Behind every sportsbook’s odds quote, there are two hidden numbers: the sportsbooks’s assumed probability that the bet wins and a built-in expected profit margin. The sportsbook won’t win every time but they price the odds so they expect to come out ahead on average by a specific percentage. In the United States, this expected profit margin is known as the hold percentage or the vig, after vigorish, an old term that apparently came from Russian, passed through Yiddish, and ended up as underworld slang. Or the juice because .. well who knows?
If you ask the internet about how to calculate the hold percentage, you encounter a lot of confusion and stuff that is wrong. A lot of “imagine the bookmaker took in this much on Team A and this much on Team B” – I recommend ignoring those explanations. It does not describe how sportsbooks actually operate.
However, as I explained in my research with Tadgh Hegarty, there is one simple condition under which you can calculate the sportsbook’s hold percentage just from the odds. If the odds are strongly efficient (as defined by Richard Thaler and William Ziemba) meaning the same expected profit margin has been applied to each possible outcome of an event, then you can calculate the hold percentage via the so-called overround, the sum of the reciprocals of the decimal odds.
And while you are at it, you can also work out the probabilities the sportsbook used when setting the odds. These are the so-called normalized probabilities you obtain from getting the raw “implied probabilities” (the inverses of the decimal odds), summing them and then dividing each implied probability by this sum. This is often seen as a logical (probabilities sum to one, right?) but still slightly ad hoc calculation. In fact, it delivers precisely the correct probabilities if the odds are strongly efficient.
The method is explained here.
There are various online calculators that offer to do this for you but many do it wrong.
So here are two simple spreadsheets that do these calculations.
First, a simple calculator that allows you to enter either fractional, decimal or American odds and two, three, four or five possible outcomes.
Second, a more general calculator that allows you to enter as many different odds as you want, e.g. for 32 teams to win the Super Bowl.
Alas, betting markets are typically not strongly efficient and so these calculations, while generally a useful guide, can sometimes be misleading. Fine Margins contains plenty of discussion of this issue and what it means for the true probability your bet has of winning and what the likely true sportsbook’s hold percentage is.