Ahead of the Third Round of this season’s Emirates FA Cup – a stage that has become synonymous with results that defy logic throughout the competition’s 150-year history – The FA has today released new mathematical research that reveals the 10 most improbable FA Cup Third Round giant-killings.

The FA teamed-up with the Institute for Mathematical Innovation at the University of Bath to commission the research that considered Opta data from more than 8,000 FA Cup ties as part of the process. Using probability theory, the University was able to verify a historical top 10 of the least likely scorelines from the last 50 years of the competition.

In order to perform their calculations, Dr Adwaye Rambojun and Professor Andreas Kyprianou from the University of Bath built a bespoke mathematical model that takes in to account the overall probability of the lower league teams reaching the Third Round, the difference in league status and the timing and sequence of the goals scored in each tie.

Goal scoring and league position trends across more than 8,000 ties from the competition since the 1959-1960 season were also considered to understand how these factors historically influence the individual outcomes. The formula used in the study is expressed in the mathematical equation below:

The final list of results features several familiar ‘cupsets’ but now, for the very first time, the fixtures have been ranked in order of the statistical probability of each scoreline occurring.

The research has ranked Harlow Town’s famous home win against Leicester City back in 1980 as the eighth least probable Third Round result in the last 50 years of the competition. Harlow Town of the Isthmian League celebrated their centenary season in style with a shock Third Round win over Second Division Leicester. The Foxes were riding high in a season that would see them promoted back to the First Division but could only manage a 1-1 draw at Filbert Street. Almost 10,000 attended the replay at Harlow Sports Centre with Leicester including a young Gary Lineker in their side. A John MacKenzie strike three minutes before half time would prove decisive.

The study revealed that Woking, then of the Isthmian Premier League, defeating Division Two (now the EFL Championship) West Bromwich Albion 4-2 at the Hawthorns in 1991 was by far and away the least likely Third Round scoreline in the last 50 years of the competition, with just a one in 15,959,312 chance of that upset taking place. To put that into context, the result was less probable than conceiving identical quadruplets (one in 15 million probability).

The full top 10 can be seen below:

Commenting on the research, Dr Adwaye Rambojun, Research Associate at the Institute for Mathematical Innovation at the University of Bath, said: “Using data from over 8,000 Emirates FA Cup matches, we produced a mathematical model that takes into account not only the relative league status of the teams involved and how many matches they won to get there but also in-game scoring sequences to compute the total probability of the biggest Third Round giant-killings in the last 50 years. Harlow Town’s result defies logic but, as history proves, on any given day the unthinkable can happen. That’s the magic of the Emirates FA Cup and we have seen it time and again throughout the competition’s illustrious history.”

Phil Tuson, Programme Editor at the time of Harlow Town’s victory, commented: “The enormity of the victory didn’t hit home until some years later. I was the club’s programme editor in my late teens and wasn’t expecting to still be writing about the match now that I’m in my 60’s. The match was the biggest ever sporting event the town had witnessed and galvanised supporters of the more traditional London clubs.

Prior to the start of that FA Cup campaign the club had only previously reached the Third Qualifying Round of the competition on two previous occasions. With two local school teachers in the side, many of the town’s school children could relate to the players and went on to be lifelong fans of the club.”

Discussing the research findings, Andy Ambler, Director of Professional Game Relations at The FA, said: "It’s fascinating to look back at some of the Third Round games that have helped define the Emirates FA Cup and elevated it to the status of the world’s most popular domestic cup competition. The commissioned research outlines the competition’s ability to regularly defy logic and will hopefully spark many fond memories. In its 150th anniversary season, the Emirates FA Cup retains the values of hope, opportunity and equality. Improbable results are part of the competition’s fabric, providing life changing moments for players, managers, fans and communities alike and I am sure there will be plenty more to come as the competition looks ahead to an exciting future.”

More details about the forthcoming Emirates FA Cup Third Round can be found on TheFA.com.