Implied Probabilities and Fractional Odds

If ‘moneyline’ is the term used in American betting, it’s ‘fractional odds’ for the UK. So, for today’s premier league match between Chelsea and Everton, the following are the odds.

HomeDrawAway
14/1910/319/5

This means that if you bet on home, i.e., Chelsea (the match is played in Chelsea’s backyard) and win, you get a profit of £14 for every £19 placed. In other words, you bet £19 and get back £14+£19 = £33.

As before, let’s estimate the implied probability based on the (fair) expected value assumption.
E.V = p x 14 – (1-p) x 19 = 0
14p + 19p – 19 = 0
p = 19/(14 + 19) = 0.576 = 57.6%

As a shortcut: for 14/19, p = 1/[(14+19)/19].

And for the next two
Draw: p (10/3) = 1/[(10+3)/3] = 0.231 = 23.1%
Away (Everton win): p (19/5) = 1/[(19+5)/5] = 0.208 = 20.8%

As expected, the sum of probabilities is not 100% but 101.5%; the house must win.