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Magic of the Cup: The greatest FA Cup upsets ranked in terms of statistical improbability

FA Cup
(Image credit: Getty)

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 equation developed by the Institute for Mathematical Innovation at the University of Bath to calculate Third Round score probabilities.

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 identified that Woking’s 4-2 victory over West Bromwich Albion at the Hawthorns in 1991 was by far and away the least likely Third Round result 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 – a one in 15 million probability. 

The fixture is firmly entrenched in the competition’s folklore, with Woking - then of the Isthmian Premier League - reaching the Third Round for the very first time and beating second-tier West Brom away from home. The result was made all the more improbable as the Baggies took the lead, but the visitors roared back in the second half with Tim Buzaglo registering an 11-minute hat-trick and Terry Worsfold adding a fourth. West Brom scored a late consolation, but Geoff Chapple's side held on for what is the most improbable Third Round victory in the last 50 years, according to the research.

Another iconic result ranks second on the newly calculated list with Hereford United’s Third Round replay success over Newcastle in 1972 revealed as a one in 32,449 probability, even less likely than growing to seven foot tall (one in 26,315) or finding a five-leaf clover (one in 24,000). The game, made famous by Ronnie Radford’s late long-range equaliser and a young John Motson’s memorable TV commentary, saw the Southern League side overcome First Division opposition despite trailing late on in normal time.

Newcastle were again on the receiving end in 2011 when League Two Stevenage secured a 3-1 win over the Premier League side, in a result that would happen only once in every 7,712 attempts.

The full top 10 can be seen below...

CupsetProbabilityReal-life example
West Bromwich Albion 2-4 Woking, 19911 in 15,959,312Conceiving identical quadruplets
Hereford United 2-1 Newcastle United, 19721 in 32,449Chance of growing to over seven foot tall
Stevenage 3-1 Newcastle United, 20111 in 7,712Rolling five consecutive sixes with a dice
Birmingham City 1-2 Altrincham, 19861 in 4,376Being dealt a four-of-a-kind poker hand
Oxford United 3-2 Swansea City, 20161 in 3,487Scoring a hat-trick in the Final and winning the FA Cup
Sutton United 2-1 Coventry City, 19891 in 3,260Chance of the FA Cup trophy landing in the UK if dropped from space
Burnley 0-1 Wimbledon, 19751 in 2,515Becoming a NASA astronaut
Harlow Town 1-0 Leicester City, 19801 in 1,800Being born on a leap day
Derby County 1-3 Bristol Rovers, 20021 in 397Coin tossing 8 heads-in-a-row
Newport County 2-1 Leicester City, 20191 in 337Conceiving identical twins

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Ed McCambridge
Ed McCambridge

Ed McCambridge is a staff writer at FourFourTwo, working for the magazine and website. Ed has been living in Berlin since 2015 and worked as a Bundesliga reporter before joining FFT. Formerly a season ticket holder at AFC Wimbledon, he's now most commonly spotted at local side Union Berlin.