Skill and chance in football goal scoring

These data appeared in my in box this morning.

Their arrival took me back to Charles Reep and Bernard Benjamin’s observation fifty years ago:

an excess of shots by one team does not mean that, by chance, the other side will not get more goals and thus win the match (1968:585)

The team that managed 13 shots on goal had an ELO Rating of 4 in Asia and 37 in the World (as of 4 September 2017). The team that had 1 shot on goal had an ELO Rating of 12 in Asia and 108 in the World (as of 4 September 2017).

The game ended as a 2v1 win for the higher ELO rated team.

Charles and Bernard concluded (shortly after the 1966 World Cup):

with rare exceptions (for example, the 1966 World Cup series) it takes 10 shots to score 1 goal. (1968:585)

Prior to the 2v1 result, the higher ELO rated team had scored 14 goals in 9 games, the lower ELO rated team had scored 5 goals (conceded 22) in 9 games.

The data come from a game played at home by the higher rated ELO team.

I am hopeful that these kind of data change our language in training environments. We might stop talking about shooting practice and start conversations about goal scoring practice, rehearsal, scenarios and consequences.

Bernard Benjamin


I ‘met’ Bernard Benjamin when I read the paper on Skill and Chance he co-authored with Charles Reep in 1968.

I include his photograph here as it has been difficult to find one of Charles.

There is no author affiliation for Bernard (or Charles) in the paper. His wikipedia entry and a 2003 obituary indicate that he was working for the Greater London Council at that time as the first Director of the Intelligence Unit (“an independent fact-finding department to which to harness forward planning”).

Bernard served as a statistician in the RAF from 1943 to 1945 (Haberman, 2003). Charles had joined the RAF in 1928 and retired from the service as a Wing Commander in 1955. Perhaps their service experience connected them.

Two years after the publication of the Skill and Chance paper he became President of the Royal Statistical Society. Steven Haberman wrote of him “He was particularly adept at conveying statistical ideas in a clear manner, without recourse to jargon or indeed mathematical notation”. (2003:681)

A copy of his Presidential Address appeared in the Journal of the Royal Statistical Society in 1971. In his discussion of the role of the statistician, he observes:

The statistician can help best by increasing the amount and relevance of information that can be made available and by using his skill to analyse this information in such a way as to enable the consequences of decisions to be predicted as, far as possible, before they are irrevocably translated into action. (1971:3)

For his own satisfaction and for maximum effectiveness the statistician will want to be so articulate as to almost signpost the ultimate choice of strategy. (1971:6)

Now more than ever there is a need for efficient statistical organization, forĀ  the skill of the statistician in assessing specific information needs and for his inventiveness tackling the new measurement problems … The statistician also has the important task, on occasion, of demonstrating that the marginal improvement information stemming from a more complicated system however fashionable and status-winning it may appear, is not worth the additional cost; just as, on occasion, he may, equally, have to prove that it is. (1971:9)

The primary object of the statistical method is to render comprehensible a mass of information which would otherwise defy the normal human mental capacity. (1971:9)

Bernard died the same year as Charles, 2002. Bernard was 92, Charles 90. I am thinking that Charles’ meeting with Bernard back in the 1960s provided the rigour required for this kind of conclusion to be drawn from the analysis of Charles’ notation:

The observation that there is a stochastic element in the number of goals arising from a particular number of shots in one match (as well as a near-constant proportion over a larger series of matches) is easy for a statistician to accept; indeed he would be surprised if it were otherwise. It indicates, of course, that an excess of shots by one team does not mean that, by chance, the other side will not get more goals and thus win the match. All this is so far removed from current soccer beliefs and tactics that general acceptance of the random element has been inhibited (though one of us, C. R., has shown that a successful style of play can be built upon it). (1968:585).


Photo Credit

Bernard Benjamin (Journal of the Royal Statistical Society, 1971)

Wales versus Ireland football international at Wrexham (Library of Wales, no nown copyright)

Age Profiles of Three 2015-2016 Premier League Teams in Round 1


Nehad Makhadmeh’s research into women’s football has taken me back to look at chronological age and place in birth year discussions in football.

I am tracking the performance of three Premier League teams this season and so I thought I might take a snapshot of birth year in Round 1 games played by Arsenal, Chelsea and Manchester City.

I am using data compiled by This site allocates a notional 90 minutes for a whole game irrespective of additional time played in the first and second halves of games.

There are data for 41 players in these three teams in Round 1.

Minutes Played By Birth Year


The 1985 cohort is: Fernandinho, Debuchy, Koscieny, Kolarov, Navas and Cahill. 1988: Aguero, Matic, Willian, Costa, Ozil, and Sanchez. 1991: Hazard, Mangala, Coquelin, and Oscar.

The quartile of birth year for these players is:




The 1980 cohort has two players born in December, John Terry and Martin Demichelis. The youngest birth year cohort, 1994, has two players born in the fourth quartile too: Kurt Zouma and Raheem Sterling. Raheem was born in December.

The 1986 cohort has the most players from the first quartile of the year: Silva, Falcao and Monreal. Gary Cahill is in the 1985 cohort but was born in December.

In contrast to data for players in the 2014 World Cup (Whitney, 2014), there were many more December birth dates (8) compared to January (2) in week one of the 2015-2016 Premier League season. Players with December birth dates in addition to those mentioned above are: Cazorla, Sanchez, Bony, and Ramsey.

I hope to return to these data as the Premier season progresses.

Photo Credit

Arsenal Members’ Day 2015 (joshjdss, CC BY 2.0)