Power method, multiplicative, and additive — the three standard vig-removal techniques agree on tight markets and disagree, sometimes dramatically, on lopsided ones. A walkthrough of the three methods, the specific pitfalls each one introduces, and a short Python snippet that lets you compare them side by side on your own prices.
Vig removal sounds like a single thing — strip the bookmaker's margin from a price to recover the underlying probability — but it is actually a family of three standard techniques that produce different answers. On most markets the differences are small enough to ignore. On the markets where the difference is biggest, ignoring it is the modeling mistake that produces the worst forecasts.
Why three methods exist
The premise of vig removal is simple. A sportsbook posts prices on both sides of a market that sum to more than 100% implied probability. The 'extra' percentage above 100% is the overround (vig). To recover the book's underlying estimate of each side's probability, you have to redistribute the overround back to the two probabilities. There are three reasonable ways to do that, and they correspond to three different assumptions about how the book embedded the margin in the first place.
The methods are equivalent on a perfectly symmetric market (50/50 sides at equal prices). They start to diverge as the market gets lopsided, because each method makes a different assumption about how the book skewed the margin distribution between favorite and underdog. The choice of method is a modeling choice, and the right answer depends on what you believe about how the book priced.
Method 1 — Additive (split the overround evenly)
The simplest method. Compute the overround (sum of implied probabilities minus 100%). Subtract half of the overround from each side's implied probability.
Example: a market at -150 (60.0%) / +130 (43.5%) sums to 103.5% — overround is 3.5%. Additive removal subtracts 1.75% from each side, producing fair prices of 58.25% / 41.75%. The method's appeal is its simplicity; the cost is that it implicitly assumes the book added the margin in equal absolute amounts to each side, which is rarely how books actually price.
Method 2 — Multiplicative (scale by 1 / sum)
Divide each side's implied probability by the sum of both implied probabilities. This forces the two sides to sum to 100% while preserving their ratio.
Same example: 60.0 / 103.5 = 57.97% and 43.5 / 103.5 = 42.03%. Note the difference from additive: the favorite is slightly lower (57.97 vs 58.25), the underdog is slightly higher (42.03 vs 41.75). The method assumes the book added margin proportionally to each side's underlying probability — that is, the favorite got a bigger absolute margin loaded on it than the underdog did.
Multiplicative is the most commonly used method in published betting models because it has a clean closed form and is reasonable for tight markets. It is also the method that misprices lopsided markets the worst, because the proportional-loading assumption breaks down at the extremes.
Method 3 — Power (solve for an exponent k)
Find a power exponent k such that p_home^k + p_away^k = 1. This is the academic standard, related to the Shin family of corrections in horse-racing literature. It produces fair probabilities that more closely match observed historical outcomes on lopsided markets, at the cost of requiring a numerical solver rather than a closed-form calculation.
Same example: solving for k yields approximately 0.99 on this market, producing fair probabilities of roughly 58.1% / 41.9%. The result sits between additive and multiplicative for tight markets and diverges from both for lopsided markets, where it typically pushes the favorite's fair probability higher than multiplicative would and lower than additive.
| -110 / -110 (sum 104.76%) | Additive 50.0% | Multiplicative 50.0% | Power 50.0% |
|---|---|
| -150 / +130 (sum 103.50%) | Additive 58.25% | Multiplicative 57.97% | Power 58.05% |
| -300 / +250 (sum 103.57%) | Additive 73.21% | Multiplicative 72.36% | Power 72.95% |
| -600 / +450 (sum 103.89%) | Additive 83.84% | Multiplicative 82.51% | Power 83.37% |
| -1500 / +900 (sum 103.75%) | Additive 92.85% | Multiplicative 90.36% | Power 92.07% |
| -3000 / +1500 (sum 103.99%) | Additive 95.84% | Multiplicative 92.94% | Power 94.78% |
The pattern is consistent: on tight markets the methods agree within a fraction of a point, but on a -3000 favorite the gap between multiplicative and additive is 2.9 percentage points. That gap is the entire modeling decision — pick the wrong method on a lopsided market and your fair-value estimate is off by enough to wipe out any actual edge you might have.
Mistake 1 — Defaulting to multiplicative on every market
Multiplicative is the most popular default because it has a closed form and is easy to teach. It is also the method that systematically underweights heavy favorites' true probability. A modeler who applies multiplicative to a -1500 line is producing a 90.36% fair-value estimate when historical outcomes on similar lines suggest the true rate is closer to 92-93%. The 2-3 point gap is the difference between a marginally-positive and a marginally-negative expected-value bet, on a market where the bettor's confidence is already concentrated.
The fix is not to abandon multiplicative — it is the right choice for most markets — but to use power on heavy-favorite lines (anything below -500 on a 2-way market). The cost is a numerical solver in your code; the benefit is fair-value estimates that match empirical reality.
Mistake 2 — Ignoring the overround structure
The same overround percentage can be distributed across the two sides very differently depending on the book and the market type. A 3.5% overround on an NFL spread might be loaded 1.75/1.75 (symmetric), 2.5/1.0 (favorite-heavy), or 1.0/2.5 (underdog-heavy). The method you choose for vig removal should depend on which loading is actually being used.
How to tell: compare the book's price to the price at a market-maker book (Pinnacle where available, Circa for sharp-friendly action). The gap between the two prices on each side is roughly the asymmetric margin loading on this book's quote. If the favorite side is mispriced by 1.5% and the underdog by only 0.5%, the book is loading margin onto the favorite — and your multiplicative removal will be biased in the wrong direction.
Mistake 3 — Not adjusting for sport-specific anchor effects
Different sports have different historical relationships between American odds and true probability, even after vig removal. NFL spreads have well-documented push concentrations at key numbers (3, 7, 10) that distort the implied probability around those margins. NBA totals have a known historical bias that compounds with vig removal in subtle ways. MLB moneylines have asymmetric volatility that makes the multiplicative method's proportional assumption particularly weak for heavy favorites.
The fix is to calibrate your vig-removal output against historical outcomes for the sport and market type you are modeling. A power-method output of 92.07% on a -1500 NHL moneyline is not the same as 92.07% on a -1500 NFL moneyline — the historical hit rates are different, and your model should account for that with a sport-specific calibration step downstream of the vig removal.
A short Python comparison
The simplest way to internalize which method is least bad for the lines you actually care about is to run all three on your own prices and look at the divergence. The snippet below takes a pair of American odds and returns the fair probability under each method. Run it on 20 markets you have tickets on; if the three methods agree to within 0.5%, you can use any of them. If they diverge by more than 1.5%, you have a modeling decision to make.
Implementation outline (Python, ~15 lines using scipy for the power-method solver). The function takes two American-odds inputs, converts them to implied probabilities, then computes additive, multiplicative, and power outputs. The power solver uses scipy.optimize.brentq bracketed on (0.5, 2.0); for the markets covered in this article, k is always within that range and the solver converges in milliseconds. Output is a dictionary keyed by method name, each value a (favorite, underdog) probability tuple summing to 1.0.
Pointing the function at your own market data is a 5-minute exercise that will teach more about vig-removal model selection than reading another 2,000 words on theory. The output for a -1500 / +900 input reproduces the bottom row of the table above within rounding.
When each method is least bad
- Multiplicative: tight markets (sides within -150/+130), high-volume liquid markets where the book's pricing model is itself near-optimal, and as a default when you do not have a strong prior about margin loading.
- Power: heavy favorites (-500 and below), thin markets where the book may be loading margin asymmetrically, and any market where you have empirical evidence that historical hit rates on heavy favorites systematically beat multiplicative-implied probabilities.
- Additive: only as a sanity check. The implicit assumption (equal absolute margin on both sides) is rarely accurate, and the method's main use is to bound the other two methods' outputs.
Why not always use the power method since it is closest to empirical reality?
Two reasons. First, the power method requires a numerical solver, which is slower and adds dependency complexity to model pipelines that may run thousands of computations per minute. Second, on tight markets the power method is no more accurate than multiplicative — the extra computational cost buys no extra accuracy. The right approach is to use multiplicative as default and switch to power when the favorite price exceeds a threshold (typically -500) where the methods are known to diverge.
What about the Shin method — should I be using that instead?
The Shin method extends the power approach by also estimating the probability of insider trading in the market, which adjusts the implied probabilities further. It is more accurate than basic power on horse-racing and thin futures markets where insider information is structural. On standard sportsbook spread, total, and moneyline markets, the marginal accuracy improvement over the power method is small (typically 0.2-0.5 percentage points) and the additional parameter estimation is fragile. For most US sports modeling work, the basic power method is the right stopping point.
How do I validate which method works best for my data?
Pull 2-3 seasons of closing-line data on the sport and market type you care about, apply each of the three methods to recover fair-value probabilities, then compare those fair-value estimates to actual hit rates in the same dataset. The method with the lowest calibration error (typically measured by Brier score or log-loss against actual outcomes) is the right default for that sport. The exercise takes a day of work and produces a sport-specific answer that no general article can give you.
Vig removal is a small piece of the modeling pipeline, but it is the piece where small errors compound into the headline numbers your model produces. The bettor who treats it as a single function and never questions which method they are using is leaving 1-3 percentage points of accuracy on the table for every lopsided market they price. The bettor who runs the three-method comparison on their own data and picks consciously is doing the work that separates a model with edge from a model that almost has edge.