Almost every prop bet comes down to six numbers, and you can run all of them on your phone. This statistics cheat sheet covers the math that actually decides bets: implied probability, the vig, sample size, expected value and staking. Learn the formulas once and you can price any line in about a minute.
Statistics cheat sheet: six formulas that cover most props
Short version first. Everything below is these rows, explained in plain English.
| What you want | Formula | Example |
|---|---|---|
| Implied probability (negative odds) | odds / (odds + 100) | -110 becomes 110 / 210 = 52.4% |
| Implied probability (positive odds) | 100 / (odds + 100) | +127 becomes 100 / 227 = 44.0% |
| Market hold (two-way) | total implied minus 100% | -110 / -110 becomes 104.8%, so 4.8% hold |
| Fair probability after de-vig | implied / total implied | 52.4 / 104.8 = 50.0% |
| Fair odds from a win rate | p / (1 – p) x 100 | 60% becomes -150 |
| Expected value | (your probability x decimal odds) – 1 | 55% at +100 (2.00) = +10% |
| Kelly stake | (b x p – q) / b | 55% at +100 = 10% of bankroll |
Key takeaway: every price has a break-even percentage, and nothing else matters until your number beats it.
How do you turn odds into implied probability?
Implied probability is the win rate the price asks for. For negative odds, divide the number by itself plus 100. For positive odds, divide 100 by the number plus 100. That is the whole trick.
So a standard -110 prop needs 110 / 210, which is 52.4%. A +105 price needs 100 / 205, or 48.8%. Those two look close on a bet slip. They are more than three percentage points apart in required win rate, which is real money over a season.
If you would rather not do division at the window, the free implied probability calculator converts American and decimal odds both ways and shows the break-even percentage next to the price.
What does the vig actually cost you?
A two-way market at -110 / -110 prices both sides at 52.4%. Add those together and you get 104.8%. The extra 4.8% is the hold, also called the vig or the juice, and it is the book’s cut before anything happens on the field.
To see the book’s honest opinion, divide each implied probability by the total. In that -110 / -110 market, both sides land at 50.0%. That is the fair number behind the price.
This is why a -110 line is a 52.4% break-even, not a 50% one. Win those at exactly half your bets and you lose steadily. The de-vig calculator strips the hold out of two-way and three-way markets in one click.
Why a 6-of-10 hit rate is not a 60% chance
A hit rate is a measurement, and every measurement has error bars. The standard error of a rate is the square root of (p x (1 – p) / n), where p is the rate and n is the number of games. Small samples swing hard.
| Sample | Hit rate | Standard error | Plus or minus 2 standard errors |
|---|---|---|---|
| 6 of 10 | 60% | about 15.5 points | 29% to 91% |
| 60 of 100 | 60% | about 4.9 points | 50% to 70% |
| 600 of 1,000 | 60% | about 1.5 points | 57% to 63% |
Read that first row again. Six of ten looks like a 60% prop. Statistically it could be a coin flip or a near lock, and you cannot tell which yet.
That is not an argument against hit rates. It is an argument for reading the sample before you trust one. Two hundred games at 60% is a signal. Ten is a hint. Any decent research tool shows the sample next to the number, the way StatsBench props list it as 60% (6/10) rather than a bare percentage.
We went deeper on this in what a 60% hit rate really means and on how much sample size is enough.
How do you calculate expected value on a prop?
Expected value compares your probability with the price. Multiply your win probability by the decimal odds, then subtract 1. Above zero means the bet makes money over a large sample. Below zero means it does not, no matter how good the stat looks.
Two quick examples:
- You think a prop wins 55% of the time and you get +100 (decimal 2.00). EV = 0.55 x 2.00 – 1 = +10%.
- Same 55%, but the best price you can find is -110 (decimal 1.91). EV = 0.55 x 1.91 – 1 = +5%.
Same opinion, half the edge, all because of 10 cents of price. That gap is why line shopping is the cheapest edge in betting. StatsBench tracks odds across roughly 60 sportsbooks and lists the best available price next to each prop, so you can see what one opinion is worth at each book.
The underlying idea is standard probability theory. Wikipedia’s page on expected value is a fine refresher, and the free EV calculator runs the numbers for you.
How much should you stake? Kelly, in one line
Kelly sizes the bet from the edge. The formula is (b x p – q) / b, where p is your win probability, q is 1 – p, and b is decimal odds minus 1.
Say you think a prop wins 55% of the time and you are getting +100. Then b = 1, p = 0.55 and q = 0.45, so the stake is (1 x 0.55 – 0.45) / 1 = 10% of your bankroll.
Full Kelly assumes your 55% is exactly right, and nobody’s estimate is that good. So most bettors use a fraction of it. StatsBench offers Safe, Balanced and Risky fractions of 0.15, 0.30 and 0.50 with a 5% bankroll cap, which keeps one bad estimate from doing real damage.
The full derivation sits on Wikipedia’s Kelly criterion page, and the Kelly calculator handles the fractional versions.
A worked example from a real StatsBench snapshot
Formulas get boring until they hit real lines. Here is a dated example from a StatsBench NFL snapshot (September 2026), used to show the math rather than to recommend a bet.
| Prop | Hit rate (sample) | Best price | Break-even | Listed edge |
|---|---|---|---|---|
| Jordan Love passing yards over/under 225.5 | 60% (6/10) | -110 | 52.4% | 3.8% |
| Christian Watson anytime touchdown over/under 0.5 | 60% (6/10) | +127 | 44.0% | 0.4% |
| Xavier McKinney tackles over/under 5.5 | 60% (6/10) | +105 | 48.8% | 0.8% |
Three props, the same 60% hit rate, three very different prices. The passing yards line needs a 52.4% win rate to break even. The touchdown price only needs 44.0%. The stat column alone would never tell you that, which is the entire point of doing the odds math first.
What this example does not say
Every sample here is 10 games, so each hit rate carries a standard error near 15 points. Treat those numbers as questions, not answers. The listed edge is a price comparison across books, not a forecast that the hit rate repeats. An edge of 0.4% on a small sample is noise with a number attached.
That is the honest way to use a reference like this: check the price math, check the sample, then decide. If you are working a passing yards market specifically, our guide to NFL passing yards props covers the matchup questions that come before any of this math. Official season stats live at NFL.com if you want to check a player’s history yourself.
Three habits that keep the numbers honest
- Write down the price you took. A pick without a price is not trackable. Our prop bet cheat sheet breaks down how to read a sheet so you log the same fields the books use.
- Treat small samples as questions. Ten games set the line. They do not settle it.
- Compare, then bet. Best price across books, every time. Most of a prop research tool’s value is doing that comparison before you click.
One last thing, and it matters more than any formula above: this is math for research, not a guarantee. Edges show up over hundreds of bets, not one Sunday. Bet within your means, 21+, and if it stops being fun, call 1-800-GAMBLER.
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Frequently Asked Questions
What is the most important number in prop betting?
The break-even percentage built into the price, also called implied probability. A -110 line needs a 52.4% win rate and a +105 line only needs 48.8%. Until your own number beats that threshold, the stat sheet does not matter.
How do I convert a hit rate into betting odds?
Divide the hit rate by one minus the hit rate, then multiply by 100. A 60% rate becomes 0.6 / 0.4 x 100, which is -150. Just remember the rate is an estimate, so a 6-of-10 sample can be off by roughly 15 percentage points.
What is a good sample size for a prop bet?
There is no magic number, but the error shrinks fast as the sample grows. A 60% rate over 10 games carries a standard error near 15 points, while the same rate over 100 games carries about 5 points. You want 100 games wherever possible.
Does a positive edge mean a prop is a guaranteed win?
No. An edge means the posted price looks better than the fair price. Over a large number of bets that is a real mathematical advantage, but any single bet can lose, and a small edge on a tiny sample is usually noise.