Compare n' Bet™
Compare n' Bet™
Five different ways to strip vig out of a sportsbook line. They give different answers. Here's which one to use, when, and why most public calculators get it wrong.
Open two devig calculators online, plug in the same line, and you'll get different fair odds. Sometimes the gap is a tenth of a percent. Sometimes it's 5 or 8 points on the same outcome. Both calculators are "right," they just have different assumptions baked in. And most of the time the person who built the calculator never thought about which assumption was correct for the market you're pricing.
There are five methods worth knowing: multiplicative, additive, power, Shin's, and logit. Each one assumes something different about how the book builds vig into the posted price. Pick the wrong method for the market you're pricing and your fair odds will be off by enough to flip a +EV bet into a -EV one. This guide goes through all five with the math, the worked examples, and which one to actually use for which kind of market.
All five methods start from the same place. For an n-way market with posted decimal odds o1 through on, you compute the implied probability of each outcome:
In a fair market, B equals 1 and there's no vig. Every real market has B above 1. A -110 / -110 moneyline sums to 1.0476, which is the standard 4.76% vig. A typical European soccer three-way at 2.40 / 3.40 / 3.10 sums to 1.0334, a 3.34% vig.
Every devig method is doing the same job: take the q values, strip out the over-round, and produce a set of true probabilities that add up to exactly 1. They just disagree about how the book built the over-round in the first place. That's the whole reason they give different answers.
This is what nearly every public devig tool uses. Each implied probability is divided by the booksum.
The assumption: the book spreads the vig proportionally. A favorite at q = 0.70 absorbs more vig in absolute terms than a longshot at q = 0.10, but they both pay vig at the same percentage rate. Symmetric, simple, fast.
Worked example. Two-way moneyline at -180 / +150 (decimal 1.556 / 2.500).
Where it breaks. Multiplicative misprices longshots in any market with favorite-longshot bias, which is the documented tendency for longshots to win less often than their posted probability says they should. Horse racing, MMA, and tennis all show it. The proportional assumption only holds when vig is genuinely symmetric, which it usually isn't. Multiplicative on a -150 / +130 line is fine. Multiplicative on a +500 longshot in a three-way market isn't.
Each outcome surrenders an equal absolute share of the vig.
n is the number of outcomes. A 5% vig in a three-way market means each outcome gives back 1.67 percentage points of implied probability. The favorite, the draw, and the underdog all surrender the same flat amount.
Worked example. Same -180 / +150 line as above.
Additive gives the favorite a higher fair probability (62.15%) than multiplicative did (61.65%) and the underdog a lower one. Half a point of disagreement on a near-symmetric line. That gap widens fast as prices get more lopsided.
Where it breaks. Additive can spit out negative probabilities for deep longshots in high-vig markets. A +5000 longshot at q = 0.0196 in a 6% vig three-way book gets assigned 0.0196 − 0.02 = −0.0004, which is nonsense. So additive shows up mostly as a quick mental sanity check, not as anyone's actual main method.
Instead of scaling each implied probability by the same factor, the power method raises each q to a power k, where k is chosen to make the sum equal exactly 1.
k is solved iteratively. There's no closed-form solution beyond the trivial two-way case. In practice, Newton's method converges in three or four steps from a starting point of k = 1.
The intuition: if vig is positive, B is greater than 1, so the q values are too high in aggregate. Raising them to a power between 0 and 1 shrinks them (each q is itself less than 1, so raising it to a fractional power makes it smaller) and pulls the sum down. Solve for the exact k that brings the sum to 1 and you get a calibrated set of fair probabilities.
Important detail: the power method shrinks small probabilities by a larger relative amount than large ones. A favorite at q = 0.70 raised to k = 0.95 becomes 0.7128, a 1.83% relative bump down. A longshot at q = 0.05 raised to the same k becomes 0.0556, an 11.2% relative bump up. So power assigns longshots a higher fair probability than multiplicative does, which actually goes the opposite direction from what favorite-longshot bias suggests.
Worked example. Three-way soccer market at 2.40 / 3.40 / 3.10.
The values above show the iteration in motion. A real solver lands at k ≈ 1.034 in three or four steps, and the final probabilities are p1 = 0.4032, p2 = 0.2826, p3 = 0.3142.
Where it breaks. Power is symmetric in a different sense than multiplicative. It works well when longshots are overbet (most racing, most combat sports), because raising the small q values to a power above 1 reduces them. It doesn't work well when the bias goes the other direction, like in soccer markets where the draw is slightly underbet.
Hyun Song Shin published this in 1992. It's an explicit model of how a bookmaker prices when they're worried about informed bettors. The setup: the book sees two kinds of customers, uninformed (who bet at posted prices) and informed (who only bet when they have an edge). To protect against the informed bettors, the book shades prices toward longshots, since the assumption is that informed action lands on longshots more often. Shin's method backs out a parameter z that represents the proportion of insider action and returns probabilities consistent with that model.
z is solved numerically. For a typical market, z runs from about 0.01 (efficient market, very little insider proportion) to 0.10 (heavy favorite-longshot bias). Larger z means the book is shading more aggressively against longshots, so Shin-adjusted longshot probabilities come out lower than the raw q values would say.
Worked example. A two-way market at -200 / +180 with a 1.85% vig fitted with Shin.
For comparison, multiplicative on the same market gives p1 = 0.6512 and p2 = 0.3488. Shin gives the favorite a higher probability (0.6557 vs 0.6512) and the longshot a lower one (0.3443 vs 0.3488). The disagreement is 0.45% on a near-symmetric line. It grows fast as prices get more asymmetric.
Where it works. Shin is the published academic standard for racing, fights, and any market with documented favorite-longshot bias. When the bias is real and present in the data, Shin gives more accurate fair probabilities than any of the simpler methods.
Where it breaks. Apply Shin to a market that doesn't have favorite-longshot bias (an efficient two-way American sports moneyline at a sharp book, for example), and it adjusts in a direction the data doesn't support. In those markets, plain multiplicative is closer to right.
Logit takes a different parametric route. You transform each q into log-odds, subtract a constant, then transform back. The constant is chosen so the resulting probabilities sum to 1.
c is solved numerically. The logit transform spreads probabilities out near 0.5 and compresses them near 0 and 1, so subtracting a constant in log-odds space has a non-uniform effect when you map back to raw probability. Some quant shops prefer logit because it's the standard form for binary regression and it plugs cleanly into model outputs.
Worked example. Same -180 / +150 line.
Logit puts the favorite at 63.05%, higher than additive (62.15%) and higher than multiplicative (61.65%). On three-way markets the gaps get bigger.
Real example. Soccer match: Manchester City home, draw, Liverpool away. Posted prices 1.85 / 3.80 / 4.20. Implied probabilities and booksum:
Apply each method:
The home team's fair probability ranges from 0.5176 to 0.5293 depending on which method you use. That's a 1.17 point swing. In fair-odds terms, you're picking between a fair line of +93 (decimal 1.932) and +89 (decimal 1.889). If you're using this for arbitrage or to evaluate posted prices for value, the choice of method directly determines whether a bet is +EV or -EV.
The away team is worse. Fair probability range is 0.2155 to 0.2308. Translated to fair odds, that's the difference between +334 and +364. Same three posted prices, five methods, and two of them disagree about whether the away side is value.
There's no single correct method. The right choice is empirical: use the method that, on the market you're pricing, produces fair probabilities that match realized outcomes most closely.
If you want to commit to a method empirically, here's the procedure:
BS = (1/N) Σ (pi − outcomei)2, where outcome is 1 if that side hit and 0 otherwise. Lower is better.LL = −(1/N) Σ outcomei · ln(pi), which penalizes confident wrong predictions more harshly.The published comparisons (Strumbelj 2014, Clarke et al. 2017, Cortis 2015) consistently find that Shin beats multiplicative and additive on horse racing, while multiplicative and power are competitive on US two-way moneyline markets. Soccer three-way markets split between Shin and power depending on era and league. Tennis usually favors Shin.
If you're building this into your own tool or model, three things worth flagging:
Numerical stability. Shin's method involves a square root that can produce a small negative discriminant on badly-fit prices. When that happens, fall back to multiplicative. Power's Newton iteration can fail to converge on high-vig markets; bound the initial guess and switch to bisection if Newton diverges.
Booksum normalization. Some published descriptions of Shin normalize qi2 by B2 instead of by B. Both versions show up in the literature. Cortis (2015) has the canonical derivation, and the formula in this guide matches that one. If your Shin implementation disagrees with a reference calculator, the normalization choice is the first thing to check.
Soccer draws. The draw in soccer is empirically slightly underbet, which means soccer markets contain a mild bias in the opposite direction from standard favorite-longshot. Shin assumes longshots are overbet, so on soccer it's technically misspecified. Both Shin and power tend to over-correct draws downward. The market-specific fix is to fit the model on draws separately, or to use an asymmetric parametric form. Most public calculators ignore this and just use vanilla Shin.
The size of the disagreement between methods sets a ceiling on the edge any devig-based strategy can find. If two respected methods give probabilities that differ by 1.5%, any bet showing a 1.5% edge under one method might be flat or negative under another. You either need to know which method is correct for the market you're pricing, or you have to accept that your EV calculation has a 1% to 2% uncertainty band baked in. That uncertainty often eats your edge.
For arbitrage and middling, the choice of method matters less, because those strategies bet both sides and lock in a result regardless of where the fair line actually sits. For directional value betting, where the whole premise is "this posted price is better than fair," the method directly determines whether the bet is on or off.
The professional habit: pick a method per market based on calibration, lock it as your default, re-test once a year. The amateur habit: use whatever the first calculator on Google does. Which is multiplicative. Which is wrong often enough to matter.
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