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.