Odds and the margin – what a price really tells you

The previous chapter covered value: the gap between what the odds claim and the true probability. This chapter opens up the odds themselves. What a price is made of, why a bookmaker's probabilities add up to more than 100 percent, and what that means for a bettor's return over the long run.

Odds are probability turned upside down

Decimal odds tell you what a one-unit stake returns if the bet wins, stake included. Odds of 2.00 return two units, odds of 1.50 return one and a half. Dividing one by the odds gives the probability the price claims: 1 / 2.00 = 50%, 1 / 1.50 = 66.7%, 1 / 4.00 = 25%.

If a bookmaker priced a match perfectly fairly, the probabilities of all outcomes would add up to exactly 100 percent. In a football match, for example, home win 45%, draw 27% and away win 28% would give odds of 2.22, 3.70 and 3.57. At these prices the bookmaker would neither win nor lose over the long run.

The margin, the bookmaker's share

In reality the odds are slightly lower than fair pricing would give. In the same match a bookmaker might offer 2.10, 3.50 and 3.40. Their reciprocals are 47.6%, 28.6% and 29.4%, which add up to 105.6%. The excess, here 5.6 percentage points, is the margin: the bookmaker's expected share of all stakes placed on this market.

The margin means that a random bettor gets back on average about 94.7 cents of every unit staked on this market (100 / 105.6). That is the basic setup of betting: without an edge of your own, you lose the margin over the long run even if you hit exactly as often as the odds claim.

Margins vary a lot. On main markets in major leagues (match winner, totals) the margin is typically 2–6 percent. In smaller leagues, specials and player markets it can be 8–15 percent or more. The bigger the margin, the bigger the edge a bettor needs for the bet to be profitable.

Fair probability

Removing the margin gives the market's fair probability. The simplest way is to divide each outcome's reciprocal by their sum: 47.6 / 105.6 = 45.1%, 28.6 / 105.6 = 27.1%, 29.4 / 105.6 = 27.8%. This is the figure shown on each pick's card as "market". It tells you what the market actually believes, not what it charges.

The Sorceress's estimate is always compared with this fair probability, not with the raw odds. That is why a card can show at the same time "our estimate 56%, market 55.8%" and "edge −4%": the estimate is slightly above the market's belief, but the price includes a margin, and by that much the estimate falls short of the stake's return. The edge is always calculated against the actual odds, because that is the price the bet is placed at.

Why odds differ between bookmakers

Different bookmakers price the same match differently for three reasons. The margin is not the same. Bookmakers weight different sources and react to new information at different speeds. And a bookmaker adjusts its prices to its own customer base: if its customers bet heavily on the home team, it shortens the home price and lengthens the away price regardless of what it thinks about the match.

This is why odds comparison is the single most important tool a bettor has. The same pick at 1.96 with one bookmaker and 1.88 with another is a difference equal to roughly four percentage points of margin. A bettor who always takes the best price in the market effectively plays at a lower margin than one who uses a single bookmaker. The Sorceress finds the best available price for every pick at publication and shows in the odds comparison how prices were spread across bookmakers.

The median shows where the market is

A single high price can also be an error or a slow update. So the Sorceress looks not only at the best price but at the bookmakers' median, the middle price. If the best price is clearly above the median, one bookmaker disagrees with the rest of the market. That can be an opportunity, but also a warning: the price may drop quickly once the bookmaker notices the deviation. On the Totals & spreads lane, the Sorceress ranks candidates by the lower of two figures: the best price, or the median raised by three percent. This way one outlying price does not push a pick to the top of the list.

What this means for the bettor

The margin is an opponent that never rests. Three things follow.

Always calculate the fair probability, not the reciprocal of the odds. Odds of 1.90 on both sides do not mean a 52.6% probability for each, but 50% and a 5.3% margin.

Compare prices before every bet. Odds comparison is the only way a bettor can reduce the margin on their own. Over the long run the difference between the best and the average price is often larger than the edge from any single piece of analysis.

Weigh the edge against the margin. A two percent edge on a low-margin main market is real; the same edge in a special with a ten percent margin is more likely an error in the estimate. That is why the Player props lane has stricter gates than the match-winner lane.

Summary

Odds are probability turned upside down, with a margin added that is the bookmaker's share. The fair probability is what remains when the margin is removed, and that is what the Sorceress's estimate is compared with. Prices differ between bookmakers because of margin, sources and customer base, so odds comparison is the bettor's most important tool. An edge must always be weighed against the margin: the more expensive the market, the bigger the edge has to be.

The next chapter covers line-ups and absences: why one missing player can move a price, and how the Sorceress checks the line-up before publishing.

Betting is for adults only. Please gamble responsibly.