The Math of Sports Betting

Every bet is a price on an outcome. The bookmaker offers you odds, those odds imply a probability, and you win money over time only if the real probability is higher than the one you are being charged for. That is the whole game. Everything below is a tool for measuring that gap precisely instead of guessing at it.

Start with implied probability

Odds and probability are the same information written two ways. American odds of −150 mean you risk $150 to win $100, which implies the bet wins about 60% of the time. Converting in your head is the first skill worth building, because you cannot judge a price you have not translated.

Implied probability covers the conversion in both directions, including the decimal and fractional formats you will meet outside the US.

Then remove the vig

Add up the implied probabilities on both sides of any market and you get more than 100%. That excess is the bookmaker's margin — the vig, also called juice or the hold. On a standard −110 / −110 line the two sides imply 52.4% each, totalling 104.8%. The 4.8% is the house's cut.

Because of the vig, the odds on the board are not the market's honest opinion. Stripping it out gives you the fair price — what the market really thinks, before it takes its fee. Comparing your number to the posted price without de-vigging first will make almost every bet look bad.

Measure the gap

Once you have a fair probability and your own probability, the difference is your edge, and turning that into money is expected value — the average result per bet if you could make it a thousand times.

A useful reference point: at standard −110 pricing you need to win 52.4% of your bets just to break even. Every percentage point above that is profit; every point below is a slow bleed. That single number explains why "I went 6–4 last week" means almost nothing.

Judge yourself on the closing line

Results are noisy. A good bet loses often, and a terrible bet cashes often enough to feel clever. The fastest honest feedback is closing line value: did you get a better price than the market settled at by kickoff?

The closing line is the sharpest number the market ever produces, because it contains every injury, every weather report and every dollar of informed money. Consistently beating it is the strongest evidence that your process works — and it tells you so after a few hundred bets rather than a few thousand.

Size the bet to the edge

Knowing a bet is good does not tell you how much to put on it. The Kelly criterion gives the mathematically optimal stake for a known edge — and then immediately teaches you why nobody should bet full Kelly, since your edge estimate is itself uncertain.

Most disciplined bettors use a quarter or a half of the Kelly recommendation, or skip it entirely for flat betting. All three are defensible. Betting whatever feels right on the day is not.

How WeBall does this for you

Every grade in the product runs this exact sequence: sample the relevant history, fit a model probability, de-vig the cross-book consensus for the fair price, and publish the difference as an edge. The grading documentation shows the steps with real numbers, and known limitations is honest about where the model is weakest.

Every guide in this section