Analytics and probability


I spend a good deal of my time collecting performance data and thinking about probability (link). I regret that I missed two posts from the Training Ground Guru in 2019 (link).


The posts discussed analytics activities at Liverpool FC and looked at ‘goal probability‘. One of the two articles reported on Tim Waskett’s talk in the Royal Institution Christmas Lectures (link). The subject of the Lectures was ‘Secrets and Lies: The Hidden Power of Maths’. Tim, an astrophysicist, has been a software developer and statistical researcher for Liverpool since 2012.

The Training Ground Guru post contains a transcript of Tim’s talk (link).

In a second post, Simon Austin investigates the ‘one currency’ Liverpool use to judge players (link). The Director of Research at Liverpool, Ian Graham, revealed that the club use a metric called ‘goal probability added’ to assess players. Ian has a PhD in physics from Cambridge University and joined Liverpool in 2012.

The post quotes Ian:

“We tried to put everything into one currency. We try to take whatever action a player does on a pitch – whether it’s a pass or a shot or a tackle if you’re a defender – and ask the question, ‘What was this team’s chance of scoring a goal before this action happened?’ “And then, ‘What was this team’s chance of scoring a goal after that action happened?’ And we call that ‘goal probability added.’

Ian discussed his approach to risk-reward pay-off of passes. He noted “the reward pay-off is very, very skewed in football. So it’s very easy to massage your statistics and get a high pass-completion percentage by playing very conservative passes that do nothing for your team’s chance of scoring a goal”.

Ian said of his role “my role is the data-analysis side of analysing football, which is the newer side. I mean, data analysis, because it’s new and because football is a very conservative sport, it’s something that is difficult to get across and it’s very understandable for a manager who has a hundred other things to worry about to just say, ‘You know what, I’m not interested in this.’ “

Jurgen Klopp embraced this approach. Ian noted “he understood it and appreciated it, which already puts him in the top 5% of managers”.


The two Training Guru posts provide opportunities to learn about analytics practice. I understand Tim’s choice of anonymity and the general issues Ian raises. I found their conversation about probability fascinating.

Back in 1968, Charles Reep and Bernard Benjamin (link) reported that “there is stochastic element in the number of goals arising from a particular number of shots in a match (as well as a near constant proportion over a larger series of matches)” (1968:585). The paper also makes mention of the expectation of scoring goals. Elsewhere Charles Reep referred to the position of maximum opportunity. Neil Lanham believes this approach “enables you to see the invisibles” and he talks a great deal about the ‘Near Constant Law of Chance’ (link). Another of Charles’ contacts, Richard Pollard, has looked carefully at the estimation the probability of a shot resulting in a goal with reference to the effects of distance, angle and space (2004) (link). In a 1997 paper, Richard observed “To assess the effectiveness of a team possession, a quantitative variable is developed representing the probability of a goal being scored, minus the probability of one being conceded. This variable, called the yield, can be used to evaluate both the expected outcome of a team possession originating in a given situation, as well as the actual outcome of the possession” (1997:541). Richard completed his PhD thesis at the University of the South Pacific in 1989 (link). It was titled A statistical analysis of team performance at soccer.

It intrigues me to think that Tim, Ian, Charles, Neil and Richard are connected over five decades of analysis. Each of them talks about probability and expectation and all of them use large numbers of games to share empirical data. Training Ground Guru and the papers from 1968 on raise some fundamental questions about the games we analyse and what we choose to share. We still have to address the existence of a ‘Near Constant Law of Chance’ in the game and how we are to understand technical and tactical preparation and their manifestation in game play.

Photo Credit

Liverpool F.C.’s Kirby Training Centre (The Guardian)

 A Football Pink report of the Swindon Town v Bristol Rovers game, played on Saturday, 18 March 1950.


Please enter your comment!
Please enter your name here