Sunday, 12 June 2016

Do decision factors affect penalty awards in football?

The rules of football stipulate that if a foul is committed inside a defending player’s own penalty area, a penalty kick is awarded to the attacking team. A high proportion of penalty kicks are converted to goals so penalties can be decisive, particularly in low scoring games. It is therefore especially important for referees’ decisions about penalty kicks to be accurate. However recent evidence [1] shows that these decisions are subject to subtle bias effects. A study of a large number of penalty decisions in the German Bundesliga concluded that referees tend to ‘even out’ penalty decisions between opposing teams.

The study analysed data from 12902 Bundesliga matches over 40 years, in which 3723 penalties were awarded. The results showed that more matches than than would be expected on statistical grounds involved two penalties. The second penalty in the match tended to be awarded to the team that was not awarded the first penalty, indicative of a ‘compensation bias’, a tendency for referees to balance out their decisions. A reasonable alternative explanation for the excess of second penalties is that after a successful penalty conversion the offending team goes on the attack to rectify the score, and is therefore more likely to be awarded the second penalty. But the study found that the bias to award the second penalty to the offending team only occurred when the first penalty was successfully converted rather than missed.

What could cause such a bias? Research on human perception has revealed that sensory information is generally much more ambiguous than we appreciate, so decisions about what we ‘see’ are more difficult than they might appear. We unconsciously resolve ambiguity by combining sensory data with stored knowledge in order to reach a decision about what we see [2].

Decisions made by sports officials are subject to the same limitations as other decisions in perception, so they often have to be made on the basis of partial or ambiguous sensory data. For instance, a football referee may have to decide whether a particular offence occurred just inside the penalty area or just outside it. For very close calls of this kind the visual evidence can be quite ambiguous (see [3] for an analysis of tennis line calls) so even the best referees are liable to make mistakes on occasion.

The problems of ambiguity and uncertainty are not confined to decisions about the location of a foul. Uncertainties can occur, for example, when deciding whether the defender made illegal bodily contact with the attacker. Attacking players are very skillful at manufacturing visual evidence consistent with contact (diving), and defenders are skillful at concealing evidence of contact (shirt pulls).

So penalty decisions depend on a complex process of combining uncertain sensory evidence with decision-making factors such as previous experience, rule interpretation and knowledge of the teams and players. The referee must maintain a criterion for deciding whether the evidence is sufficient to award a penalty. The criterion may well shift unconsciously during a game on the basis of, for example, which players are involved. The compensation bias found in the Bundesliga study may reflect a shift in the referee’s criterion in favour of a more lenient evidence threshold for penalties awarded to a previously offending team.

On average one penalty is awarded every 3.48 Bundesliga games. In other words there are about 0.29 penalties per game. How does this rate of penalty awards compare with major international competitions involving European teams, namely the World Cup and the Euros?

The recent history of both competitions shows some interesting trends. In World Cup competitions since 2000 there has been a decline in penalty awards from 0.28 per game in 2002 (similar to the Bundesliga) to 0.21 per game in 2014 (a 25% fall). In the Euros over the same period there has been a much more marked decline from 0.39 per game in 2000 to 0.13 in 2012 (a 66% fall). The large fall in Euro penalties suggests that referees may be more reluctant to award a penalty than they used to be; compared to the Bundesliga they award less than half the number of penalties per game. This shift could reflect the adoption of a much more strict evidence criterion for the award of a penalty in the Euro competition.

Alternative explanations are that Euro games have became ‘cleaner’, or that players are now more skilled at hiding their offences, and these changes have led to a decline in penalty awards. However the number of cautions shown in both the World Cup and the Euros does not support this interpretation: caution rates are in decline in the World Cup but not in the Euros, and 25% more yellow cards were shown during each game in the most recent Euro competition (2012) compared to the most recent World Cup (2014) despite the fact only a third as many penalties were awarded in Euro 2012 [4, 5].

It will be interesting to track the rate at which penalties are awarded in Euro 2016. Only one penalty has been awarded in the seven matches played so far (0.14 penalties per match), in line with recent Euros but below other competitions.

Reading and sources

1. Schwarz, W. (2011) Compensating tendencies in penalty kick decisions of referees in professional football: Evidence from the German Bundesliga 1963–2006, Journal of Sports Sciences, 29:5, 441-447.

2. Mather, G., Sharman, R.J. (2015) Decision-level adaptation in motion perception. Royal Society Open Science, 2 (12), 150418.

3. Mather G (2008) Perceptual uncertainty and line-call challenges in professional tennis. Proceedings of the Royal Society Series B, 275, 1645-1651.



Friday, 15 January 2016

Light bulb moments in research: Finding the switch

Light bulb moments are flashes of creative inspiration that send your research ideas off in a new direction, and generate new datasets or publications. Many people assume that creativity is the exclusive domain of artists but the best science also requires the highest levels of originality, innovation and creativity. In the Reith lectures in 2013, and in an accompanying book (“Playing to the Gallery”), the artist Grayson Perry described his experience of becoming an artist, in a talk called “I found myself in the art world”. I was struck during his talk about the parallels between his experience as an artist, and mine (very probably those of others too) as a researcher.

For the fledging researcher in science the prospect of developing a distinctive and uniquely personal profile can appear daunting, just as it is for artists. In Grayson Perry’s words:

“…that most difficult moment I think for a young artist is the moment when you leave art college after all those years of education and suddenly it’s just you and the world - unprotected, undirected.

After years of training as a research student, perhaps followed by periods as a post-doctoral researcher working under the wings of a senior investigator, many early career researchers experience the same moment Perry describes when they begin their first established post in a university and are faced with the prospect of making their way in the academic world as an independent researcher. Which research direction should you choose? How can you begin to generate new and distinctive research ideas? Here are some tips.

1. Dedication is vital
Grayson Perry says of artists:

Most of the artists that I’ve met, most of the successful artists I’ve met are very disciplined. You know they turn up on time, they put in the hours”.

Successful artists such as, for example, Pablo Picasso and Lucian Freud think about and make art all the time. They spend all day, every day in the studio. Picasso is estimated to have produced 50,000 works. Scientists are no different in terms of the need for dedication and hard work. This accords with my own experience of the successful vision scientists I have been fortunate enough to know or have worked with. They are devoted to their work; committed, focused and thorough. They put in many hours, hone their skills, expose their ideas to the harshest scrutiny, plan ahead, meet their deadlines, obsess about details.

2. Be persistent
But how do you create something truly original in your research? Is there even such a thing as originality any more, or is originality just for people with very short memories? According to the World Health Organisation there are about 250 babies born in the world every minute. I sometimes think, when a research paper I am reading triggers an idea for a new hypothesis or experiment, that there must be dozens of researchers somewhere out there in the world thinking exactly the same idea, particularly if they are reading the same paper. But then I remind myself that this rarely seems to be the case. Everyone thinks differently. Even if they are reading the same paper, sitting in the same lecture, or pondering the same research question different researchers inevitably come up with different ways of approaching the same issues. No two researcher’s experiments are ever identical. It then becomes a question of which approach is better; more original, coherent, clever, skilful, incisive.

I like this story about originality which again comes from the arts, actually from a Finnish photographer called Arno Minkkinen. It is a story which was also told by Grayson Perry about artists, but it applies equally well to science. It is called the Helsinki BusStation Theory. I’ll mostly paraphrase Minkkinen’s own words, changing things here and there to make it relevant to science:

In the bus station some two-dozen platforms are laid out in a square at the heart of the city. At the head of each platform is a sign posting the numbers of the buses that leave from that particular platform. The bus numbers might read as follows: 21, 71, 58, 33, and 19. Each bus takes the same route out of the city for a least a kilometre, stopping at bus stops at intervals along the way.
Now let’s say that each bus stop represents one year in the life of a scientist, meaning the third bus stop would represent three years of research.
Ok, so you have been working in vision science for a couple of years collecting data on the CafĂ© Wall Illusion. Call it bus #21. You present a poster on those two years of work on the illusion at the European Conference on Visual Perception and an eminent, seasoned visitor to your poster asks if you are familiar with the paper by Fraser in 1908. Fraser’s bus, 71, was on the same line as yours. Or you give a talk in London and a member of the audience suggests that you check out Lipps (1897), bus 58, and so on.
Shocked, you realize that what you have been doing for two years others have already done. So you hop off the bus, grab a cab (because life is short) and head straight back to the bus station looking for another platform. This time you are going to study a new illusion you discovered, called the Moving Wall Illusion.
You spend a year at it, with some funding from BA/Leverhulme, and produce a series of experiments that elicit the same comment when you present it: haven’t you seen the work of Gregory and Heard (1983)?
So once again, you get off the bus, grab the cab, race back and find a new platform. This goes on all your scientific life, always presenting new research, always being compared to others.
What to do?
It’s simple. Stay on the bus. Stay on the f****** bus.
Why, because if you do, in time you will begin to see a difference. The buses that move out of Helsinki stay on the same line but only for a while, maybe a kilometre or two. Then they begin to separate, each number heading off to its own unique destination. Bus 33 suddenly goes north, bus 19 southwest.
For a time maybe 21 and 71 dovetail one another but soon they split off as well, the other researchers never used your experimental techniques anyway.
It’s the separation that makes all the difference, and once you start to see that difference in your work from the work you so admire (that’s why you chose that platform after all), it’s time to look for your breakthrough.
Suddenly your work starts to get noticed. Now you are working more in your own way, making more of the difference between your work and what influenced it. Your vision takes off.

The moral of the story is that you need to be persistent and not easily put off; stay with your initial inspiration. You have to work a lot, as the previous tip about hard work indicated. You have to immerse yourself in research thinking. This can be done in many different ways and many places.

3. Go to conferences
You can avoid some of the problems described in the Helsinki Bus Station Theory by making sure that you know your field inside out, and this is one of the reasons why you need to be dedicated. By going to conferences and reading the literature you learn about the history of your research field, and will develop an awareness of important current trends and the issues which are attracting attention and debate. These issues point the way towards research ideas that have the potential to make more impact on the field.
Think of a few people in your research field who you regard as thought leaders. Their published papers, especially review papers, may identify issues which will set the research agenda (and attract funding) over the next few years. Journal papers can age quite quickly, so it is really important to go to conferences that the leading researchers attend, and be sure to attend their talks. Seek them out in poster or social sessions to ask them questions (almost all researchers love talking about their work). Leading researchers are the most reliable guides to future directions, and often sit on funding panels.

4. Go to research seminars and research group talks
Don’t pass on other opportunities to attend talks, whether internal to your institution, elsewhere in the UK, or anywhere you can find them. I am not talking about disseminating your work – that is a whole different issue – but about listening to others talking about their work.

If the talk is close to your own area of research, then it can often directly prompt new ideas for you to follow up, of course. Talks outside your area give you a chance to hone your critical thinking skills. What are the weak spots in the rationale or experimental design of the speaker’s research? Are their claims justified? Early in her career the eminent astrophysicist Jocelyn Bell-Burnell had a good strategy for listening to talks and making an impression in a male-dominated discipline. She would listen intently to the first 5-10 minutes of the talk, when speakers generally lay out the background and general assumptions behind their work. These are almost always fundamental to the research and conclusions and can be very revealing about the clarity of the speaker’s thinking, the rigour of their reasoning. Sometimes their assumptions limit the scope of the work in ways that only become clear later on, though the speaker may prefer not to draw your attention to these limitations. Jocelyn Bell-Burnell would focus her questions on the validity of those assumptions, and how they relate to the conclusions. E.g ‘If your assumption about blahblah was incorrect, would your conclusion still be valid?’ ‘How solid is the assumption?’

The questions other people ask at talks are also instructive. Did the presentation leave loose ends for an attentive listener to pick up? Did you think of them? Do they indicate a weakness in the ideas on the one hand, or lack of clarity in the presentation on the other? How did the speaker respond to them? Did they evade a question, or come clean about a problem, or deal with it convincingly?

Even of you can salvage realtively little from a talk, just going to it gives you mental space, and puts you in the mindset for thinking critically about research. As academics, none of us can spend all day everyday thinking about and doing research so we have to take advantage of every opportunity that we can to keep in the mindset.

5. Learn new techniques
Dynamic research fields are continually evolving. Creative researchers develop new techniques, or co-opt techniques from other disciplines, which open up new avenues of research and theorising. Keep an eye out for technical developments and think about how you can exploit them, preferably before other researchers latch on to them. Invest in the time needed to learn and apply the techniques, but beware of a potential pitfall. Some researchers fall back on technical tinkering as a safe harbour from the stormy waters of critical debate if you set sail with a new idea or experimental result. Techniques are useful only as instruments rather than ends in themselves.

As an example, a technical innovation worked well for me in the early part of my research career. There had been a couple of research papers in visual motion perception in the early 1970’s based on a technique in which human actors were filmed in dark conditions while wearing lights (or reflective material) positioned at their joints. All that was visible in the film was a collect of a dozen bright points flitting across a dark background. The paper reported that viewers spontaneously perceived the complex movements of the disconnected dots as meaningful human forms (examples can be viewed on my website). The work raised lots of interesting questions, and some possible explanations, but not much was done to follow it up because the creation of these videos was quite laborious before personal computers came along. I came across a technical paper from the late-1970’s which listed a computer program to simulate the displays. At the time very few researchers seemed to be using this technique but I could see that it had a lot of potential so I spent quite a bit of time translating the program code into the language I was using, got it going on my computer graphics system, and carried out some pilot work. On the back of this initial work I applied for and won a research council grant in the late 80’s and early 90’s, with post-doc, to do the research. The proposal focused on the new possibilities the technique opened up, motivated by the theoretical importance of the results. The publications based on this work are among my most cited papers.

6. What kind of ideas?
What kind of research ideas should you focus on, particularly in the context of generating ideas that lead to fundable research proposals. It’s always best to start with research that you would like to carry out, of course and try to shape the ideas into a fundable project, rather than think of a funder and try to come up with a project which fits its remit.
Funders are not going to be impressed by a proposal that just allows you to carry on what you are already doing, such as what you did in your PhD. Incremental research which follows-on from previous work, tying up loose ends (like a lot of follow-on PhD projects) is not an exciting prospect for a funder. You have to begin thinking differently. You need your work to take a quantum leap in a novel direction, in which you are clearly making an independent and valuable contribution to the field. For example:

- Collect a new data set which has a major impact on current theories.

- Develop a theoretical innovation which alters the interpretation of current data sets.

- Introduce or apply new technique which opens up many new possibilities for future experiments which challenge current theories.

Don’t be too ambitious, and try to solve everything at once. If the funding scheme allows it, you need to shape the idea into a project that requires someone else – a pre- or post-doctoral research assistant. This is really important for building your research capacity, your ability to scale up the amount of research you will be able to conduct, and it is usually by far the biggest cost element in the project. But the justification has to be clear.

Wherever possible, and this partly depends on your research field, start from a clear theoretical position and spell out the implications of your work for this theory. That was an important element of my case for the motion work in the previous tip. There is a temptation in research to fall back on data collection - when a researcher is not sure what to do next, apart from learning a new technique they may conduct another experiment just to see what happens, hoping that the new data will prompt some new ideas. This is a risky and inefficient strategy which funders do not like– if the experiment is not soundly based, it could be a waste of time and money. Reviewers are practiced at spotting poorly motivated research (they go to lots of talks, and read lots of proposals!). Of course there are situations when you need some basic empirical data as a starting point for thinking about research questions, but the motivation has to be very clear and focused.

Wednesday, 6 January 2016

Body Proportion in Giacometti's art

Alberto Giacometti is well known for his elongated sculptures of standing or walking human figures. At the recent exhibition of his portraiture at the National Portrait Gallery I noticed that the artist tended to both sculpt and paint portraits with disproportionately small heads. The text accompanying the work at the exhibition suggests that the proportions used by Giacometti reflect his attempts to be faithful to his visual experience of seeing the figures from far away. This would explain the small size of some of his sculptures, but not the  body proportions he sculpted and painted. At the exhibition it occurred to me that Giacometti may have manipulated body proportion in an artwork as a way to confound our perception of the figure’s stature, to break our perception of its size away from its physical size. 

According to the Roman architect Vitruvius, in a well-proportioned body the height of the head (from chin to crown) should occupy 1/8 or 0.125 of the total body height. Leonardo’s Vitruvian man depicts the ideal ratio of 0.125 between head and body (head-body ratio or HBR). As Albrecht Durer later recognized, real human bodies often deviate from this ideal. Much of the deviation is due to stature. Several years ago I analysed anthropometric datasets from almost 5000 NATO personnel in four countries, and found that there is a consistent relation between stature and HBR: People over 192cm (6’ 3”) tall tend to have a HBR of 0.11 or less, while people below 165cm(5’ 1”) tend to have a HBR of 0.14 or more. 

Classical sculptors may have used HBR to convey the stature of the human figure. Statues of David such as Michelangelo’s famous David in the Accademia, Florence, have a HBR over 0.14 (consistent with his small stature), whereas statues of tall figures such as the Roman bronze Hercules have a HBR of 0.11 or less. 

The drawing shows these two statues on either side of an Ancient Greek Riace Warrior, which has the ideal HBR of 0.125. The figures are drawn at relative heights that are appropriate for their HBR, though they bear no relation to the physical size of the sculptures. The statue of David stands 4.09m tall, the Riace Warrior stands at 2.0m, and the Capitoline Hercules is 2.41m tall. 

Giacometti’s “Standing Woman I” (J. Paul Getty Museum) has a very all HBR of 0.09. In “Three Men Walking II” (Metropolitan Museum of Art) the three figures have tall HBRs below 0.10.

Perceptual research which I reported in 2010 showed that it is possible to manipulate a viewer’s impression of the stature of a figure in a photograph by manipulating the figure’s HBR. 

So perhaps Giacometti’s sculptures and portraits have small heads to induce a paradoxical impression of monumental size and stature even in a physically small object. Some of Giacometti's whole figure sculptures have disproportionately large feet as well as a small head. This may heighten the paradoxical impression that one is viewing a very tall figure in which the legs are much closer to the eye that the upper body.

Further reading
Mather, G. (2010). Head – body ratio as a visual cue for stature in people and sculptural art. Perception, 39(10), 1390-1395.