Reading a line: odds, the margin and implied probability

Every prop has two numbers: the line (24.5 points) and the price (the odds). The price tells you how much you win, and it also tells you what the bookmaker thinks the chances are.

Decimal and American odds

Decimal odds are the return per unit staked, stake included. At 1.91, a 10 euro bet returns 19.10: 9.10 profit plus your 10 back.

American odds use 100 as the base:

• Negative (-110): what you stake to win 100. -110 means stake 110 to win 100.
• Positive (+120): what you win on a 100 stake.

To convert: -110 is 1 + 100/110 = 1.91. +120 is 1 + 120/100 = 2.20.

From a price to a probability

The implied probability of a price is 1 ÷ decimal odds:

The margin

Look at a normal prop: over 24.5 at -110, under 24.5 at -110. Each side implies 52.4%. Together that is 104.8%, not 100%. The extra 4.8% is the bookmaker's margin (the vig, or juice). It is how they make money whichever side wins.

To get the fair chances, divide each side by the total: 52.4 / 104.8 = 50% each.

Break-even: the number that matters

Because of the margin, at -110 you need to win 52.4% of your bets just to break even. Win 50% and you lose about 4.5% of everything you stake over time.

This is why the model's record on NBA House is shown against the break-even, not against 50%. A 54% record at -110 is a real edge; 51% is a slow loss.

What to take from it

• Always compare your chances with the price, not just with the line.
• A better price on the same line is free money over a season: that is what line shopping is for.
• When a price looks too good, check the line first. A higher price often hides a worse line.