#Abbotsthon17: visualising patterns – Alan, boxing and Sankey

Introduction

During last Thursday’s #Abbotsthon17 conversations, we were discussing pattern recognition. Alan Swanton suggested sharing some of his boxing data to exemplify some of the ideas we were exploring.

I suggested we defer the sharing given the flow of conversation that was occurring. With Alan’s permission, I am sharing two of his slides here that I think make a very important contribution to the wider discussion of how we share data stories with audiences.

The first is a matrix of data:

The second is why I suggested we did not share at the time Alan proposed it.

I think this second visualisation, a Sankey diagram, could have taken us on a fascinating journey that might otherwise have been constrained towards the end of a long day of concentration. It is one I am keen to explore now.

Transforming Data

Alan has been working with the Irish boxing program for some time. He has been very assiduous in his collection of performance data and has been keen to share these data in ways that provide coaches with actionable insights.

I think his Sankey diagram transforms the descriptive data shared in his matrix. I am intrigued by Alan’s choice of this visualisation.

A Sankey diagram is a flow diagram in which the width of the arrows used is shown proportionally to the flow quantity. Perhaps because it is such a powerful way to visualise energy, it is a ‘natural’ way to present energy flows in a combat sport.

I wonder what you think as you compare the two images (repeated again here):

I do not have access to Alan’s original diagram. My attention in visualisation 2 (Sankey) is triggered by the Jab route in successful attack phases. I imagine this has led to very powerful conversations with coaches and athletes.

This embodies for me the role of the analyst in an informatics age: data rich actionable insights shared in an elegant way.

Henri Poincaré wrote of this kind of elegance:

What is it that gives us the feeling of elegance in a solution or a demonstration? It is the harmony of the different parts, their symmetry, and their happy adjustment; it is, in a word, all that introduces order, all that gives them unity, that enables us to obtain a clear comprehension of the whole as well as of the parts. But that is also precisely what causes it to give a large return; and in fact the more we see this whole clearly and at a single glance, the better we shall perceive the analogies with other neighboring objects, and consequently the better chance we shall have of guessing the possible generalizations. Elegance may result from the feeling of surprise caused by the unlooked-for occurrence together of objects not habitually associated. In this, again, it is fruitful, since it thus discloses relations till then unrecognized. It is also fruitful even when it only results from the contrast between the simplicity of the means and the complexity of the problem presented, for it then causes us to reflect on the reason for this contrast, and generally shows us that this reason is not chance, but is to be found in some unsuspected law. Briefly stated, the sentiment of mathematical elegance is nothing but the satisfaction due to some conformity between the solution we wish to discover and the necessities of our mind, and it is on account of this very conformity that the solution can be an instrument for us.

I do hope Alan has forgiven me for not pursuing his data analysis on Thursday. I am delighted that he has now shared his analysis with all thirty attendees at the hackathon.

I do see this as the start of a whole new conversation … that will take us from Irish boxing back to Charles Minard‘s Map of Napoleon’s Russian Campaign of 1812.

Charles Minard's Map

It is a conversation about narratives and how we transform their content into powerful messages.

Photo Credits

Olympic Women’s Boxing (Ian Glover, CC BY-NC 2.0)

Minard’s classic diagram of Napoleon‘s invasion of Russia, using the feature now named after Sankey. (No known copyright restrictions.)

Elegance, Simplicity, Beauty

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Henri Poincaré, in Science And Method (1908) asks ‘What is it that gives us the feeling of elegance in a solution or a demonstration?’

His answer:

It is the harmony of the different parts, their symmetry, and their happy adjustment; it is, in a word, all that introduces order, all that gives them unity, that enables us to obtain a clear comprehension of the whole as well as of the parts.

I was reminded of this today whilst reading a paper by Semir Zeki and his colleagues in Frontiers in Neuroscience. Their study of the experience of mathematical beauty and its neural correlates concluded that ‘the experience of mathematical beauty correlates parametrically with activity in the same part of the emotional brain, namely field A1 of the medial orbito-frontal cortex, as the experience of beauty derived from other sources.’

James Gallagher wrote about the research for BBC’s Science and Environment page. In it he noted the impact of Euler’s identity. One professor of mathematics, David Percy, said of it “At first you don’t realise the implications it’s a gradual impact, perhaps as you would with a piece of music and then suddenly it becomes amazing as you realise its full potential.”

In the Wikipedia page on Euler’s Identity, Keith Devlin is quoted “Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler’s equation reaches down into the very depths of existence.”

I have very limited mathematical intelligence but I do appreciate elegance.

Last week, I enjoyed Howard Hamilton’s review of the OptaPro Analytics Forum. He reviewed the nine projects presented at the forum and summarised the the themes that connected them:

  • The start of game models in football
  • The introduction of player similarity
  • The usefulness of subjective data
  • The appearance of statistical rigor
  • The unease of the professional football analysts

I find it invaluable to have access to this kind of synthesis.

I was thinking about Howard’s observation about statistical rigor (‘What I liked about the talks was that most of the presenters were serious about statistical rigor at some level.  That’s not to say that there were proofs, but the researchers were open and precise about the processes they used to arrive at their results.’) when I came across Martin Eastwood’s Expected Goals For All post.

Martin has been collecting xy co-cordinates for shot locations to investigate the relationship between ‘the probability of scoring a goal and how far away from the goal line the shot is taken from’. His post explores how to model this relationship. One option he shares is a Power function (‘We can do this pretty easily by taking the log of the data, fitting a linear regression against it and plotting this against our non-logged data’). Martin’s model overall gives ‘a root mean square error of 8.2 goals, which seems a pretty reasonable starting point for developing the model further’.

I liked Martin’s willingness to share his thinking openly. Martin is a data scientist with a passion for football. I found his work thanks to a link from Simon Gleave.

Every time I find new expressions of mathematical and statistical insight, I marvel at the biographical influences that enable people to apply disciplined approaches to data. By coincidence, as I was concluding this post, I received a link to Lisa Harvey’s paper, Statistical power calculations reflect our love affair with P-values and hypothesis testing: time for a fundamental change. Lisa’s paper reminded me about Will Hopkins work and his conference summaries.

Thanks to Semir Zeki and his colleagues, I now have an insight into my aesthetic sense of data and analysis. I marvel that each day I have opportunities to exercise this sense. My hope is that a fascination with elegance, simplicity and beauty will help me develop my ‘less is more’ interests in observation and analysis.

Photo Credit

Maths 55/365 (Tim Geers, CC BY-SA 2.0)