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Opinions expressed on this blog reflect the writer’s views and not the position of the Capgemini Group

Betting on Trouble by Dougie Mackenzie and Iain Hubert

On the eve of England’s World Cup opener against Italy, many around the country are pondering our chances in Brazil.  The realistic (or pessimistic) among us are not getting our hopes up, and probably justifiably.  So how far do you think England can survive in this World Cup campaign?  And why is it important for officials to understand the chances of England progressing?

Recent news articles imply that there may be some positive correlation between crime and the England national team playing football  One suspects that the police ought to care about England’s stage of elimination in this tournament as it could be deduced that there may be a number of distressed fans heading into towns and cities across the country with shorter tempers than normal, regardless of how inexcusable any such behaviour is. 

An official government report from early May would suggest that even the Home Office doesn’t fancy Roy Hodgson’s men to set the world on fire  This week’s article highlights how they use betting odds to determine how far England will get in the tournament.  Apparently the government aren’t too concerned with potential trouble that may be caused late at nights in pubs for the latter stages of the tournament since they don’t believe England will be there to draw the crowds in.  The Home Office looked into this, primarily to consider licensing, but also to help with the other questions. 

In the same way in which the Home Office used betting odds, we’ve done a small analysis on the betting odds of our stage of elimination.  In simple terms only six things can happen to England this World Cup, represented below as stages of elimination with their corresponding odds.

* Odds taken from BetVictor on 11/06/2014

These can be converted to approximate probabilities by converting to decimal odds and inverting.  More specifically, let’s consider the odds of England being eliminated in the final at 20/1.  If you place £1 at 20/1 you will win £20, and get £21 back, if the bet wins.  However, you don’t get the £1 back if the bet doesn’t win so to convert this back to probability the chance is 1/21, not 1/20.

However, the eagle eyed among you will spot that these probabilities add to a number greater than one (1.12) and since these outcomes are mutually exclusive and completely exhaustive their sum should be one.  This is far from surprising though as this is how the bookmakers ensure that they make money, namely, there is no amount of money that you could bet on every outcome to ensure that you made profit. 
Consequently, to convert to some actual probabilities we need to normalise i.e. divide all everything by their sum (1.12), which gives the following:


From this it may be advisable for the government to ensure that there are sufficient plans in place to accommodate for the country’s dream still being alive through the group phase, but to perhaps be prepared for some extremely disappointed fans when the country comes crashing back down to reality in the second round or the quarter final.

Analysing bookmakers’ odds is a good way of using crowdsourcing ( techniques to predict an event.  However, in this case it does not appear to give the result that many of us desire.  To get that, we may want to use other information to predict the outcome of the 2014 World Cup, such as the following that has been doing the rounds on social media:


However, as the Mirror has pointed out, this technique can also be used to predict many other teams winning the tournament  We could always just look to nature for some foresight...

About the author

Iain Hubert
Iain Hubert
2 Comments Leave a comment
Great article Iain - I also suspect the propensity for violence (after a match) is positively correlated with the temperature ... which is a bit worrying as we're apparently in for a scorcher!
Very nice and well written post! I'm unclear as to why you believe the listed probabilities are iid. Aren't they conditional? You can't win in the second round if you don't get out of the group stage? Shouldn't your Expectation estimae be: Probability ( Winning Second Round|given advancing from the first round)? I recognize that you are using the compliment (Probability of elimination, not winning). I'm sure I'm missing an obvious point. Thanks, Daniel *** I'm an American; Glad to see the old empire defeated in the New World again;)

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