Judging Correlation in the Mundial de Tango (more Fun with Data)

Ok, in the previous post I said that there's no agreement among the judges during the final of the Mundial de Tango (Pista) or Tango World Championship. I showed you the charts that convinced me, but I didn't properly measure and show the degree of disagreement.

This second Power BI report has a page for each year available. You can select any two individual judges and see how far they agreed with each other about how to rank the couples. So, if you think, for example, that two of the judges dance a similar style to each other, you can see* if their opinions about the finalists' quality of dance correlate with each other. (Spoiler: nope.)**

To change the year, move to the next page using the arrows at the bottom centre. If the report is too small, misbehaves, or won't fit on your screen properly, try popping it out with the diagonal arrow thing at the bottom right hand corner. You might have to scroll the selectors right and left to see all the judges.


The judges' rankings of the couples do not correlate with one another.

1.00 is a perfect correlation: each judge agrees perfectly with him-or-her self. A low correlation between two judges means they didn't agree much, and a negative correlation would mean they ranked the couples in the opposite way to each other. There are one or two cases of small negative correlations.

I'm sure all the judges' opinions on people's dancing, in various circumstances, are highly valuable - that's why they were picked to judge - but they have nothing to do with one another, and their collective decisions are therefore, to put it mildly, not much help to anyone else in distinguishing between the finalists.

One reasonable interpretation of this result is that the judges have an impossible task; all the couples in the final dance in much the same way, and there is no real difference between them that the judges could possibly agree about. It is as though you, I, and five of our mates solemnly and conscientiously gave scores to the aesthetic qualities of six eggs from the same nest.

Why are the eggs all from the same nest? Perhaps because any excellent dancer with a visually-apparent difference of style and musicality would, on the face of it, have much to lose and nothing to gain by entering this competition. But even if the dancers were different, while all good, it's not clear that would help; it might be even more meaningless to decide between them.

There may be different interpretations: go ahead and put them in the comments, and let's see if we can think of a way to tell which is right. One would be that there are real differences, but the judges don't agree about which ones are important; they are using totally individual and independent criteria. No information is published about what criteria they use.

In order to distinguish between the couples, the judges would have to agree both on what differences exist and on which ones are important. For example, because of the way the couples get to the final, one of them is usually much older and less mobile than the others. It seems to me that the judges have agreed that the differences which go with that are not important, although I don't have the couple-number data to show that; the only way to get it is to watch the video.

As for what it means, and whether it is a good thing, we began to talk about this in the comments on the previous post.

I think it is a good thing that the Mundial is not like a ballroom competition, with the rigidity and the arms-race that implies; that could be very toxic for something that wants to remain a living social dance.  I don't think that finding the best dancers out of a good bunch is what the Mundial is really for. As I said before, it makes more sense to think that its purpose is to bring a steady stream of decent young salonsters to public notice, while honouring the occasional veteran; it's a very pretty industry-promotion and heritage-publicity thingie, not a sport.

Indeed, perhaps the Mundial has a somewhat paradoxical role in protecting tango from ballroomisation. All the finalists indisputably have good looking technique, whereas there are ballroom schools teaching a genuinely ballroomised argentine tango with a totally different  technique and approach, completely clueless about the social scene. The international dance associations even include it in some of their competitions (and that, for UK readers, was what Vincent and Flavia were up to with their "Tango World Champions" thing, which I've explained elsewhere). We can fairly confidently say that nobody dancing that way would ever get to the Mundial final, at least not in the Pista category - and that is a good thing. It's good that the Mundial exists and people can discover, quite easily, that the ballroom competitions are not it. But the relationship between regular ballroom schools, various international dance organisations, and Argentine tango, is another interesting subject for further research.

It would be great to have judge-level scores from earlier rounds. I'd expect to see a lot more agreement at the lower end; if we could combine that with video, we'd be able to learn something about what criteria are really being applied. And, if so, I'd expect to find that those criteria are by their nature useless in the final. Unfortunately, that data isn't published. If you think you can obtain it, please comment.

Bottom line: there's no evidence here that there's any point in remembering who won.

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*You'll notice some straight vertical and horizontal lines in the charts. Judges rank a lot of couples equal with one another. They don't give forty different marks to forty different couples. I haven't done the calculations over the marks seperately from the rankings; I thought doing rankings would be clearer, as the judges don't work around any common average. Some judges give out marks only from a restricted set of integers, but others try to make fine distinctions. They see each couple dance three tracks. The see them in groups of ten to a dozen couples, and the couples don't all dance the same tracks - have a look at the post on Music in the Mundial for a description of the procedure, and links to video. 
** To be fair, there is one case of a nearly 0.7 correlation, which is very impressive compared with all the others, and you probably could say the two judges involved went together. I won't spoil that one, as it would be much better if you tried to predict who it would be and then looked. Maybe it's real, or maybe it just had to happen accidentally somewhere. There are also some cases of unimpressive 0.3 or 0.4 correlations looking strong against a background of zero to negative correlations. People who are personally acquainted with the judges might feel there was something to say there, but I'm sceptical that it isn't pure chance.

Judging in the Mundial Final (Fun with Data)

You would think it would be easy to download the scores for a fairly simple dance competition. There are forty-odd pairs of competitors, there are seven judges, the judges observe the competitors doing their thing, and each judge utters a score for each pair. The scores are recorded and tabulated, an average is calculated for each pair, and they are ranked accordingly. It's that simple. They don't even do a 'sporting average' - which would mean they knocked off the highest and lowest scores before calculation. Repeat yearly.

As it turned out, it's rather a pain, but the data for 2015 was published by someone who apparently knew what they were doing and could create a relatively sensible PDF table of results, so I started there. But below, you can explore results for each year from 2012, which is where we start to get half-way useful data. [Edit: I forgot to mention that I use, here, only the Tango Pista (improvised Tango de Salon) competition in the Mundial. I do not look at Tango Escenario (choreographed 'Stage Tango'). That might be a useful comparison.]

The data is not perfect; in particular there are errors in the names of couples where I had to look these up from different documents that were very poorly formatted and I didn't have time to fix all the problems. There are lots of messed-up accented characters, and some town or country names mixed in with the couple names. But relationship between couple ID number and score should always be right, and the name recognisable, where it's available at all.

It's possible that there is cleaner data somewhere else, but I decided to go entirely from the official website and do the data cleaning myself. If two people do this independently, that's no bad thing.

Before starting, I had some questions.

1. How much agreement is there between the judges about which couples are better than others?
2. If the highest and lowest scores were rejected before calculating the average, as is done in most competitions with subjective scoring, how much difference would it make to the results? 
3. Supposing there is agreement between the judges, is there anything we can observe about the couples that explains high or low scores?

Below, I've embedded a Power BI dashboard addressing these questions.

It's interactive. You can navigate between the pages using the arrows at the bottom, and select the year using buttons.  It has a page of notes, but I'm going to repeat the gist of them below. The big tables take several seconds to load. If you can't see it well, it may behave better if you make it full screen using the arrow thing at bottom right.



The data all comes from http://festivales.buenosaires.gob.ar/, but you can download my cleaned-up compilation instead (from a few minutes after posting time).

For some years, the names of the couples are not given in the final rankings, only their competition numbers. Where possible, I have looked up the names from the published scores of preliminary rounds. I assume that the couple's ID number stays the same throughout the competition. Not all couple numbers appear in the scores of preliminary rounds, perhaps because they reached the final via other rounds in other countries or other competitions. In these cases, the couple name reads "Not Provided" with the year and ID number.

In this report, as well as the official average, I also calculate what I call the "sporting average" as used in most subjectively scored competitions; that is, the average if you ignore the couple's highest and lowest score. Finally I calculate the standard deviation of the scores.

The pages are as follows:

1. Scores chart - shows the scores given by each judge in the selected year.
2. Hi/Lo chart - shows the high and low scores averages for each couple.
3. Ranks chart - shows how far the judges agreed on how to rank the couples.
4. Scores table - shows how many places each couple moves if you ignore high and low scores in calculating the average.
5. Ranks table - shows detail of how each judge ranked the couples. If they gave two couples equal scores, those couples get the same rank.
6. Competition ID - we'll come back to this below.
7. Notes, basically this information.
8. A table of all the data, not as it looks in the underlying spreadsheet, but as it looks after Power Query mashes all the years into one data set for calculations. This also shows the average score and the standard deviation calculated over the population as a whole; you can select individual years and judges.

Question 1: agreement between the judges

There is not very much consensus between the judges on either the score or the ranking of any particular couple. They make it difficult for themselves to make fine distinctions by not awarding the full range of marks. Marks are out of ten, but the lowest that appears in any of the clasificatorias (not shown in this data) is 3.75.

I see a floor in the marks for the final; in 2015 the flat lines at 7 stand out in the scatter of scores, as though the judges felt collectively that anything lower would be impolite.

The second-placed couple in 2015 has a high score of 10 and a low score equal to that of the lowest couple. The first-placed couple were not ranked first by any judge. The only couple ranked first by more than one judge was placed 9th. To find the lowest-ranked who were placed top by at least one judge, we have to go down the couple ranked 25th overall. The lowest-ranked couple with a top-three ranking from at least one judge were placed 39th of the 41 couples. Looking at the other years, 2015 does not look atypical. In 2012 and 2013, exactly one of the top five was placed first by more than one judge, and in 2014 two of them were, including the winners.

There seems, looking at the Hi-Lo charts, to be slightly more consensus at the bottom than at the top, but this could be just because of the unofficial floors (which it looks as though not every judge agrees on). When I look at the chart of rankings, rather than scores, I don't see any more agreement at the lower end than the higher end.

In the ranking table, you can de-select a particular judge or combination of judges to see how your favourite couple might have done without them.

On only two occasions from 2012 has any one of the top five couples been placed first by more than one single judge.

On the final page of the report you can look at the standard deviation in the scores awarded by individual judges. Some judges appear in more than one year, sometimes with their names formatted differently, as full names were given in only one year. If a judge has a higher standard deviation, it means they awarded a wider range of marks; presumably, they were more convinced that some couples were better than others. A lower standard deviation means they awarded similar marks to everyone. Unfortunately the judges don't seem to agree on which couples they are, or are not, so convinced about.

Question 2: Sporting Average

Because the marks are, in my view, all over the place anyway, eliminating high and low scores before calculating the average doesn't make a lot of difference to the competition overall. It does make a difference to individual couples: it would have reversed the top 2 in 2015, and the couple placed 30th would have risen 8 places. This is the largest gain in any year, and also occurred in 2014. The largest loss is 12 places in 2012, and there seem to be bigger losses than gains for individual couples generally; someone goes down by a lot and everyone they drop below gains one. This seems consistent with the observed 'marking floor'; when a judge disagrees with their peers, they apparently tend to do so by awarding a very high mark rather than by going below the general 'floor' for that year.

Question 3: Is there anything we can observe about the couples that goes with high or low scores?

There isn't, in my view, enough agreement between the judges - or enough good video - to say much about this question.

I noticed is that there was a pattern to the numbers pinned on the couples' suits; there are a lot more lower ones. Closer inspection of the source data shows that this probably has something to do with the geographical origin of the couple and their route to the final. The system of awarding numbers is not covered in the published rules, but it seems the lower numbers are given in Buenos Aires and the higher numbers further afield.

So, taking this as a proxy for where couples came from, I checked to see if it was also related to their scores, and this is shown in the final chart, "Competition ID". Answer: not really.

The line in the same chart shows the average score for each block of 10. There are more couples with lower numbers, so perhaps we'd expect their average score to end up closer to the overall average of all couples than it is; it's rather higher. But those couples are also likely to have had more serious competition in previous rounds, which should also drive their average up compared to everyone else arriving via other routes. There isn't an obvious relationship between couple number and score as such. The foreigners are fine too, there just aren't that many of them.

More precise geographical origin of the couples is at least partially given in the source data, but as it's mostly in the form of tiny flags in graphics it would be a lot more work to get it, which I haven't done.

So, basically, no, there isn't anything I can say about how to do well, based on this data. There's no couple who did so clearly well or so clearly badly that you could watch and learn.

General remarks

In my own opinion, it's rather unrealistic of me to look at the Mundial as though it were a sporting competition. If it were you were really going for an exciting sporting competition, or some sort of mechanism for identifying the best dancers, then you would probably design a rather different event. It might, for example, include challenging tests of the ability to dance well to a variety of music, including milonga and vals, on a floor more than one-third full. There might be more rounds, with the judges taking longer looks at fewer couples in each. Judging criteria would be a matter of public record, rather than rumour. And there would be a system for creating agreement between the judges over time, beyond simply agreeing that scores below 7 were impolite. What it is, rather, is a marketing exercise for the 'Tango Salon' industry, designed to honour the heritage and disseminate awareness of the music and dance, while bringing lots of young couples who dance in a certain popular, standard-ish way, to public attention and prosperity.

If you are choosing a teacher, having reached the final in the Mundial indicates that a couple dance well in a particular style and have good tango technique, at least when dancing with their competition partner - as opposed to the very different sort of technique that is used for "Argentine Tango" on Strictly Come Dancing. It is not evidence that even one judge in the final thought they were the best. They may have been, but the chances are the judges didn't know - or if they thought they knew, they certainly didn't agree - in which case, I definitely don't know, and you don't know, either. Their ranking within the final says very little, if anything at all.

This is, in my opinion, pretty much how it should be. I don't think a true sporting competition in these circumstances would necessarily be a good idea. It didn't do ballroom any good, as a social dance.

In particular, I think it's probably a good thing that the judges don't agree. Standardisation would be toxic.

I do have a couple more questions.

• Can we seperate the level of disagreement between the judges from the question of whether there is any real difference between the couples that they could possibly measure? I can compare the real data with simulated data based on having and not having a real difference, and the results are amusing, but I think I end up assuming what I set out to prove. It might be more interesting to compare the Campeonato de la Ciudad.
• Does the order in which the couples are called - in four rondas - have any relation to their scores? I do have at least partial data for this, but putting it together requires some more work.
• It would be nice to have tidy data about geographical origin, but again, it's a lot of work to peer at all the little flags in the published data and write down what they are, and it probably doesn't tell us much more than the competition ID numbers do; most of the people who are both interested in entering this competition, and competent enough to do well, are Argentinians.

Anyway, enjoy interacting with the report, and go ahead, share and comment. I'll upload the data so you can download it and do your own analysis.

Mundial Dialogue (Fun with Data)

This dialogue is an imaginary summary of at least a full day of faffing about trying to get the data together.

HEDGEHOG

Hello. I notice there is rather a lack of anything fact-based about how the Mundial actually works, the judging, and so on. I'd like to download all the published results from previous years and analyse them to see if I can say anything interesting about it.

MUNDIAL

Hello. We have a website that covers each year since 2009, and most of the results are probably there somewhere, except for 2009 when they aren't.

HEDGEHOG
Great, I can get all the files and mash up the data with Power Query.

MUNDIAL

We don't publish any individual judge scores, even for the semifinal or finals, before 2012.

HEDGEHOG

Not to worry. Four years is a good start.

MUNDIAL

Before 2012, the results are sensible tables. From 2012 onwards, the semi-finals and finals are just PDFs of pictures of the scores. We don't name the couples. For 2014 and 2015 we do name the couples, but seperately from the scores, and in different formats.

HEDGEHOG

I have access to some pretty good OCR technology, I have a great text editor, I know Regular Expressions, I have Power Query, and if it comes to that, I can put the PDF on my tablet on a book-chair and retype it all at 50wpm. I bet you named most of the couples in the classification rounds.

MUNDIAL

The links for the 2012 Final and Semifinal are broken. Those documents are just Error 404s.

HEDGEHOG

But I know exactly how these things work, and I can guess, by analogy with documents that are there,  that for the final, instead of http://www.tangobuenosaires.gov.ar/festivalymundial12/web/resources/FinalesTangoSalon.pdf

you meant http://festivalesanteriores.buenosaires.gob.ar/tango/festivalymundial12/web/resources/FinalesTangoSalon.pdf. And for the Semifinal, instead of http://festivalesanteriores.buenosaires.gob.ar/tango/festivalymundial12/web/es/Semifinal_Salon.pdf, you made a different mistake and you actually meant http://festivalesanteriores.buenosaires.gob.ar/tango/festivalymundial12/web/resources/Semifinal_Salon.pdf.

MUNDIAL

Do you think this is a good idea?

HEDGEHOG
Do you think you're going to win this?