How Bookie's work

Have you ever wondered what shapes the bookmakers odds?  The traditional wisdom would have you believe that the odds are based on where the money is.  Obviously if the majority of the money is on one particular outcome then the bookie will not want to be offering long odds on that outcome.  Is this true?

Paddy Power recently published some information on where the bettors are putting their money on the Premier League outright market this year (see right).  Based on these stakes, you would think that Paddy Power would ideally want to offer Man Utd at 2/1, Liverpool, Arsenal and Chelsea at about 4/1 and Man City at about 9/1.  These payouts would guarantee a profit for the bookmaker no matter who wins.  However the reality is far removed from that.  

Take Liverpool for example.  Paddypower opened the market in June offering 13/2 on the Anfield Reds.  Liverpool clearly received strong backing from the punters.  The obvious reaction from the bookmaker would be to shorten their odds to limit their potential payout.  Instead Paddy Power lengthened the odds to 12/1 which would see them payout almost double the original odds offered.  The trend graph below shows Liverpool odds continued to drift despite strong backing.



If Liverpool would win, then Paddy Power would have to pay out roughly 12/1 on 18.4% of the stakes.  They would keep the stakes wagered by the other 81.6%.  Overall this scenario would see this successful bookmaking firm pay out well in excess of double of what they take in.  Below table estimates what they would be forced to payout per €100 staked for each of the favourites.  Paddy Power would appear to be losers unless Chelsea or Man City win.   

The above are just estimates because of course all the 18.4% of stakes were not at 12/1.  The early wagers would have been at 13/2.  

If you want to beat the bookie, you need to understand how the bookies think.

There is something similar going on in the Top Scorers market.  According to Paddy Power's blog article here, 42% of the cash on the five most popular scorers is on Alexis Sanchez.  At the time the bookmaker was offering 16/1 on Arsenal's new Chilean signing.  For the five most popular scorers Paddy Power leave themselves liable to paying out 16/1 on €42 out of every €100 staked - this works out at paying back a whopping €715 out for every €100.  If Alexis Sanchez tops the scoring polls I estimate that Paddy Power will pay out more than 7 times what they took in.

So what is going on here?  The answer is that I really don't have the answers.  I have no inside knowledge.  However, it seems the bookmaker is happy to run on a long term average.  They will lose on some events and win on others.  They are not balancing their odds to guarantee a win on every event.  They seem to want to maximise their overall expected value while at the same time offering the punter good value.  So when you look at their actual estimated probabilities for the Premier League (below) then the odds that they are offering make a whole lot more sense.  (We explained the idea of expected value from the punters point of view before.)

In Liverpool's case and from the bookie's point of view, they have a 7% probability of winning.  In other words the bookmaker expects to pay out 7% of the time on an outcome like Liverpool.  So 7% of the time they lose €12 and 93% they are up €1.  This gives an expectation of -12 x 0.07 + 1 x 0.93 = 0.09.  This is a long run average of 9c profit on every €1.  They could shorten their odds and increase the expected value but then they risk the punter playing at another bookmaker site.  The odds offered match with the best value that they can offer the punter while still maintaining a small margin for themselves over the long run.  The margin they operate at depends on how competitive they wish to be against other bookmakers.