Deriving Asian Handicap odds

[Bazman]

Hi there,

I am confused by Asian Handicap odds: 

They are described in the link below as follows:

(https://www.sportsbookreview.com/forum/attachment.php?attachmentid=62968&d=1386982455)

"Quarter balls actually mean that the stake of the bet will be divided in two separate bets where one is with 0:0 handicap and the other with ½:0 handicap."

This makes it sound like the quarter should simply bet the average of the (0:0) and (½:0) handicap.

However on pages 6-9 of the link above they show that although the payoffs of the (¼:0) are the simple averages of the payoffs for the  (0:0) and (½:0) handicaps for both teams. Only the odds for the team that does not benefit from the handicap has odds that are the simple average of it's (0:0) and (½:0) handicaps. Can someone please explain to me why the odds for the team that receives the ¼ goal advantage has odds which are different to the simple average of the (0:0) and (½:0) handicaps. Given that the payoffs are the same it seems that the probabilities must be different but why are they different?

Thanks Baz

PS(I realise this a similar question has been asked before but the answers given there don't answer my question)

 

 

[harry_rag]

Only had a cursory glance at this (more than enough for me) but I suspect it will be a by-product of the key difference; for the team receiving the start a draw is half push and half win whereas for the favourite the draw is half push and half loss.

That should set you on the way to figuring it out!