Probability based on the odds

Published on 21 January, 2009 | Leave a comment from N Todorov

Here`s how to calculate the probability based on bookmaker`s odds:

The example is with a game from Euro 2008 – Switzerland vs Czech republic. The odds are: 1X2 – 2.87|3.20|2.37

Index 1 (for home win) = 1/2.87 = 0.34843206 (34.84% in percentages)
Index 2 (for draw) = 1/3.20 = 0.3125 (31.25% in percentages)
Index 3 (for away win) = 1/2.37 = 0.4194093 (41.94% in percentages)

Collecting the percentages of all indexes you will get 1.08287298 %, which is a little higher than 100%. The percentages that are above the 100% (in this case 8.287298 %) is the bookie`s margin, which actually guarantees profit for the bookie. This means that the bookie actually considers the probability of home win is 32.18% (which is 3.11 in odds), but the odd on the market is lower, 2.87 (therefore the probability is higher – 34.84%). This means that if there are 1000 bets with 1 unit on the odd of 2.87 there will be 322 winnings, which is 924.14 units with 1000 staked.

The bookie pays off 92.346934% and it`s calculated like this:
100 x (1/the sum of the indexes)=
=100 x (1/1.08287298)=
=100 х 0.92346934=
=92.346934 %

This shows that you will win with 7.653066% than you should win in real.

Calculating the real percentages (before adding the bookie`s margin):

Index 1 x the percentages that the bookie pays off
Index 2 x the percentages that the bookie pays off
Index 3 x the percentages that the bookie pays off

this means:

for home win – 0.34843206 х 92.346934 = 32.18 %
for draw – 0.3125 х 92.346934 = 28.86 %
for away win – 0.4194093 х 92.346934 = 38.96 %

Actually this are the real probabilities that the bookie calculated for this game.

Here you can download full table so you can calculate the real probabilities very easy by yourself – Download full table for calculating real probabilities.
Category : Betting Tools
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