- Joined
- Jul 11, 2008
- Messages
- 1,476
- Reaction score
- 182
- Points
- 63
This guide is for bettors who want to understand the four main methods for calculating no-vig odds (proportional, additive, power, and Shin), when each method is appropriate, why they produce different results, and which method professional bettors actually use in practice.
Why Remove Vigorish at All
Bookmaker odds include built-in profit margin called vigorish or vig. A fair coin flip should be +100/+100 (50% probability each side). Books offer -110/-110 instead, which is 52.38% implied probability per side. The probabilities add to 104.76% instead of 100%, with the extra 4.76% being the book's edge.To compare fair value across different books or identify mispriced odds, you need to remove this margin and calculate what the probabilities would be if they summed to exactly 100%. This is "no-vig" odds or "fair odds."
The problem is there are multiple mathematically valid ways to remove vigorish, and each method makes different assumptions about how the bookmaker distributed their margin across outcomes. The method you choose affects the no-vig probabilities you calculate, which affects whether you think you've found value.
Most bettors don't think about this - they use whatever calculator they found online without understanding the underlying method. This creates situations where you think you have edge based on one calculation method when a different method shows no edge at all.
Proportional Method (Most Common)
The proportional method assumes the bookmaker's margin is distributed proportionally to the implied probabilities. If one outcome has higher probability, it gets proportionally more of the margin removed.Formula: Remove vig by dividing each implied probability by the sum of all implied probabilities.
Example with -110/-110 (52.38% each side, 104.76% total):
- Team A: 52.38% / 104.76% = 50.0%
- Team B: 52.38% / 104.76% = 50.0%
Example with -200/+170 (66.67% and 37.04%, 103.71% total):
- Favorite: 66.67% / 103.71% = 64.29%
- Underdog: 37.04% / 103.71% = 35.71%
This method is simple and most commonly used in betting calculators. It works well for two-outcome markets and produces reasonable results in most situations. The main advantage is ease of calculation and intuitive understanding.
The assumption is that bookmakers apply their margin proportionally, which isn't always true but is close enough for practical purposes. For markets with similar odds on both sides, proportional method works fine.
When Proportional Fails
Proportional method struggles with large favorite/underdog gaps. A market priced at -800/+500 gets vig removed proportionally, but in reality bookmakers often add more margin to the underdog because that's where recreational money goes.In multi-outcome markets (three-way soccer markets, futures markets), proportional method can produce strange results because it doesn't account for how bookmakers actually price complex markets. A three-way market with 10% margin might have that margin distributed unevenly across outcomes.
The method also doesn't handle overround variation well. A market with 2% margin should have vig removed differently than a market with 8% margin, but proportional method treats them identically beyond the different overround percentages.
For most bettors betting two-outcome markets with relatively balanced odds, these limitations don't matter much. The proportional method is good enough and the simplicity is valuable.
Additive Method (Simplest)
The additive method assumes the bookmaker added the same absolute amount of probability to each outcome. Instead of proportional distribution, the margin is split equally.Formula: Remove equal probability from each outcome until the sum equals 100%.
Example with -110/-110 (52.38% each, 104.76% total):
- Overround: 4.76%
- Remove from each side: 4.76% / 2 = 2.38%
- Team A: 52.38% - 2.38% = 50.0%
- Team B: 52.38% - 2.38% = 50.0%
Example with -200/+170 (66.67% and 37.04%, 103.71% total):
- Overround: 3.71%
- Remove from each side: 3.71% / 2 = 1.86%
- Favorite: 66.67% - 1.86% = 64.81%
- Underdog: 37.04% - 1.86% = 35.18%
Notice in the second example, the additive method produces slightly different results than proportional (64.81% vs 64.29% for the favorite). The difference is small but exists.
Additive method works better when you believe bookmakers add similar amounts of margin to each outcome regardless of probability. This might be true for professional books serving sharp bettors, less true for recreational books.
Power Method (Multiplicative)
The power method assumes the bookmaker's margin is applied multiplicatively - each probability is raised to a power that removes the overround. This method is more mathematically complex but handles extreme odds better.Formula: Raise each probability to the power of (log(1) / log(sum of probabilities)), then normalize.
Actually, that's not quite right - the formula is more complex than that and involves solving for the exponent that makes the adjusted probabilities sum to 100%. The math gets ugly but betting calculators handle it.
Example with -200/+170 (66.67% and 37.04%, 103.71% total):
- Using power method: Favorite ≈ 64.50%, Underdog ≈ 35.50%
The power method produces results between proportional and additive methods usually. It's theoretically more sound when dealing with extreme favorites or underdogs because it accounts for the multiplicative nature of odds.
The practical problem is the power method is complicated to calculate manually and the differences from proportional method are usually small enough that they don't change betting decisions. Most bettors don't use it because the added complexity isn't worth the minor accuracy improvement.
When Power Method Matters
For extreme odds like -1200/+750, the power method produces meaningfully different results than proportional. The heavy favorite gets less vig removed and the big underdog gets more vig removed compared to proportional method.If you're betting long shots or heavy favorites regularly, the power method might give you more accurate fair value estimates. For betting near even money, the differences are trivial.
Some professional bettors use power method for futures markets with wide odds ranges. A futures market with 30 outcomes ranging from +200 to +50000 needs a method that handles that range well. Power method does this better than proportional.
Shin Method (Accounting for Asymmetric Information)
The Shin method is the most sophisticated and assumes the bookmaker is protecting against informed bettors who know the outcome with some probability. It calculates both the true probabilities and the percentage of informed money in the market.The math involves solving equations that estimate how much the bookmaker has shaded odds to protect against insider information. This produces fair odds that account for information asymmetry rather than just removing margin mechanically.
I'm not going to pretend I can explain the full Shin calculation without just copying formulas. The key concept is it recognizes that bookmakers don't just add margin for profit - they add margin to protect against bettors who might have information advantages.
In practice, very few bettors use Shin method because:
1. The calculations are complex and require specialized tools
2. The assumptions about informed money percentages are difficult to validate
3. The resulting fair odds often don't differ enough from power method to matter
Shin method is academically interesting and theoretically superior, but practically it's overkill for most betting applications. You need to be betting at a level where half a percentage point of probability matters before Shin method's added complexity is worthwhile.
Comparing the Four Methods Practically
Take odds of -150/+130 (60% and 43.48%, 103.48% overround). Here's what each method produces:Proportional: 58.0% / 42.0%
Additive: 58.26% / 41.74%
Power: 58.13% / 41.87%
Shin: (varies based on assumed informed money %, but around 58.1% / 41.9%)
The differences are under 0.5% in most cases. For a bettor placing $100 bets, this difference is worth maybe 25-50 cents of expected value. Not nothing but not life-changing either.
For even-money or close-to-even odds, all methods converge to nearly identical results. The differences only become meaningful when odds are skewed or when the overround is large.
The practical question is whether the added complexity of power or Shin method is worth the minor improvement in accuracy. For most bettors, no. Proportional method is good enough and you should spend your energy finding edges rather than optimizing your vig removal to the third decimal place.
Which Method to Use
For casual betting and general edge identification, use proportional method. It's simple, widely available in calculators, and accurate enough for practical decisions.For professional betting at high stakes where small edges matter, consider power method. The added accuracy might be worth it when you're betting thousands per position.
For academic analysis or if you're trying to estimate market efficiency precisely, Shin method provides the most theoretically sound approach. But understand you're optimizing something that probably doesn't change your betting decisions.
Don't waste time agonizing over which method to use. Pick one (probably proportional), stick with it consistently, and focus on finding actual edges rather than optimizing your mathematics.
Using No-Vig Odds to Find Value
Once you've calculated no-vig odds, you can compare them to your own probability estimates to identify value. If you think Team A has 55% chance to win and the no-vig odds imply 52%, you have a 3% edge.The method you used to calculate no-vig affects whether you think you have edge. If proportional method says 52% and you think 55%, that's value. But if power method says 54% and you think 55%, your edge is smaller.
This is why consistency matters more than method choice. Use the same method every time so you're comparing apples to apples. If you switch methods randomly, you'll think you have edges that don't exist or miss edges that do exist.
Also remember that no-vig odds show what the bookmaker thinks, not what's true. If the book has made a mistake, no-vig odds still reflect their wrong assessment. You're looking for gaps between the book's assessment (no-vig) and reality (your estimate), not assuming the book is right.
Line Shopping and No-Vig Comparison
Comparing no-vig odds across books tells you which book has the best price after removing their respective margins. Sometimes a book with higher vig on one side has better no-vig odds because of how they distributed their margin.Book A: -115/+105 (53.49% / 48.78%, 102.27% overround)
Book B: -110/-110 (52.38% / 52.38%, 104.76% overround)
Using proportional method:
Book A no-vig: 52.3% / 47.7%
Book B no-vig: 50.0% / 50.0%
If you want the favorite, Book B offers better value (50% implied vs 52.3% implied). If you want the underdog, Book A offers better value (47.7% implied vs 50% implied).
Line shopping with no-vig comparison identifies which book is offering the best price on the specific side you're betting. The book with the lowest overall margin isn't always the book with the best price on the side you want.
Hold Percentage vs Actual Value
Hold percentage (the overround) tells you the book's total margin but doesn't tell you where that margin is distributed. A 5% hold might be evenly distributed or might be loaded on one side.Sharp books like Pinnacle have low hold (2-3%) and distribute it roughly proportionally. Recreational books have higher hold (4-8%) and often load more margin on popular sides - favorites and overs usually.
When line shopping, check no-vig odds on your specific side, not just overall hold. The book with the best hold might not have the best price on what you're betting.
Three-Way Markets Are Different
Soccer and other sports with three possible outcomes (win/draw/win) require different handling. All four methods work but the differences between methods become larger because there are three probabilities to adjust instead of two.Example: Home +150, Draw +230, Away +200 (40% / 30.3% / 33.3%, 103.6% overround)
The proportional method removes 3.6% proportionally across all three outcomes. The additive method removes 1.2% from each outcome equally. Power method applies an exponent. Shin method would need assumptions about informed money across three outcomes.
For three-way markets, proportional method is still the standard choice. The added complexity of other methods doesn't provide enough benefit to justify the effort. Unless you're betting professionally on soccer and need maximum precision, stick with proportional.
Futures Markets and Long-Shot Bias
Futures markets with 20-50 outcomes have massive overrounds (often 120-150%) because bookmakers need protection across many possibilities. Removing vig from these markets is trickier because different methods produce widely different results.Long shots in futures markets are typically overpriced even after vig removal. Bookmakers load margin on the long shots because that's where recreational money goes. People love betting +5000 long shots.
No-vig calculations on futures should be treated skeptically. The methods assume margin is distributed rationally but futures margins are often distributed to exploit public biases. The no-vig odds might say a long shot is 2% probability but the true probability might be 0.5%.
If you're serious about betting futures, use power or Shin method and still be skeptical of the results. Proportional method definitely breaks down on futures with wide odds ranges.
Building Your Own No-Vig Calculator
Proportional method is simple enough to calculate manually. Sum the implied probabilities, divide each by the sum, convert back to odds.For American odds to probability:
- Favorites: (-odds) / (-odds + 100)
- Underdogs: 100 / (odds + 100)
For probability back to American odds:
- Probability > 50%: (-probability) / (1 - probability) × 100
- Probability < 50%: (1 - probability) / probability × 100
Actually, those formulas aren't quite right for conversion. The correct formulas are:
- Favorites: (negative odds) / (negative odds + 100) × 100
- Underdogs: 100 / (positive odds + 100)
Look, the point is you can do proportional method in a spreadsheet easily. Power and Shin methods require more complex calculations that are better done with specialized tools.
When No-Vig Calculation Doesn't Matter
If you're betting based on analysis that doesn't involve calculating expected value precisely, vig removal might be unnecessary. Some bettors use qualitative assessment rather than probabilistic modeling.If you're betting on extreme longshots or heavy favorites, the vig removal method matters less than understanding that bookmakers load margins on those outcomes regardless of method used.
If you're betting live where odds change rapidly, spending time on precise no-vig calculation is probably wasted effort. The odds will move before you finish calculating.
If your edge is large (5%+), the difference between methods is noise. If your edge is small (1-2%), the difference between methods might matter but you probably shouldn't be betting small edges anyway because variance will kill you.
Don't let the complexity of no-vig calculations paralyze you. Pick a method, use it consistently, focus on finding actual edges rather than optimizing mathematics to the third decimal place.
Common Mistakes With No-Vig Calculations
Using different methods randomly and thinking you've found value when really it's just method inconsistency. You calculated no-vig with proportional yesterday and power today, got different results, assumed one side now has value when nothing actually changed.Trusting no-vig odds as "true probability" rather than understanding they're just the bookmaker's margin removed. The book might be wrong. No-vig tells you what they think, not what's real.
Overvaluing small differences from no-vig calculations. If your estimate is 51.5% and no-vig is 51.0%, that's not a meaningful edge when you consider uncertainty in your own estimate.
Not accounting for method differences when comparing analysis from different sources. Someone else's fair odds might be calculated with a different method, making direct comparison invalid.
Spending an hour optimizing no-vig calculations when you could spend that hour finding better bets. Precision is good but not at the expense of opportunity.
Forgetting that no-vig odds are theoretical. You can't bet them. You can only bet the actual odds offered which include vig. Use no-vig for analysis but remember your returns come from the real odds you get.
Using the wrong method for the market type. Proportional for futures with massive overrounds produces nonsense. At least use power method for complex markets.
FAQ
Which no-vig calculation method is most accurate?Depends on the market. For two-outcome markets with balanced odds, all methods produce similar results and proportional is fine. For markets with extreme odds or large overrounds, power method is more accurate. Shin method is theoretically best but practically the added complexity isn't worth it unless you're betting professionally at high stakes. Use proportional for 90% of situations - the simplicity is worth more than the minor accuracy improvement of other methods. The difference between methods is typically 0.3-0.8 percentage points which is less than the uncertainty in your own probability estimates.
Do professional bettors use no-vig odds in their analysis?
Some do, many don't bother. Professional bettors are more concerned with finding mispriced lines than with precise fair value calculation. They use whatever method is convenient (usually proportional) and focus their energy on edge identification rather than mathematical optimization. The most successful professional bettors I'm aware of use simple methods consistently rather than complex methods inconsistently. No-vig calculation is a tool for analysis, not the analysis itself. Don't confuse mathematical precision with betting skill.
Can I use no-vig odds to compare value across different sports?
Not reliably. Different sports have different market efficiencies, different typical overrounds, and different margin distributions. A 2% edge in NFL might be easier to find than a 2% edge in tennis, not because the math is different but because the markets are different. Use no-vig calculations within a sport to compare across books or to evaluate your own estimates, but don't use them to decide which sport to bet based on edge size alone. Market efficiency matters more than mathematical edge for long-term profitability.
Last edited: