Bookmaker Margin and Fair Odds: How to Remove the Vig (4 Methods Compared)

Walk into any betting shop or open any app and every price on the screen has a little something baked in. You won't find it written down. There's no line on your slip marked "fee". But it's there on every selection in every market, every Saturday, and over a season it decides whether you're playing a fair game or a loaded one.

That something is the bookmaker's margin. Call it the overround, the vig, vigorish or juice; it's all the same thing. The bookie prices every outcome a touch shorter than it should be, so the book makes money whatever the result.

You can reverse it, though. Remove the vig and what's left is the fair odds: the bookmaker's honest read on each outcome's chances, and the number every serious punter should be measuring their bets against. We'll work out the margin, show why it lands harder on some outcomes than others, then run four ways of stripping it out on one match so you can see exactly where they agree and where they split.

Every decimal price is a probability in disguise. Divide 1 by the odds and you've got the chance the bookmaker is implying (our probability in sports betting guide covers the conversions in more depth). Fractional prices convert by dividing and adding one, so 6/4 becomes 2.50, which implies a 40% chance.

In a perfectly fair book those implied chances add up to exactly 100%. The classic football example is Evens, 2/1 and 5/1:

Evens (2.00):  1/2.00 = 0.500
2/1   (3.00):  1/3.00 = 0.333
5/1   (6.00):  1/6.00 = 0.167
Total                = 1.000   ->  a fair book, no margin

You'll never see a real book like that. Trim each of those prices and the total creeps above 100%. The excess is the margin.

Two-way markets

Tennis match odds, Asian handicaps and goal lines usually have two outcomes. Here's a tight two-way market:

Player A 1.926:  1/1.926 = 0.5192
Player B 2.020:  1/2.020 = 0.4950
Total                    = 1.0143  ->  margin of about 1.4%

That's a sharp price. The everyday version is 1.91 on both sides (roughly 10/11), which adds up to 104.71%, a 4.71% margin.

Three-way markets

Football's 1X2 market works the same way, with a draw in the middle:

Home 2.00:  1/2.00 = 0.500
Draw 3.60:  1/3.60 = 0.278
Away 3.60:  1/3.60 = 0.278
Total              = 1.056   ->  margin of 5.6%

That total is the booksum. Take away one and you have the margin. That's the whole calculation, and after a few goes you'll be doing it in your head off a price board.

Margins vary by bookmaker, by league and by market, and they've been quietly creeping up.

Low-margin specialists like Pinnacle price Premier League 1X2 books at around 2%. The industry average sits nearer 6%, and some bookmakers push the booksum as high as 110%, a 10% toll on a single match. Stretch that over a season and the gap between paying 2% and paying 10% is enormous.

League matters just as much. The further down the pyramid you go, the thinner the betting interest and the fatter the margin:

Two things jump out. Top leagues typically sit between about 4% and 5%, while second tiers and below often run to 7% or more. And every single row has gone up over five seasons, with the Premier League toll climbing from 4.12% to 4.65%. Our guide to the best leagues for betting odds digs into where the cheapest markets live.

Margins don't add up across an acca. They compound. If each leg of a four-fold returns roughly 95p in the pound, the whole bet returns about 0.95 × 0.95 × 0.95 × 0.95, or 81.5p in the pound. Four small tolls become one big one. No wonder the bookies love an acca.

A bookmaker could take the same percentage off every outcome. Most don't, and the reason is one of the oldest patterns in betting.

Punters love a longshot. The favourite-longshot bias describes how outsiders get over-bet relative to their real chances while favourites are under-bet, something racing has documented for decades. If the public will happily take 6.50 about a horse or a team that should be 7.50, the bookmaker has no reason to offer more, so the bigger prices tend to carry a bigger slice of the margin. Our favourite-longshot bias guide covers the psychology behind it.

There's a sharper reason too. In 1992 the economist Hyun Song Shin published a model in the Economic Journal built on one simple worry: some of the money coming in belongs to insiders who know more than the bookmaker does. A longshot is where an insider does the most damage, because a winning bet at big odds costs far more than one at odds-on. So the bookie protects itself by shading the outsiders hardest.

Both explanations point the same way. On a typical football coupon the favourite is the cheapest bet in the market and the outsider is the dearest. That matters when you strip the margin out, because the method you pick decides who you think is paying it.

First, the notation. Each raw implied probability is q = 1/odds. Add them up to get the booksum S, and the margin is M = S − 1. There are n outcomes, and p is the fair probability we're after.

1. Multiplicative (proportional)

The simplest and the most widely used. Divide each implied probability by the booksum:

p = q / S

It assumes every outcome is overpriced by the same proportion, so every bet "costs" the same. Quick and clean, but blind to the favourite-longshot bias.

2. Additive (equal margin per outcome)

Take the same slice of probability off every outcome:

p = q − M / n

A longshot has less probability to begin with, so losing the same slice hits it proportionally harder. You'll also see this sold as Differential Margin Weighting, popularised by Joseph Buchdahl, which applies the margin in proportion to the odds. Do the algebra and it boils down to exactly the same formula, so it's one method wearing two hats. The catch is that on very long odds it can spit out a negative probability, which is plainly nonsense.

3. Power

Find a single exponent k that makes the probabilities add up to one:

find k such that  q1^k + q2^k + q3^k = 1
then              p = q^k            (k > 1 when there's a margin)

Raise a small number to a power and it shrinks proportionally more than a big one, so outsiders lose more of their implied chance. It never produces a probability below zero or above one, and a few lines of code will find k for you.

4. Shin's method

This one is built on Shin's insider model. You solve for z, the model-implied share of insider money, so that the fair probabilities sum to one:

p = ( sqrt( z^2 + 4(1 − z) · q^2 / S ) − z ) / ( 2(1 − z) )

It looks fearsome, but a computer finds z in milliseconds. On a two-way market Shin and additive give identical answers. Add a third outcome and they part company.

Time to run all four on a single market. Picture a big Premier League favourite at home: Home 1.55 (11/20), Draw 4.20 (16/5), Away 6.50 (11/2). These are illustrative prices, the sort you'll see most weekends.

Home 1/1.55 = 0.6452
Draw 1/4.20 = 0.2381
Away 1/6.50 = 0.1538
Booksum S   = 1.0371   ->  margin of 3.71%

Now strip it out:

Look at the away column. The fair price on the outsider runs from 6.74 to 7.07 depending on the method, a swing of about 5%. On the favourite, the methods sit less than 2% apart. Your choice of method barely matters for the jolly and matters a lot for the longshot.

Flip it round. If each method's fair probabilities are right, what does a £1 bet on each outcome cost you?

• Multiplicative says every bet costs the same: −3.58% on the home win, the draw and the away win alike.
• Shin says the home win costs −2.34%, the draw −4.80% and the away win −6.88%.
• Additive goes further: −1.92% on the home win, −5.19% on the draw and −8.04% on the away win.

That's the favourite-longshot bias in plain numbers. Under the methods that allow for it, backing the 6.50 shot costs you roughly three to four times what backing the 1.55 favourite does. Same match, same bookmaker, very different toll.

Go back to that 1.91/1.91 two-way market. Every method gives fair odds of exactly 2.00 on both sides, because the methods only disagree when the prices are unbalanced. On a level handicap or a coin-flip tennis match, plain divide-by-the-total is all you need.

Erik Štrumbelj of the University of Ljubljana tested this properly. He took final pre-kick-off odds from Betfair and 13 fixed-odds bookmakers, including Bet365, Ladbrokes, bwin and Unibet, across 37 competitions in five team sports, football among them. Shin's method produced the most accurate probabilities in 217 of the 412 bookmaker-and-competition pairs he examined. He also found the advantage shrinks as markets get bigger, which makes sense: the more money in a market, the less room there is for distortion.

A second study, by Clarke, Kovalchik and Ingram in 2017, threw the power method into the mix. Across three large bookmaker datasets in three sports, they found it "universally outperforms the multiplicative method and outperforms or is comparable to the Shin method". It never produces impossible probabilities, either.

Here's where we land:

• For a quick look, multiplicative is fine. On a balanced market it's near enough.
• For anything you're staking real money on, use power or Shin. They respect the favourite-longshot bias, and the evidence says they're more accurate.
• On big favourites and longshots, steer clear of multiplicative. That's exactly where it goes wrong, and exactly where the value questions get asked.

Whichever you choose, stick with it. Consistency beats fiddling. The free Python packages shin and penaltyblog both do the heavy lifting, or you can roll your own. The power method takes a dozen lines:

def power_devig(odds):
    q = [1 / o for o in odds]
    lo, hi = 1.0, 2.0
    for _ in range(60):              # bisection on k
        k = (lo + hi) / 2
        if sum(p ** k for p in q) > 1:
            lo = k
        else:
            hi = k
    return [p ** k for p in q], k

power_devig([1.55, 4.20, 6.50])      # k comes out at about 1.0417

This is where de-vigging earns its keep. Fair odds are the foundation of value betting, and there are three practical ways to put them to work.

Test your own view against the right number

Say your model gives the home side in our example a 66% chance. Your expected value at 1.55 is:

EV = odds × your probability − 1
   = 1.55 × 0.66 − 1
   = +2.3%

Drop your estimate to 64% and it turns into −0.8%, because the break-even point is 1/1.55, or 64.5%. Always compare your estimate with the break-even of the price you can actually get, not the fair price. The fair odds tell you what the market believes. The offered odds tell you what you'll be paid.

Fair odds keep you honest, too. The market's margin-free view here is about 62% to 63%. Claiming 66% means you reckon you know three or four points more than everyone else, so you'd better have a reason: team news, a tactical mismatch or a model with a track record. Our guide to value betting in football walks through building that case.

Spot soft prices

De-vig a sharp, low-margin book and you've got a strong estimate of the true price. Any bookmaker offering bigger than that fair price, even with their own margin built in, deserves a closer look. That's the logic behind line shopping, and you don't need a model to do it.

Grade yourself against the close

The fairest test of a bet is whether you beat the closing price, and the fairest version of that test compares your odds with the de-vigged close. Raw closing odds flatter you, because the margin is still in them. Our closing line value guide shows the full method, and those same margin-free prices make the best benchmark going if you're building your own ratings, such as the Elo ratings many bettors start with.

One bookmaker's de-vigged prices give you that bookmaker's view and nothing more. Štrumbelj found some books are measurably better forecasters than others, and that exchange prices aren't always the sharpest in smaller markets. Take your fair price from the strongest source you can find.

• Know your toll before you bet. Add up the implied probabilities on any market you're about to play. Ten seconds tells you whether you're paying 2% or 10%.
• Favour the big leagues and the low-margin books. A Premier League 1X2 market at around 4.5% gives you a far better shot than a League One market at 7%.
• Treat longshots with suspicion. They carry the heaviest share of the margin, so a big price is often a bad price. Back them when you're confident the market has got it wrong, not because the number looks tempting.
• Use power or Shin when it matters. On short favourites and long outsiders, multiplicative will mislead you. On balanced two-way markets, any method will do.
• Beat the offered price, not the fair one. Fair odds tell you what the market thinks; your bet only has value if your probability clears the break-even of the price you're actually taking.
• Keep accas short. Every extra leg compounds the margin, and a four-fold at 95p in the pound per leg is already down to around 81.5p.
• Grade yourself against the de-vigged close. It's the most honest scoreboard in betting.

De-vigging shows you what the market thinks; it won't hand you an edge on its own. Keep your stakes flat and sensible, and let the numbers, not the excitement, decide when you play.

• Probability in sports betting: the complete guide to odds, EV and value
• Value betting in football: how to find EV bets
• The favourite-longshot bias: why bettors love underdogs and lose
• Best leagues for betting odds: compare bookmaker margins and find value
• Closing line value (CLV) explained

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