Chelsea Finally Lose

As predicted by Mourinho Chelsea won't go the season unbeaten after losing on Saturday to Newcastle.  Since this is getting a bit of media attention mainly because of Mourinho's comments earlier in the season I have decided to write a quick article about it.  How was Mourinho so sure that he wouldn't remain undefeated, hadn't Arsenal achieved this before?  How likely is it anyway?

 Lets look back to 2003/04 to when Arsenal achieved the feat, only the second time in English football league top flight history after Preston Northend remained undefeated for all 22 league matches in 1888/89.

 See below Arsenal's run of undefeated matches along with the bookies' odds, implied probability and adjusted implied probability.
Click to enlarge.  Full list of Arsenal's invincible season including odds.
For example Arsenal were 3/2 to beat Liverpool on 4th Oct.  This translates to about 40% chance but I have also adjusted for the bookies edge.  Bookies probabilities add up to over 100% and so we can't really do real probability arithmetic on these, so I adjust all the probabilities so that they do add up to 100%.  We can see the likelihood of a draw as well.  Add the probability of an Arsenal win to the probability of a draw (both are mutually exclusive, so we can) to get the probability that Arsenal are undefeated in a given match.  then we can multiply all these together to get the probablitiy of Arsenal going undefeated the full season.

 The final figure comes to 0.00054 probability or about 5 chances in 10,000!!

 So Arsenal overcame odds of roughly 1 in 2,000 to remain unbeaten - through luck, or through some other unquantifiable measure - at least unquantified by the bookies.  

 This seems unlikely to happen again any time soon based on these calculations and probably why Mourinho was so sure that defeat would come.

 This analysis is based on the accuracy of the bookies' odds.  If anyone rejects this I would ask them where are the bookies wrong in their odds so that I can put a wad of cash on those matches!?  Also see below table.
Bookie implied probabilities vs reality

 I have banded the bookies odds by implied probability for 100,000 plus outcomes.  You can see that the bookies' implied probability is a little higher in almost every case (while remaining quite accurate).  The little extra helps the bookie make a profit.

 This basically says that when the bookie gave 9/1 - the long run average saw roughly 9 of those outcomes fail to 1 outcome succeed.  Exactly as predicted.  

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