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Leicester City were recently confirmed as winners of England's top football (soccer) league. Last year they were facing relegation a dozen matches before the end of the 38 game season and, at the start of this season, betting odds on winning the premiership were 5,000-1 (in the realm of bets on Elvis being found alive or an alien spacecraft landing in England). Some fans placed bets at those odds.

Many football pundits were still claiming a Leicester victory to be impossible mid-season and some made foolish promises conditional on such a victory. Simulation modellers (usually more reliable than betting odds) had the probability of a Leicester win as about 5 in 100,000.

Several sites have described the victory is the most improbable win in betting history. For example, ESPN says:

There is no previous example of an underdog the likes of Leicester City beating odds as long as 5,000-1.

Are they right? Has no underdog won when odds have been set against them (by major bookkeepers) at 5000-1?

  • According to this BBC article, its odds were actually more than twice as unlikely than Elvis being found alive, which only had 2,000/1! – user568458 May 4 '16 at 14:19
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    To be clear, many improbably events occur but the odds of them occurring are not like this. An individual's odds of winning a lottery, for example, are very low. But millions play so the chance that someone wins is large. Accumulator bets on multiple events are similar and won't really count as good comparisons. – matt_black May 4 '16 at 14:36
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    @jamesqf Two reasons: one, underdogs don't win the premiership (only four other teams have won it in 20 years) and two, the betting odds given at the start of the season (which anchors an improbable story in the world of actual statistics since bookmakers don't calculate them randomly). – matt_black May 4 '16 at 18:00
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    @jamesqf: depends whether you're a frequentist or a Bayesian. If the former, then mathematically it's because they've never won it before in many attempts, whereas other teams have won it before, and we refer to those others as being more likely to win. If you're a Bayesian, it's because as of last August they'd shown no signs of being anything other than rubbish and we model the Premiership as being won by good teams. If you're a bookie then it's economic rather than mathematical, but in short they were less probable to win it because (almost) nobody wanted to bet on them winning it. – Steve Jessop May 4 '16 at 20:29
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    @jamesqf "underdogness" isn't just opinion in football. There is a strong statistical pattern where rich teams win the premiership and poor teams don't. That's not just opinion. And the betting odds are not irrelevant: bookmakers are not perfect, but their business depends on not often being wrong on probabilities. Hence the question ties to observable, statistical evidence and not just opinion (though the consensus opinion would have agreed with the status of Leicester at the start of the season). – matt_black May 5 '16 at 9:32
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Almost certainly yes, if you only count single bets with "underdog" long odds on single sporting outcomes - several sources have looked into this, including betting companies themselves, and found nothing that comes close.

If you allow any type of bet and aren't fussy about it being an "underdog" story (something that was added to the question after I wrote this), and you simply look for the longest odds won for a single competitor winning in a single competition, series or fixture, then arguably Frankie Dettori's "Magnificent 7" at Ascot Champion's Day in 1996 edges out Leicester with accumulated odds of 25051-1. According to the BBC, this cost the betting industry an estimated £40m, compared to Leicester's £20m, but there are several reasons why it might not be comparable.


Counting any win in a single event, league or series, by a single competitor

If we treat this as any case of one competitor winning one event, series or league, arguably, the longest odds would be jockey Frankie Dettori winning all 7 consecutive races in one day at Ascot Champion's Day, 1996, at odds of 25,051-1.

Great British Racing magazine:

The cumulative odds of these wins was 25,051-1

The Daily Telegraph newspaper also describe the odds as being 25,051-1, and the Independent tell the story of some of the lucky punters that day.

This is debatable though, since it's classed as an "accumulator" bet, and isn't a classic "underdog story" like that of Leicester (Dettori was a respected jockey riding horses whose individual odds were not especially remarkable), but it does refer to a single improbable achievement in a single sporting fixture or competition by a single sporting competitor.


Counting single bet "underdogs" only

If, however, you discount accumulators or pools and count only events treated by the bookies as single bets and given very long odds, I can't find anything close to 5,000-1.

It's hard to prove a negative, but ESPN have an analysis that concludes that Leicester have the record (written shortly before their win was confirmed):

Why Leicester City could become the biggest long shot champion in sports history

If they hold on to claim the title, it would be the biggest upset in sports history, according to William Hill press officer Joe Crilly. ... There is no previous example of an underdog the likes of Leicester City beating odds as long as 5,000-1. There have been a few 100-1 or longer shots that either shockingly came through or fell tantalizingly short.

They then list 10 examples, of which the longest odds were 1,000-1.

Sporting Life magazine also make a reasonable case that it is the most unlikely sporting event ever (if only single bets are counted):

Sport's greatest-ever upset

... the greatest sporting upset of the modern era, according to the bookmakers ... Sky Bet reporting it is the first time they have ever paid out a single outright bet at 5,000/1 ... It has also resulted in their largest-ever payout ... with the industry as a whole paying approximately £20 million.

They then go on to list seven other sporting upsets, the most unlikely of which had odds of 500-1. They also mention in passing that some of the odds listed might have been longer if there was something comparable to modern betting comparison websites forcing competition for unlikely bets.

These two articles cover sports from an American (ESPN) and European (Sporting Life) perspective. Two articles from Asian outlets Gulf News and Channel News Asia and one African sports blog also reach the same conclusion (but they aren't nearly as thorough), as does the internationally-minded Reuters.


Thanks to Jeremy French's comment, here's a BBC article that gives two more betting companies reporting it's the longest single bet odds they've ever paid out.

A quote from a representative of Coral:

"In the history of betting, certainly since it was legalised in 1961, a [single event] winner with odds of 5,000-1 has never happened ... Every bookmaker is crying out in pain"

A quote from a representative of Ladbrokes:

"This is the biggest sporting upset of all time"

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    Whether Dettori was an underdog is irrelevant. That wasn't a single event. Accumulator odds are essentially unbounded so it's pointless to consider them. – OrangeDog May 4 '16 at 17:27
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    I'm getting a little tired of people repeating the same caveats in comments that are already written into the answer... After I've already explained once that the "underdog" condition was added to the question later... – user568458 May 4 '16 at 18:14
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    @DavidRicherby I was kinda hoping people would read the first two sentences, which I specifically added so people could get the gist without reading the long answer... – user568458 May 4 '16 at 20:21
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    @user568458 Well, your second sentence, essentially, says "And now I'm gonna talk about a whole lot of irrelevant stuff" and it's also inaccurate. Dettori did not "[win] a single event, series or league": he won seven separate races. That's no more a "single event, series or league" than, say, a baseball team winning all their games in a particular week. – David Richerby May 4 '16 at 20:24
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    @user568458: think of it as doing the public a service, they love their "gotcha! someone's wrong on the internet!" moments. You can't really expect them to actually read what they're criticising. – Steve Jessop May 4 '16 at 20:24
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No

According to the BBC, in October 2010, Michael Elliot was paid £3,001,511 for a £2 stake in the football pools. Football pools is a betting system based on predicting the (partial) outcome of 10-12 games of football (a.k.a. soccer).

These are equivalent to odds just over 1.5 million to 1.

There may be even larger payouts, but this is enough to demonstrate the claim is incorrect.

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    The claim is that no underdog has won when odds were set against them at 5000-1. Pools are not the same domain of bets. – user30557 May 4 '16 at 14:33
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    Ah, but this is more like winning a lottery: highly improbable as an individual event, but collectively likely as many people play. So not quite the same thing as a single bet on a single event. – matt_black May 4 '16 at 14:33
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    This is about predicting the score in eight unrelated games, involving different teams in different countries, all of which were draws. It's pretty hard to see that as an event or improbable sporting victory. – user568458 May 4 '16 at 15:28
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    Also, £3 million from £2 is not equivalent to odds of 1.5 million to one. That's not how pools work. There's a prize pool, based on how many gamblers enter, and gamblers score points based on the outcomes of football games they choose. How much of the pool they win is relative to their scores compared to that of the other players. A high payout is linked to how many gamblers played and how few points the competing gamblers won, not the probability of the particular sporting results. Rules here (warning: it's complicated...) – user568458 May 4 '16 at 16:12
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    Well, yes, given the numerous references to probability and sporting results in the question... The person in your example did not place a bet with odds of 1.5 million to 1. They paid £2 to enter a lottery-like game, chose a selection of unrelated sporting games, and won £3m as a factor of the quantity and points scored by of other players in the same lottery-like game. – user568458 May 4 '16 at 16:17

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