Expected Value

The Premier League is about to finally kick off.  Still time for that last minute punt on the outright winner.  You will hear a lot of people make predictions on winners from Gary Lineker to Eamonn Dunphy to your mate down the pub.

So why is the smart money on Man City?

Well the information that the pundits usually leave out is how sure they are.  Are they 50% sure?  100% sure?  Before making an informed betting decision you need to know the probability that they will win.  The Football pundits may be experts on football and can easily pick out the strongest team but would struggle to give the probabilities.  They generally are not experts on probability theory.  To get our probabilities we can turn to data analysis projects like bloomberg.  See here for their current league predictions.

The concept of Expected Value can then guide us as to whether it is worth making a bet or not.  The Expected Value of a betting outcome is very easy to calculate because there are only two outcomes - either you win or you lose. 
Expected Value[Payout]= Probability you win * payout for a win + Probability you lose * payout for a lose

The value of a lost bet is obviously zero so the Expected Value simplifies to. 

Expected Value[Payout]= Probability you win * payout for a win 

Any bookmaker site will give us the value of a win.  But finding accurate probabilies is more difficult.  In our example calculations we will use Bloomberg's predictions.  See the table below (odds correct as per 10am on Aug 16th).  Clearly any Expected Value less than €1 is not worth considering since you need at least €1 to cover your stake.


Betting on Man City gives us the highest Expected Value.  Now obviously if you place €1 on Man City you either win €3.75 or you lose, it is not possible to win €1.44 (the expected payout).  Similarly the long run average of a dice roll is 3.5 but you can't roll a 3.5.  The expected value tells us the long run average if you could replay the same Premier League Season over and over.  Each replay could have a different winner due to unpredictable events (injuries, referee decisions, weather, the bounce of the ball, even natural disasters etc).  It is not a guaranteed profit, but it is expected to average out at a profit in the long term if your probabilities are accurate and if you make a enough of these sorts of bets.  

Also to note, although we think that Chelsea are going to edge Man City to the title (they have a slightly higher probability) we are actually going to bet on Man City to win!  This seems like a contradiction but it's not, the bookies are just offering better value on Man City.  So if they do win the payout is bigger and worth it.    

How accurate are bloombergs predictions likely to be?   More details on the prediction can be found on the bloomberg site.  The Man City prediction in particular seems at odds with the bookmakers.  Man Utd and Arsenal are very low in the bloomberg predictions, the bookmakers seem to be predicting a more open title race than the two horse race bloomberg expects.  Does it take into consideration the departure of Luis Suarez, the appointment of Louis Van Gaal, the lack of any exciting arrivals at Man City, the signings of Diego Costa and Alexis Sanchez at Chelsea and Arsenal?  Bloomberg do reveal some details.

"the projections are uniquely data-driven and take into account numerous years of performance for each club, supplemented by the additional value that each club gained from the transfer window."

Numerous years of data should smooth out the David Moyes effect for Man Utd.  It also seems as though they are taking transfer value into account.

Bloomberg also claim:

"Last season BSports ‘Match Analysis’ forecasts proved highly accurate, delivering 14.2% Return on Investment (ROI) on match odds across the Premier League, La Liga and Bundesliga. During the World Cup, ‘Match Analysis’ would have delivered 36.54% ROI on match odds throughout the tournament."


It seems quite legitimate to me and worthy of experimenting with the bloomberg predictions to see if they are in fact the real deal.  I wouldn't be betting the house just yet.  I remain very skeptical, the bookies are proven experts at this game - otherwise they would be out of business.  Some of bloomberg's probabilities are quite far off what the bookies seem to expect.

Very interestingly Man City also have a favourable Expected Value (but only slightly) if we recalculated the expected values based on the probabilities published (on twitter!) from Airton Risk Management aka Paddy Power. It would appear that Paddy Power have taken in so much money on Man Utd, Liverpool and Arsenal that they are willing to offer extremely good value even based on their own risk calculation to attract some money on Chelsea and Man City.

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