Well in my opinion a good parallel can be made between sport betting and bookmakers on the one hand and derivative pricing and market makers of those derivative on the other hand. I'll try to explain that if I can.
If you are given a set of bookmakers taking bets for let's say one underlying outcome and that they quote this event as a percentage (as for binary options). Then if they are smart enough they shouldn't care about the statistics of the event itself, what they shall try to do is to balance their quotes with respect the positions of their outstanding books. I mean by this that they should do the P&L scenarios of each outcome of the bets in their books and try to balance things so they can earn a living while taking as little risk as possible. This will make dynamicaly evolve the quotes of the events as the bets come to their books. Of course the clients do care about statistics and so they will think twice before taking bets that rarely occur (or pay too much for it).
If you think at the market making of binary options, the situation is quite the same as the one with the bookie, but at the end what you get is the Risk Neutral Probability. It is set by market participants and is in a way "an opinion". This RN Probability is not always coherent with the statistics of the history of the underlying.
This however can make sense if all the market makers are in some way minimizing the aggregate risk of their returns (I don't explain the word 'risk' here on purpose but here the limits set by risk managers should enter into play).
Of course all this is not properly and mathematically formalised but the appropriatness of the parallel of both situations appears quite striking to me.