No team from outside the top 5 wage bills has ever won the Premier League. No team outside the top 3 in wage bills has won the league for 16 years. Leicester's wage bill is probably about 15th.
Other longshots
5,000-1: Leicester in August 2015 to win the the 2015-16 Premier League title.
2,500-1: The odds at which a grandfather, Peter Edwards, wagered £50 in the year 2000 that his grandson, Harry, then three, would one day play football for Wales. Wilson, now a 19-year Liverpool winger, made his Wales debut aged in October 2013, aged 16, winning his granddad £125,000.
1000-1: In 1964, a man from Preston called David Threlfall bet £10 that a man would walk on the moon before the end of the decade. He had been inspired by J F Kennedy, the president of the USA, saying more than once that it was an aim. It famously happened in 1969. Threlfall won £10,000 (worth £156,600 today) and bought himself a sports car, in which he was killed in a crash.
999-1: The longest odds successfully overcome by a US sports team in a major league, by the St Louis Cardinals of MLB baseball to win the 2011 World Series. They looked dead and buried during the regular season but secured last-gasp wild card qualification for the post-season, then beat the Philadelphia Phillies in the division series, the Milwaukee Brewers in the National League Championship Series and the Texas Rangers in the World Series.
500-1: The longest known odds on a single football match upset (according to William Hill), when the USA beat England 1-0 in Belo Horizonte at the 1950 World Cup, courtesy of Joe Gaetjens’ goal.
500-1: The odds on an England victory on the final morning of the Third Test of the 1981 Ashes series against Australia. The tourists seemed in such a strong position for victory, a win was all but assured. Ian Botham and Bob Willis had other ideas and pulled off an astonishing comeback. Australia’s Dennis Lillee and Rod Marsh had bet on England for a joke and won £7,500.
300-1: The longest Super Bowl odds converted into success from the start of a season, by the St Louis Rams in the 1999 NFL campaign. In 1998 the Rams posted a 4-12 win-loss record. Then pre-season they lost Trent Green, their star quarter-back on a new $17.5m contract, to a long-term knee injury. But they posted a 13-3 regular season record and won all three play-offs games for glory.
250-1: The longest odds on a winning horse in any race in Britain since records began. This seems utterly extraordinary given there have been around 2 million races since the 1600s. But it is true: the longest priced winner was an animal called Equinoctial in the 2.45 at Kelso race course, in a novices hurdle over 2 miles and 6 furlongs on Wednesday 21 November 1990. By comparison, the longest odds winners of the Grand National were all 100-1 shots including Foinavon (1967) and Mon Mome (2009). The longest odds Derby winners were all also 100-1 shots: Jeddah (1898), Signorinetta (1908) and Aboyeur (1913).
150-1: This was the price defied, by among others, Goran Ivanisevic (to win the men’s Wimbledon title in 2001 as a wild card), Greece at Euro 2004, and Jeremy Corbyn to become the leader of the Labour Party last year. All three polarised opinion on their way to winning, and all came from left field.
42-1: The odds on Buster Douglas to beat Mike Tyson in 1990, which he did, in what is considered one of the greatest sporting shocks of all time. Not that the price reflected it. Or that it is a patch on Leicester.