00 imps (1714), 47.90 MP (2717)
3NT averaged 1.26 imps (1039), 57.78 (1180)

Seat 3.
1H -0.11 (4007), 48.78 (3895)
1NT +0.29 (1978), 54.21 (1431)

Final contract of
4H -0.14 (1237), 45.99 (1344)
3N +0.32 (670), 56.28 (670)

Seat 4,
1H -0.12 (1705), 48.49 (2243)
1NT 0.60 (1030), 55.36 (752)

Final contract of
4H -0.07 (767), 49.65 (1009)
3NT 0.94 (728), 58.81 (474)

To figure out the overall averages, you can sum the number of hands times the score for each of the four positon, and divide the total number of hands. I didn't bother, since 1NT seems a clear winner in each case even when partner has exactly 3 hearts. There is no way, from this study, to examine how the auction went, many of the 3NT contracts might have started 1NT and many of the 4H contracts might have started 1NT.

Also note, the number of hands opened 1H or 1NT decreased as the number of the seat increased. This was because of someone bidding or preempting before they got a chance to bid. Those hands are obviously exlcuded from the search criteria as opener has to be the hand with the five hearts and 15 to 16 hcp to be included in the results.

The next study will examine the hands that would start 1H-2H at tables where 1 H was opened.

[inquiry]

For this study, I added two stipulations to the last study. First, responder had to have 8 to 10 hcp. Second, responder had no more than 3 spades. The distributions were the same.

From first postion, there was only 2411 hand that matched the requirement of 8 to 10 hcp and less than 4 spades (but not a spade void) that opened 1H compared with nearly 13 thousand hands that opened 1H when the only restriction on responder was the possession of 3H's.

In this case, the 1H opening bid, itself, average -0.15 and 49.01 MP

We can see that responders responses of:
RDBL = 2.69 (10) and 56.45 (7)
DBL = 1.53 (12) and 61.07 (10)
1NT = -0.72 (107) and 48.84 (135)
2H = -0.05 (563) and 48.71 (889)
3H = -0.23 (101) and 51.03 (157)

Final contracts of
4H -0.26 (447). 46.26 (717)
3NT 1.58 (51), 56.97 (101)

As for Keylime's question, the specific auction, 1H-(any)-2H, ending in 4H occurred 587 times (1452 2H was bid). 4H earned +0.17 (218) and 43.46 (369) times. Interesting, After 1H-(any)-2H, 3NT was the final contract 46 times, +1.1 (19) and 49.04 (but only 27 times).

If I had to speculate what this, and the last study showed, it would be that 5332 hands are more suited for NT than suit play, and that 5332 is not a very strong "offensive" hand in the 5 card suit. To test this hypothesis. I did a simple study looking at 15-16 hcp, opposite the same responders hand, but giving opener 5431 distribution.

This time, opening 1H averaged 0.01 imps and 49.64. This is not surprizing, as with 5431, nearly everyone opens 1H, and if everyone opens the same bid, the average result (0.00 and 50.00%) will be achieved.

But now, 4H earned +0.46 (871) and 51.63 (1729). Responder still had the same 8 to 10 hcp and 3 card fit as above. 3NT did just as well, +0.83 (54) and 51.9 (92). Any ideas how to refine the questions asked? One thing for sure, down grade 5332 for suit contracts just as the experts tell you to do, seems like a good idea.

[kenberg]

I am often skeptical of this sort of statistical study, but in this case I find it intriguing, as long as not too much is claimed for it.

About this "you should be able to get to the correct contract, at least in an uncontested auction, whichever opening you choose" idea. Perhaps so (it's not obvious to me that it is so) but the result in the case of 1H-2H-2N-3N may not be the same as the result when the auction goes 1N-2N-3N. The opponents know less in the second auction, and this may matter. On the other hand, if the auction is 1N-2C-3H-3N they may know more. [Added: I see jtfamclub made much the same point earlier. I apologize.]

The study suggests questions, perhaps more than can be handled. In any study such as this, I am always interested in how the results stratify, if that's the right word. For example, suppose you took only hands that came from online acbl tourneys. Of course the level is not constant there, but the extremes at both ends are much less strongly represented there than in the general playing area. This may matter. Also, does the advantage to opening 1NT seem to come about through a lot of small swings of an imp or so, or is it more like five scores of minus one imp and then a score of plus seven imps? Also: Some will not open 1N with five cards in one major and two in the other, fearing they may end in the 5-2 when a 5-3 was there to be had. What's the effect of that choice?

My guess before the run would have been the results would have come out the other way. I am not ready to switch from my occasional 1N openings on five to frequent openings on five, but the statistical result is definitely interesting to me. Thanks for presenting it.

Ken

[awm]

I'm a bit suspicious of the conclusions people are drawing here. The issue is, I suspect that most beginners, looking at a five-card major, would not consider opening 1NT (in fact I have noticed that many beginners don't consider a 1NT opening with a five-card minor). So the 1NT-opening crowd automatically filters out the weakest players. If true, this would explain many of the observable issues, including:

(1) Why do more people open 1NT on okbridge? Because okbridge generally charges for their services, there are fewer casual players online there. This makes the field (on average) stronger than it is on BBO.

(2) Why does opening 1NT get better results? Because the 1NT-openers, on average, play the cards better.

Of course it's going to be hard to test this theory, but here's one simple check:

Stipulate that the 1♥ and 1NT openers both end up playing 4♥ by opener. Of course there is a slight difference in information content because the auctions are different, but I suspect this will matter a lot less when you reach 4♥ than other contracts. How do they score? If the 1NT openers are (on average) the better players, you'll see them still scoring better despite reaching the same contract from the same side.