For a decade now I have been involved with the maths department at the University of Stirling - from undergraduate degree to PhD to lecturing. Since 2011 the department has run a series of public lectures, aimed at engaging the wider public with maths.
It was my great honour to be given the chance to present one of this year's lectuers. Naturally, I chose to do my talk on how maths and sport interact. The full title and abstract of my talk was:
How to win at sport using maths
Until recently, most cases of maths in sport were either relatively simple (such as designing point-scoring systems) or using maths to explain how certain sporting techniques worked (such as the Fosbury flop). After the high-profile success of 'Moneyball' strategies in baseball, using mathematics to influence on-field tactics has rapidly spread across the sporting world. This talk will look at some of the latest methods that are being used, and discuss where the industry of sporting analytics can go next. For example, can we come up with a formula that will help Scotland win the World Cup (almost certainly not).
The recording was taken from microphones on the desk where I was stood - therefore the audio dips when I move around the room, particularly when I was pointing at things on the screen.
Conics & rugby
This was my favourite way of using sport to highlight mathematics, that I only recently came across in the fantastic book The Hidden Mathematics of Sport by Eastaway and Haigh (a review of which is available on this site's Reading page).
Regression to the mean
The idea that regression to the mean easily explains sporting phenomena is a relatively well-established one. I wrote about this on this site six years ago - the coin experiment I mention in the article was done in reality during my talk.
Olympic vs. Paralympic success
This is probably the part of the talk that is the most my own work, as it is drawn on my articles looking at Olympic & Paralympic success for Summer and Winter Games. The data and results from the talk is up-to-date, and I hope to publish a new article with the results in full.
(I know I made a mistake - Barcelona hosted the 1992 Olympics, not the 1996 ones - it doesn't really affect the point I make).
Game theory and penalties
The first full article on this website, and my first real foray into maths & sport - this was always going to be included in my talk. The majority of my original project, and this part of my talk, comes from my personal favourite book Why England Lose by Kuper & Szymanski, which is again available on this site's Reading page. The academic paper that provides the key statistics used come from Palacios-Huerta's paper Professionals Play Minimax.
Chapter 2 - The Moneyball revolution
Drawing on various profiles of Bill James and the dawn of sabermetrics, I briefly covered the findings and legacy of the cult of Moneyball.
Chapter 3 - Maths enters the field of play
Wing Commander Charles Reep
I relied on information from another great football analysis book The Numbers Game by Anderson & Sally for information on this controversial figure. The data used in the talk was drawn directly from his paper Skill and Chance in Association Football, whilst supplementary information came from the football tactics bible Inverting the Pyramid by Wilson.
For another explanation of expected goals, see my article from last year which focuses on the Scottish Premier League.
Chapter 4 - The future of sports analysis
The educated guesses I make in this section are slightly influenced by The Numbers Game, but more than that I hope the talk in general may have sparked some imaginations on how mathematical techniques can be used to gain an advantage in sports. Remember - if you want to write an article on maths, sports or both - then please contact me as I am always keen to host guest articles.