The Charles Reep and Bernard Benjamin Paper 50 Years On (1)

It is 50 years since a paper written by C. Reep and B. Benjamin appeared in the Journal of the Royal Statistical Society. Series A (General) Vol. 131, No. 4 (1968), pp. 581-585. The paper was titled ‘Skill and Chance in Association Football‘.

The paper was five pages in length, contained four tables and had no references to other texts.

I aim to write a number of posts to celebrate its 50th anniversary of publication. In this post, I focus on the second author B. Benjamin.

B. Benjamin is Bernard Benjamin. I have provided some biographical information about him in another post.

His presence as a co-author of the paper gave the paper substantial gravitas. It was published in a Journal of the Royal Statistical Society. Seven years after the publication of the paper, Bernard received the gold medal from the Institute of Actuaries. The presentation address was given by the President of the Institute, Gordon Bayley.

In that address it was noted that Bernard had published papers that covered medical, statistical, demographic studies, computer usage and operational research in a range of journals that included the Journal of the Institute of Actuaries, the Journal of the Royal Statistical Society, the Lancet and the British Medical Journal.

Bernard held positions as Chief Statistician in the General Register Office, Director of Statistics in the Ministry of Health, Director of Research and Intelligence of the Greater London Council and Director of Studies for Statistics at the Civil Service College. He was a President of the Institute of Actuaries, a President of the Royal Statistical Society and a Secretary-General of the International Union for Scientific Study of Population.

Bernard concluded his career as Professor of Actuarial Science at the City University, London. It was the first chair of Actuarial Science at an English University.

Bernard did write a second paper, ‘Skill and Chance in Ball Games‘, with Charles (and Richard Pollard) in 1971. He was President of the Royal Statistical Society when this second paper was published. He received the Society’s gold medal in 1986.

Photo Credit

The Queen presents the 1966 World Cup to England Captain, Bobby Moore (Daily Herald Archive, no known copyright restrictions)

Returning to Charles, Bernard … and Richard

I have returned to my Charles Reep Project this week.

I have been re-reading Charles and Bernard’s 1968 paper, Skill and Chance in Association Football.

I have been focussing on their data. This led me to a revision of the data they shared as Table 2 in 1968 as Table 1 in Charles, Richard (Pollard) and Bernard’s 1971 paper, Skill and Chance in Ball Games.

As I re-read the papers, I was thinking about how we might visualise these data now.

I have transcribed the data from the 1968 paper and the 1971 re-working of Table 2 (as Table 1 in 1971) onto this Google Sheet.

I have created a GitHub repository for these data.

The following files are available:

I am hopeful these raw data might be of interest to a range of people interested in the origins of conversations about goal scoring in association football.

On re-reading the 1968 and 1971 papers, it struck me that their methodologies and data could form the focus of a short open course in which we might explore:

  • Real-time observation
  • Notation
  • Lapsed-time observation
  • Data presentation
  • Data re-presentation
  • Visualisation
  • Impact of research on practice

It would be fascinating to link Charles’ contemporaries with present day practice … and add to our understanding of performance.

Photo Credit

Sheffield Wednesday (Sheffield History)

Burnley (Burnley FC History)

A Week With #CharlesReep


It has been quite a week on the Charles Reep project.

I found a Football Pink report of the fabled Swindon Town v Bristol Rovers game, played on Saturday, 18 March 1950, thanks to a remarkable archive maintained by Swindon-Town-FC. Charles had to wait until the 82nd minute to notate his first goal sequence. A goal that was scored by Harry Kaye, the Swindon Town left half. It was a rare event, it was Harry’s only goal of the season.

My week:

  1. I have created and updated a bibliographic resource on Google Docs.
  2. I have a Neil Lanham resource too on Google Docs.
  3. I have corresponded with Neil.
  4. I have corresponded with Ian Franks and Mike Hughes to learn about the story behind their 2005 paper on normalisation.
  5. I hope to be introduced to Richard Pollard.

One of my activities later in the week was to re-read the 1971 paper Skill and Chance in Ball Games. I had not appreciated the nature of the changes to data analysis in that paper. There are some important changes to the 1968 data set. In the introduction to the 1971 paper, its statistical provenance is attested to by mention of the Greenwood and Yule hypothesis (1920). I have not seen this reference in any other football analysis paper.

The presence of Bernard Benjamin and Richard Pollard as co-authors with Charles gives the statistical aspects of the papers particular importance. Neil Lanham consulted an eminent statistician, Dr D A East a member of staff of the Statistical Laboratory at the University of Cambridge in regard to the data in his 1993 paper.

I think it is profoundly important to acknowledge this statistical underpinning of Charles and Neil’s papers.

As I have worked my way through the archive this week, my deciphering of the published papers has led me to think much more carefully about how we disclose data and operational definitions. My approach is to share data openly to enable community access to data and discussion about a shared resource.

I can see that I will need to do much more deciphering of the papers. I need to check with Ian and Mike about their paper too. I am hopeful that we might have access to their World Cup data from 1990 and 1994.

There is one point I will need to clarify with Ian and Mike. In their paper (2005: 510), they note:

The 1990 World Cup involved 24 teams and a total of 52 matches, whereas the 1994 format was expanded to 32 teams and a corresponding total of 64 matches.

I think the move to 32 teams occurred in 1998.

It has been that kind of week with Charles.

By serendipity, I found reference to him in Ron Atkinson’s (2016) autobiography.

It was December 1954; I was fifteen, a ground-staff boy at Wolverhampton Wanderers watching Honved players walk out onto the pitch, a pitch that i and the rest of the Wolves staff had done our best to turn into a bog. The Daily Mail said it resembled the surface of a four day-old cattle show.

Wolves employed an analyst called Wing Commander Charles Reep, who argued that most goals resulted from three passes. It formed the basis of the theories that Graham Taylor was to use so successfully at Watford. Reep dominated Molineux to the extent that, if you played a square pass in your own half of the pitch, there would be trouble. If Stan Cullis saw it, he would go absolutely barmy.

Before the game, Cullis took us all into the Molineux Hotel at the top of the ground to watch a film of the Hungarians beating England 6-3 at Wembley the year before. We analysed the first goal: Hungary score almost straight from the kick-off.

 … and then I found a Pathe News recording of the game.