De-vig methods compared: what 725,000 results say
When you de-vig a price, you have to decide how to split the vig between the favorite and the underdog. Take the same share off each (multiplicative)? The same number of points (additive, or Shin in a two-way market)? Load it onto the longshot (power)? On a big favorite the choice moves the no-vig price by 20 cents or more. We scored each de-vig method against 725,000 results. The short answer: power was most accurate on Pinnacle’s sharp moneylines and on soccer 1X2, multiplicative on US-league moneylines at retail books, and on spreads and totals near even money the method makes no difference.
The short answer: the most accurate de-vig method by market, from 725,000 results
- Sharp moneylines (Pinnacle, mostly tennis)PowerHigh
- Soccer 1X2PowerHigh: the clearest result in the study
- US-league moneylines at retail booksMultiplicativeModerate: the NBA drives it
- Juiced and alternate spreads and totals (retail)Power (tied for best)Moderate
- Spreads and totals near even moneyAnyNo difference
- ExchangesAnyNo difference
To try them on your own prices, the no-vig calculator switches between multiplicative, additive, Shin and power.
Three de-vig methods: multiplicative, additive (Shin) and power
Every two-way price adds up to more than 100% once you convert it to implied probabilities. The extra is the book’s margin. Removing it (de-vigging, often written devig) is easy; deciding which side it came from is the hard part. There are really only three answers in a two-way market:
Worked exampleMoneyline −300 / +240. Implied: 75.0% + 29.4% = 104.4%, so there are 4.4 points of margin to remove. The three methods disagree about the underdog:
Multiplicative takes the same share off each side. Divide each probability by the total and you are done.
Additive takes the same number of percentage points off each side. Two other well-known methods, Shin’s and MPTO, give exactly the same answer in a two-way market, so we treat them as one; a fourth, the odds-ratio method, lands almost on top of it.
Power raises each probability to the same exponent, chosen so they sum to 100%. It takes the most off longshots of the three.
If you were offered +265 on that underdog, multiplicative says it is a good bet and power says it is a bad one. On a −110 / −110 spread, all three say +100.
In formulas, with implied probabilities pA and pB, side A’s no-vig probability is:
multiplicative: pA / (pA + pB)
additive: pA − (pA + pB − 1) / 2
power: pAk, with k chosen so pAk + pBk = 1
Show the numbers
| Method | Off fav. | Off dog | No-vig dog | No-vig price |
|---|---|---|---|---|
| Multiplicative | 3.17 | 1.24 | 28.2% | −255 / +255 |
| Additive (= Shin) | 2.21 | 2.21 | 27.2% | −268 / +268 |
| Power | 1.69 | 2.72 | 26.7% | −275 / +275 |
It helps to see these as settings on one dial. Statisticians call it the Box-Cox family, with a single number, λ (lambda), for how the margin is split. At λ = 0 you get multiplicative, at λ = 1 additive, and at about 1.5 power. Above that the split takes even more off the longshot than power does. Fitting λ to results tells you which settings the data allows, which is a sharper question than which named method happened to win.
How we tested each de-vig method
The test set is 725,000 results from public odds datasets, each with closing prices and the final outcome. We split it by market type (moneylines, spreads, totals, soccer 1X2), by sport, by price range, and by sharp books (Pinnacle, Betfair Exchange) versus retail books.
Each method turns every price into no-vig probabilities, and we score those against what happened with log loss, which punishes confident misses hardest. The Brier score, a second standard yardstick, agreed with it every time either one found a clear difference. Every gap comes with a 95% interval from a paired bootstrap, shown in square brackets, so we can say when a difference is real and when it is noise. Anything we fitted, such as λ, was fitted on the earliest 60% of each dataset and tested only on the latest 40%. We also checked reliability: do underdogs priced at 10% actually win 10% of the time?
Differences are quoted in millinats, thousandths of a unit of log loss, per market. For scale, 0.42 millinats is roughly the difference between pricing that −300 / +240 underdog at +255 and pricing it at +275.
Which de-vig method is most accurate, market by market
Sharp moneylines (Pinnacle): power wins, and the tails are where it matters
Across 77.5k Pinnacle two-way markets (mostly tennis: 66.7k matches), power beat every other fixed method. Additive and Shin were worse by 0.09 millinats per market [0.03, 0.16], and multiplicative by 0.42 [0.26, 0.58]. The fitted dial setting was λ = 2.0 [1.5, 3.1]: power or stronger, never additive or multiplicative.
The gap lives in the tails. Near even, nothing separates the methods. From a 65% favorite upwards power pulls ahead, and at favorites of 85% or more multiplicative is worse by 2.48 millinats. In the reliability check, Pinnacle tennis underdogs in the 5–10% bucket won 5.6% of the time. Power predicted 6.2%, multiplicative 7.7%. Even power slightly overstates tennis longshots: Pinnacle’s favorite-longshot bias is at least as strong as power assumes. MMA closing prices from retail books (BestFightOdds) point the same way, with power beating additive by 0.26 [0.05, 0.47].
US-league moneylines at retail books: multiplicative does better
On 71.5k NFL, NBA, NHL and MLB closing moneylines from retail and consensus sources, underdogs won more often than power says. Multiplicative was better than power by 0.16 millinats [−0.02, 0.34], just short of a clear difference (the interval still includes zero), and additive by 0.12 [0.05, 0.20]. On the later seasons held out for testing, the gains grew to 0.38 [0.10, 0.68] and 0.21 [0.10, 0.34]. The fitted dial setting was λ = 0.4 [−0.4, 0.8], which rules out both power and additive.
Underdogs in the 10–15% bucket won 11.8% of the time; multiplicative predicted 12.7% and power 10.4%. The NBA carries most of the result (18.9k games, multiplicative better by 0.64 [0.05, 1.20]). It matches the “reverse favorite-longshot bias” economists have reported in US team sports (Woodland & Woodland on baseball and hockey): the public overbets favorites, so books shade the favorite’s price rather than load the dog.
Show the numbers
| Dog bucket | Sides | Observed [95%] | Mult. | Add. | Power |
|---|---|---|---|---|---|
| Pinnacle tennis | |||||
| 0–5% | 1,085 | 2.2 [1.5, 3.3] | 3.6 | 2.8 | 2.3 |
| 5–10% | 3,094 | 5.6 [4.9, 6.5] | 7.7 | 6.8 | 6.2 |
| 10–15% | 4,436 | 10.3 [9.5, 11.3] | 12.6 | 11.8 | 11.4 |
| 15–20% | 5,535 | 16.8 [15.8, 17.8] | 17.6 | 16.9 | 16.5 |
| 20–25% | 6,900 | 21.0 [20.0, 21.9] | 22.5 | 21.9 | 21.6 |
| 25–30% | 8,528 | 26.0 [25.0, 26.9] | 27.6 | 27.1 | 26.8 |
| 30–35% | 9,131 | 31.5 [30.5, 32.4] | 32.6 | 32.1 | 31.9 |
| 35–40% | 9,604 | 37.7 [36.8, 38.7] | 37.5 | 37.3 | 37.1 |
| 40–45% | 10,137 | 42.4 [41.5, 43.4] | 42.5 | 42.3 | 42.2 |
| 45–50% | 7,960 | 47.8 [46.7, 48.9] | 47.3 | 47.3 | 47.2 |
| US leagues, retail moneylines | |||||
| 5–10% | 789 | 7.2 [5.6, 9.3] | 7.8 | 6.4 | 5.4 |
| 10–15% | 1,505 | 11.8 [10.2, 13.5] | 12.7 | 11.3 | 10.4 |
| 15–20% | 2,047 | 18.3 [16.7, 20.1] | 17.7 | 16.5 | 15.8 |
| 20–25% | 2,902 | 21.9 [20.5, 23.5] | 22.7 | 21.8 | 21.3 |
| 25–30% | 4,481 | 27.6 [26.3, 28.9] | 27.7 | 26.9 | 26.6 |
| 30–35% | 7,591 | 32.2 [31.2, 33.3] | 32.7 | 32.1 | 31.8 |
| 35–40% | 13,726 | 38.2 [37.4, 39.0] | 37.6 | 37.3 | 37.1 |
| 40–45% | 18,322 | 42.7 [42.0, 43.4] | 42.6 | 42.4 | 42.3 |
| 45–50% | 18,552 | 46.9 [46.2, 47.6] | 47.4 | 47.4 | 47.3 |
Is it the market or the book?
Tennis lets us check, because the same matches were priced by both a sharp and a retail book. Bet365’s prices fit λ = 1.2 [1.1, 1.3]; Pinnacle’s fit λ = 2.1 [1.5, 3.3]. On identical events, the retail book loads proportionally more of its 6.9% hold onto favorites. So the US result is at least partly a retail-book effect, not something about US sports alone. That is why the right method depends on where the price came from, not just on the sport.
Spreads and totals: it only matters on juiced lines
When both sides are near even (inside about ±125), the method does not matter. On 160k near-even lines every method landed within 0.03 millinats of power, and the no-vig prices differ by less than a cent. Juiced and alternate lines (run lines, alt totals, soccer Asian handicaps, off-main over/unders) are different. On 225.4k retail lines the fitted setting was λ = 1.3 [1.0, 1.7], power was tied for best, and multiplicative was worse by 0.08 [0.02, 0.14]. A juiced spread is really a moneyline on “covers”, and these retail lines behave like retail moneylines outside the US.
Soccer 1X2: power beats Shin and every other method
This is the clearest result in the study. On 235.6k three-way soccer markets, power was best and separated from every other method, the only segment where that happened. Additive was worse by 0.05 [0.02, 0.08], Shin by 0.11 [0.06, 0.16] and multiplicative by 0.71 [0.56, 0.85]. It held on the test seasons too, and reliability for power is close to perfect: in the 5–10% bucket, outcomes won 6.0% of the time against 6.4% for power and 8.0% for multiplicative.
Exchanges: too little margin to matter
Betfair Exchange closing prices (1,788 markets) carry an overround of only 0.5%. Every method was within 0.07 millinats of every other. With so little margin to remove, the choice cannot matter.
Hybrids and blends: none beat the simple per-market choice
We also tried mixing methods: averaging power with Shin or with multiplicative, switching from multiplicative to power once the favorite passes 70%, and picking the best method per segment from training data. The switch tied power on sharp data (+0.01 [−0.03, 0.06]) and lost on 1X2. None of them beat the simple per-market choice out of sample, so none earned its complexity.
Show the numbers
| Market | n | λ [95%] |
|---|---|---|
| Sharp: Pinnacle closing prices | ||
| Tennis, ATP + WTA | 66,669 | 2.1 [1.5, 3.3] |
| Tennis, ATP | 38,423 | 2.0 [1.2, ≥ 4.0] |
| Tennis, WTA | 28,246 | 2.1 [1.5, 3.8] |
| MLB moneyline, 2016 | 2,461 | 1.4 [≤ −2.0, ≥ 4.0] |
| Retail, outside US leagues | ||
| UFC moneyline | 6,891 | 2.5 [1.3, ≥ 4.0] |
| Tennis, Bet365 | 75,033 | 1.2 [1.1, 1.3] |
| Soccer over/under 2.5, Bet365 | 156,615 | 1.5 [1.1, 1.9] |
| All retail spreads and totals | 225,413 | 1.3 [1.0, 1.7] |
| Retail, US-league moneylines | ||
| US leagues pooled | 71,504 | 0.4 [−0.4, 0.8] |
| NBA | 18,941 | 0.1 [≤ −2.0, 0.7] |
| NHL | 19,281 | 0.2 [≤ −2.0, 2.1] |
| MLB | 27,939 | 1.5 [−0.5, ≥ 4.0] |
| NFL | 5,343 | 1.2 [≤ −2.0, 3.5] |
Which de-vig method vigged uses, and why
vigged’s main no-vig price pools sharp sources: Pinnacle, Circa, Polymarket (its international and US books count as one source) and Kalshi. Each source is de-vigged on its own, then pooled by weight for freshness, liquidity and bid/ask spread. The study confirmed every default in that recipe:
- Power for sharp moneylines, spreads and totals, and power across all three outcomes in soccer 1X2. That is where power was right or tied for right.
- Multiplicative for exchange midpoints (Polymarket, Kalshi). Their tiny overround is a bid/ask spread, and no method beat another.
- Edges are judged against the most cautious method. EV on the +EV bets page is always measured against the lowest of the multiplicative, Shin and power no-vig probabilities for the side being bet, so the choice of method can never create an edge on its own. On a heavy favorite or a longshot that can sit below the no-vig price the board shows, so an edge's tooltip names the cautious price and gives the EV against the shown one too. That rule also covers rare cases the data cannot settle, such as US underdogs under 5%: only 85 such sides in the US retail data, far too few to separate the methods.
- Live markets keep the same methods. No live odds history with results exists to test them against.
One change came out of the study: the books backup. When no sharp source quotes a game, vigged shows a Low-confidence no-vig price taken from the median of the US retail books. On two-way moneylines in the NFL, NBA, MLB and NHL that price now uses multiplicative, because it is exactly the price type where power scored worst. College football, college basketball and the WNBA follow the pro leagues by assumption. Everything else on the books backup stays on power. A book’s prices also count toward the backup only if its own margin is between 0% and 15% (25% for three-way markets), which keeps stale or broken quotes out of a median that may rest on just two books. Edges still use the cautious rule above, so they do not move.
Before switching, we checked whether a blend would do better. On the 28.6k held-out US games, no mix of power and multiplicative beat plain multiplicative. A 50/50 blend was worse by 0.133 millinats [−0.006, 0.274], and pure power by 0.426 [0.134, 0.717].
Show the numbers
| Weight on power | ΔLL vs mult. [95%] |
|---|---|
| 0 (multiplicative) | 0 |
| 0.1 | +0.015 [−0.011, 0.042] |
| 0.2 | +0.036 [−0.018, 0.090] |
| 0.3 | +0.062 [−0.020, 0.145] |
| 0.5 | +0.133 [−0.006, 0.274] |
| 1 (power) | +0.426 [0.134, 0.717] |
| US-books median | Before (power) | After (multiplicative) |
|---|---|---|
| −110−110 | +100+100 | +100+100 |
| −150+130 | −140+140 | −138+138 |
| −170+150 | −161+161 | −157+157 |
| −300+240 | −275+275 | −255+255 |
| −500+380 | −454+454 | −400+400 |
| −1000+650 | −878+878 | −682+682 |
The full recipe for the no-vig price is on How no-vig odds work.
What the data could not settle
- Near-even spreads and totals: every method is within 0.03 millinats, so there is nothing to choose.
- Sharp juiced lines: Pinnacle’s MLB run lines and totals and its EPL Asian handicaps and over/unders came to only 8.2k markets, too few to separate the methods.
- Sharp US moneylines: the only sample was Pinnacle MLB 2016 (2.5k games), where every method landed within 0.02 millinats. Keeping power for sharp US prices rests on indirect evidence: the Pinnacle tennis results, power’s wins on MMA and soccer 1X2 prices, and the sharp-versus-retail gap measured in tennis.
- NFL, NHL and MLB retail moneylines individually are within noise. The pooled US retail result is driven by the NBA.
- College sports and live betting: no usable public odds history with results was available for them, nor for Polymarket or Kalshi prices.
- Whether the Polymarket US prices are asks or midpoints. If they are asks, additive would be the exact correction rather than multiplicative. That is a question about the data format, not something results can answer.
What would change our mind: about 20,000 Pinnacle NBA, NFL and NHL closing lines. If those fit well below power, with a λ interval that rules out power, the same switch to multiplicative would apply to the sharp no-vig price. We fixed that test before seeing any such data.
Data sources and references
vigged ran this study in October 2026, scoring the same de-vig code that computes the site’s live no-vig prices. Odds and results come from public datasets:
- football-data.co.uk: 38 soccer leagues, 2000–2026 (Bet365), plus Pinnacle and Betfair Exchange closing prices for the Premier League
- tennis-data.co.uk: ATP 2004–2019 and WTA 2007–2019, with Pinnacle and Bet365 prices on the same matches
- Pinnacle’s pinnacle.data R package: MLB 2016
- the SBR odds archive, as compiled by “The Closing Line” project: NBA and NHL 2007–2022, MLB 2010–2021
- nflverse: NFL 2006–2026
- the Ultimate UFC Dataset: UFC 2010–2026 (BestFightOdds closing prices)
Thanks to everyone who publishes this data for research. The methods draw on Shin (1993), Economic Journal 103; Štrumbelj (2014), International Journal of Forecasting 30(4); Clarke, Kovalchik & Ingram (2017), American Journal of Sports Science 5(6); and Woodland & Woodland on the favorite-longshot bias in baseball (1994, Journal of Finance 49(1)) and hockey (2001, Southern Economic Journal 67(4)). For the basics of removing the vig, start with no-vig odds explained, or try the no-vig calculator.
Frequently asked questions
Which de-vig method is most accurate?
It depends on the market. On sharp moneylines (Pinnacle tennis) and soccer 1X2, the power method scored best. On retail closing moneylines in US leagues, multiplicative did better, because underdogs won more often than power predicts. On spreads and totals near even money, every method gives the same answer.
Is the Shin method different from additive?
Not in a two-way market. With two outcomes Shin gives exactly the same no-vig probabilities as additive, which takes the same number of percentage points off each side, and the odds-ratio method lands within a hair of it. Shin and additive only part ways in markets with three or more outcomes, such as soccer 1X2.
What is the difference between multiplicative, additive and power de-vig?
Multiplicative takes the same share of the margin off each side, additive takes the same number of percentage points, and power takes the most off the longshot. On a −300 / +240 moneyline they give the underdog about +255, +268 and +275. On a −110 / −110 spread all three give +100.
Which de-vig method is best for soccer 1X2 odds?
Power. On 235,600 three-way soccer markets it scored best, the only market in the study where the winner beat every other method by a clear margin. Shin, a common choice for three-way markets, was worse by 0.11 millinats [0.06, 0.16], and multiplicative by 0.71 [0.56, 0.85]. In the 5–10% bucket, outcomes won 6.0% of the time; power predicted 6.4% and multiplicative 8.0%.
What is a worst-case de-vig?
Some de-vig calculators offer a worst-case option: work out the no-vig price several ways and keep the one least favorable to your bet. vigged does this for every edge. It takes the lowest of the multiplicative, Shin and power no-vig probabilities for the side being bet, so the choice of method can never create an edge on its own.
Why does vigged use different methods for different markets?
Because the evidence differs by market. Sharp books load more of their margin onto longshots, so power removes it best there. US retail books shade favorites instead, so multiplicative suits their prices. vigged uses power for sharp no-vig prices, multiplicative for exchange midpoints and for the US books backup on moneylines, and judges every edge against the most cautious of three methods, so the method alone can never create an edge.
Does the de-vig method matter for spreads and totals?
Hardly, when both sides are near even money. Across 160,000 near-even lines every method scored within 0.03 millinats of power, and the no-vig prices differ by less than a cent. It starts to matter on juiced and alternate lines, where power was tied for best on retail prices.
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