A sportsbook price carries two things at once: an estimate of how likely the outcome is, and the margin the book charges for taking your bet. Separate them and you know what a bet is actually worth. This page walks through the exact math Guru-frat runs on every line, using one game from today's board: the Chiefs at the Raiders.
PRESEASON During the Season 1 preseason the board runs on illustrative odds. The prices below show how the math works; they are not quotes from the books named.
Implied probability
Odds are a probability in disguise. Decimal odds are the total return per unit staked, stake included. American odds are the profit on a 100 stake when positive, or the stake needed to profit 100 when negative. Fractional odds are the profit per unit, so 5/2 is decimal 3.50. Convert any of them to decimal, take the reciprocal, and you have the implied probability.
Read it as a break-even rate: at +173, a bet on the Raiders only pays for itself over the long run if they win at least 36.63% of the time.
The bookmaker's margin
Add both sides together and you get more than 100%. The excess is the margin: bettors call it the vig or juice, books call it the overround or hold. It's how the book gets paid: whichever side wins, its backers are paid a little less than fair odds.
Guru-frat reports hold as the plain excess over 100%, computed the same way for every book and market so the numbers compare directly. Lower is better for you: the hold is a cost built into every price you take, win or lose. Strictly, a book whose action is balanced so it pays out the same whichever side wins keeps 1 − 1/(pA + pB) of the money wagered: 2.33% here rather than 2.38%. Both measures rank books in the same order.
Removing the vig
To get fair probabilities, the margin has to come out. Guru-frat uses the proportional method (also called multiplicative, or normalization): divide each side's implied probability by the total. Each side keeps its share, and the two now add up to exactly 100%.
The assumption is that the book spread its margin in proportion to each side's probability. It's transparent and you can check it by hand. On this game the alternatives covered further down land within about 0.5 percentage points of it.
Fair odds
Turn a fair probability back into a price and you have the no-vig line: what a book with zero margin would offer.
A fair two-way line is always a mirror image, here −180 / +180. Pinnacle's actual −192 / +173 is shaded on both sides: 12¢ worse than fair on the Chiefs and 7¢ worse on the Raiders. Together that's a 19-cent line, the margin in the units American-odds bettors quote.
Why Pinnacle is the reference
Any book's prices can be de-vigged. Guru-frat uses Pinnacle's because two things make them the most widely trusted public estimate of the true probability.
- Low margin. Pinnacle's model is high limits on thin margins, and the less margin there is, the less the de-vig method has to assume. On today's illustrative board, Pinnacle's moneyline hold averages 2.39% across 68 games, against 3.50% at DraftKings, 3.60% at FanDuel and 3.93% at BetMGM.
- A sharp market. Pinnacle is known for accepting large bets and for welcoming winning bettors instead of limiting them, so it moves its line when sharp money arrives. Its prices absorb information from the best bettors quickly, which is why its closing line is the usual benchmark for a fair price (see closing line value), and why Guru-frat flags a Pinnacle move of 10¢ or more within five minutes as steam (see line movement).
Pinnacle is the measuring stick, never the play. It is never listed as a bet on Guru-frat and you don't need an account there; it isn't licensed in many jurisdictions anyway. Every graded price comes from DraftKings, FanDuel or BetMGM. Whichever book you use, make sure it is licensed where you live.
From EV to a grade
With a fair probability in hand, any price can be scored. Expected value is the average profit or loss per unit staked, if the fair probability is right.
The best Raiders price on the board is BetMGM +199, better than the fair +180. At a fair 35.78%, that's an expected +7.0% per unit staked: grade S, Franchise play. The best Chiefs price, DraftKings −205, is worse than fair −180 and scores −4.4%: grade F. With a margin built into almost every line, most prices sit below fair: 1,123 of the 1,196 soft-book prices on today's illustrative board grade F.
- SFranchise playEV 6%+
- AAll-StarEV 4–6%
- BStarterEV 2.5–4%
- CBenchEV 1–2.5%
- DPractice squadEV 0–1%
- FFadeEV below 0
Thresholds, colors and what each grade asks of you are in Grades explained.
Worked example: Chiefs at Raiders
Every step on one card, straight from today's board. Pinnacle sets the fair price; the soft books are scored against it.
| Step | KCChiefs | LVRaiders |
|---|---|---|
| 1Pinnacle price | −192dec 1.521 | +173dec 2.730 |
| 2Implied probability | 65.75% | 36.63% |
| 3Pinnacle hold | 2.38%65.75% + 36.63% = 102.38% | |
| 4No-vig probability | 64.22% | 35.78% |
| 5Fair odds | −180dec 1.557 | +180dec 2.795 |
| 6Best soft-book price | DK−205 | MGM+199 |
| 7EV and grade | F−4.4% | S+7.0% |
Every book's hold on this game
| Book | KC | LV | Implied | Hold |
|---|---|---|---|---|
| DKDraftKings | −205 | +168 | 104.53% | 4.53% |
| FDFanDuel | −215 | +176 | 104.49% | 4.49% |
| MGMBetMGM | −205 | +199 | 100.66% | 0.66% |
| PINPinnacle | −192 | +173 | 102.38% | 2.38% |
The three soft books average 3.22% on this moneyline, against 2.38% at Pinnacle. BetMGM looks cheapest at 0.66%, even below Pinnacle, but that isn't generosity: its Raiders price (+199) is out of line with the market, and that one stale price is the S-grade play. A hold that's suspiciously low on one book is often the first sign of an edge (see stale prices).
Other de-vig methods
The proportional method assumes margin is spread in proportion to probability. Bettors tend to overpay for longshots (the favorite-longshot bias), so books can load more of their margin onto the underdog. Two common methods account for that:
- Power. Raise each implied probability to the same power
k, chosen so the results add up to 100%. Small probabilities shrink proportionally more. - Shin. Models the margin as the book's protection against bettors with inside information, which also lands hardest on longshots. On a two-way market it gives the same answer as subtracting half the hold from each side (the additive method).
| Method | fair | EV at +199 | Grade |
|---|---|---|---|
| ProportionalGuru-frat | 35.78% | +6.97% | S |
| Shinmatches additive | 35.44% | +5.96% | A |
| Power | 35.27% | +5.47% | A |
The three methods disagree by only 0.5 points of probability on the Raiders, but EV multiplies that by the decimal price: at BetMGM +199 (decimal 2.990) the choice of method moves EV by 1.5 percentage points, enough to change the grade (S or A). The gap grows with the hold and with how lopsided the line is, which is one more reason to de-vig the tightest market available. Of the three, proportional is the most generous to the underdog, so if you mostly back longshots, treat a play sitting right on a grade boundary with extra care.
Three-way markets, like soccer's home, draw or away, spread the margin across three prices, and the choice of method matters more; power and Shin are common choices there. Every market Guru-frat grades today is two-way (moneylines, spreads and totals), so the proportional method is used throughout.
Keep going
In the app, Play-by-Play lists each +EV price as it appears, graded against the no-vig line, alongside arbs, middles and steam. Game Center charts every book against the fair price, game by game. Pricing lists which grades each league unlocks.