Help wanted to investigate arrow-switching
A club wants to investigate arrow-switching and they have agreed that I post their request here.
The attached paper https://drive.google.com/file/d/14tMepX9aIQfwA-1aWJd6w6bTHsjqFh90/view?usp=sharing entitled 'Effects of Arrow Switching' provides analysis I carried out on 6 club sessions. My observations suggest that arrow switching is a flawed technique. You may not consider the analysis of just 6 sessions sufficient evidence. However you may previously received concerrns from other members or clubs on this issue. You could invite clubs to participate in a wider study by asking them to submit the analysis of 2 or 3 sessions in a similar fashion as I have done. The calculation of rank could be done centrally when submissions are made.
For the purposes of central analysis, returns could be standardised by
1. Sessions containing 7 to 10 tables
2. Same number of positions. 8 places in my study.
3. Format of returns as my paper.If you need to have an overall winner, perhaps the method suggested in my second paper https://drive.google.com/file/d/1NIh3dk7xQc515m2HZJ6EkGILk5wBhpLc/view?usp=sharing entitled 'Alternative to Arrow Switching' may provide a suitable and fairer alternative.
Comments
Even with a much larger sample size they would not constitute meaningful evidence.
Alan
I would certainly like to see the effect of removing a round that was NOT arrow-switched on the data. In a 12 round Mitchell (24 boards) there is 8.33% up for grabs in each round, In my experience 8.33% is going to make quite a large difference in a player's position. I am sure there is an article on the analysis of arrow-switching on maximising competition.
There is a paper on the EBU website ebu.co.uk/documents/media/bridge-movements-the-maths.pdf which deals with arrow-switching.
In order to say that arrow-switching is a "flawed technique", one needs to consider the alternatives. Arrow-switching is not intended to produce perfection, but to reduce imbalance in imperfect situations.
Imagine we have eight tables and wish to play 24 boards. Clearly a two-winner share-and-relay will do a good job of creating two ranking lists. But what if we want or need one winner? Can we run a Howell? Well not unless we are prepared to play 30 boards or curtail the movement. What if we don't have the desirable eight tables? What do we do with 11 tables - play only eight rounds and have lots of surplus boards in the movement; play only 22 boards; or play a hesitation Mitchell with 12 rounds and everyone playing all the boards? To my mind, the latter is the best, but if we are going to do this, I think there is little doubt that arrow-switches at tables other than the switch table will improve the balance of the movement.
I've had a brief look at the second paper in the original post, but if I have understood it correctly it seems pretty random to me. First of all it isn't producing a single ranking list, just splitting the title between the two top pairs. Secondly, depending on which boards happen to be chosen to be used, you will get a different result from the same set of data!
So is arrow-switching perfect? Certainly not, but I do think it is a lot less flawed than the alternatives when it comes to dealing with real-life situations. Of course it can be improved, and one thing that helps in that is to seed the field so that the NS line and the EW line are of similar strength. That's something that those who dislike arrow-switching might consider for their two-winner games too
Looking at the first paper again, I see it starts by saying "If the hypothesis is that Arrow Switching does NOT affect positions..."
Well of course that is not the hypothesis! If it didn't affect positions, there wouldn't be any point in doing it!
The other half wear full scuba diving kit.. Aqualung and flippers
At the end you can rank both halves but you can't compare them together.
If you try to get them to swap over after 150 metres you might get a fairer comparison but you can't ever claim to be truly fair.
A full Mitchell does well to rank all EW pairs and separately rank NS pairs. The NGS does well with its measure of opposition scores.
You may want a single winner but you can't get a valid result from a Mitchell. Anything less than a full Howell is a very rough approximation. Maybe all the NS were better than all the EW.
Arrow switches with Mitchell movements are not fair but they are the best you can get.
Alan
It is funny you know, I have noticed that no matter the number of tables and movement used, the better players tend to come towards the top and the poorer players come towards the bottom.
If the end game of fair movements is to gain a fair result, it seems that this is achieved with 3/4 Howells, Mitchells with arrow switches, hesitation Mitchells etc.
What seems to really be the aim, is to find a perceived fair movement.
The reality is, bridge is not fair. Is it fair that you get a bottom because the ops bid a lay down slam that the rest of the room failed to bid? Is it fair that your ops get a bottom because you bid an obvious sacrifice that others failed to notice? Or that particular hand that really suited a particular system that only one pair plays on a given night?
There still remains a lot of luck in duplicate bridge, winning with 56% one night and 3rd with 62% another; did a pair that came second by 0.03% really play worse than the winner in any meaningful way? We have all had nights when the ops always find the right contract or line of defence; we have also had nights where everyone keeps messing up, giving overtricks away, crazy sacrifices etc...
So, you cant remove luck from the game, minimising it should result in some level of consistency in the outcomes - if the best players achieve (generally) higher scores than the worst, then the 'fairness' of the system must be there at some level.
I generally find that those that moan about movements and fairness are generally reasonable players looking for excuses :) the best players get on with doing their best, the worst players know no different.
Having said this, I don't particularly like 3/4 Howells as I always seem to miss playing against the weakest partnership.
:)
Of course, in a 'perfect' 3/4 (if such existed), you will be compensated for this by having more comparisons (sitting in the same direction) against those weaker pairs. This will at least be partially true in most 3/4 Howells.
This is also why, incidentally, the 'magic' number of one round in eight applies to single-session switched Mitchells, and not (as some people think) somewhere in the region of one in three. just one round in eight means that you have more comparisons with those pairs that you haven't met, and fewer comparisons with those you have met.
Amongst the online articles on arrowswitches, there are 'proofs' (I prefer 'demonstrations') that an 8-table 8-round MItchell with just one round switched is pretty close to being perfectly balanced. The only imbalance is with the pair against which you play during the arrowswitched round. I could go on, but this is becoming less and less relevant to the OP.
Fundamentally, it is true that Switched Mitchells are not perfect, even the 8-table version! But the alternatives suggested in the OP seem particularly daft no better.
Which is why I, for one, am out of sympathy with the obsession with statistics which seems so prevalent nowadays (totally off-topic, sorry!).
In general the perceived problem with arrow switches seems to be the view that "We only play against one/two pair/s in the other direction". Basically this comes from forgetting that you compete against pairs you are not playing against. In Switched Mitchells people forget they are competing with one/two pairs in the opposite direction on every board.
I am a firm believer that as near as possible to total fairness in a single session movement is the 7-table Full Howell, which I consider fairer than a two winner Mitchell since you play everyone against whom you are competing instead of no-one. But I also believe as Martin says it makes no real difference: the better I play the more likely I am to win in any movement.
In digressing about the general 'balance' of arrow-switched movements, I didn't really give sufficient consideration to the Original Post, and in particular the alternative suggested. Having looked at it more closely, I think that I was rather polite in striking through my 'particularly daft' comment. However, it might have been appropriate to strike through 'particularly', and replace it with a stronger adjective.