Archive by Author

Goal scoring probability over the course of a football match

M. J. Dixon and M. E. Robinson, "A birth process model for association football matches", The Statistician, 47(3): 523-538, 1998.How does the probability of the final score change with the relative strength of the two teams, home advantage, time elapsed, and the current score?  This publication describes what's called a "birth process" model and it […]

What I’m learning from the Soccer Pythagorean

I've had an opportunity to apply the soccer Pythagorean to various leagues and competitions, and I'm noticing some characteristics of the formula.First of all, the Pythagorean exponent does vary significantly from league to league, and perhaps from season to season in a league, but I haven't checked that out yet.  The exponent does stay between […]


I've been getting a lot of hits from Germany in the past few days.  I don't know if they're all from the same person or not, but welcome and thanks for stopping by!  I took a couple of days off after writing about my extended Pythagorean over the past week, but there are some posts […]

Pythagorean results: 2008-09 English Premier League

I've reached the final step in my effort to test my extended Pythagorean formula, using the 2008-09 English Premier League as a test case.  There was a last-minute snag in my plans, however.  I was looking over my equations one more time, and I decided to re-derive everything from the beginning, which is a good […]

Pythagorean exponents in the 2008-09 English Premier League

A couple of nights ago I presented goal distributions for all twenty teams in the 2008-09 English Premier League season, in an attempt to calculate the exponent that would be used for my expansion of the Pythagorean.  I realized after my calculation that I needed to consider the sum of the squares of both the […]

Goal distributions in the 2008-09 English Premier League

I'm using the 2008-09 English Premier League as a test case of the three-parameter Weibull distribution that is the basis of the Pythagorean formula.  Below I present the exponent values that I obtained from the least-squares estimation, as well as a few plots that show how the resulting Weibull distribution fit to the score data. […]

My 15 seconds of fame

This isn't really soccermetrics-related, but it is about me in a technical field, so I'm posting it here.As a few people know, I work as an aerospace engineer in my day job.  I'm also an active member of the American Institute of Aeronautics and Astronautics (AIAA), which is the premier professional society in my field.  […]