Vigorish Adjustments and Implied Probability
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I had a long-running argument with a colleague who insisted Bet365’s NBA spread prices were “always better” than William Hill’s. He’d compare the two side-by-side, pick the higher decimal, and feel pleased with himself. When I made him work through the implied probability of the same lines on both books, he discovered Bet365 was charging more juice on the favourite and less on the dog, and his “always better” was actually “sometimes meaningfully worse.” The conversation ended his streak of betting only the side with bigger numbers, and his bankroll noticed within a month.
Implied probability is the number behind the number. Every odds price encodes a probability, and converting from price to probability is the only way to compare lines, books and markets cleanly. Without it, you’re guessing.
Strategic Arithmetic Formulas for Competitive Line Analysis
Implied probability is the probability the bookmaker’s price is asking you to accept. The conversion from decimal odds to probability is one division: probability = 1 / decimal odds. So 1.91 = 1/1.91 = 52.4%. 2.00 = 1/2 = 50%. 1.50 = 1/1.50 = 66.7%. The lower the odds, the higher the implied probability.
From fractional, the formula is probability = denominator / (numerator + denominator). 10/11 = 11/(10+11) = 11/21 = 52.4%. Same answer. 5/6 = 6/(5+6) = 6/11 = 54.5%. The fractional path is slightly clunkier but produces identical numbers.
For an NBA spread, both sides are usually priced near 10/11 (1.91 decimal, 52.4% implied). Add the two implied probabilities together: 52.4% + 52.4% = 104.8%. The 4.8% above 100% is the bookmaker’s overround – the margin built into the market. On a two-way spread, that 4.8% is, in practical terms, your guaranteed friction. The book’s margin per £100 of total stakes is roughly £4.55, calculated as the overround divided by the total implied. Standard NBA spread pricing produces something close to this.
Why does the maths work this way? Because the bookmaker is offering you a synthetic “either” bet. If both sides are priced fairly at 50%, the implied total would be exactly 100% and the bookmaker would make no money. By moving both prices toward shorter odds – 1.91 instead of 2.00 – they push the implied probabilities above 50% on both sides, and the sum exceeds 100% by their margin. That excess is the vig.
Hold and Overround on NBA Two-Way Spreads
“Hold” is the bookmaker term for the percentage of total wagered money they keep on average. On a two-way market, hold is calculated as overround / (1 + overround). For the standard NBA spread at 4.8% overround, hold is 4.8 / 104.8 = 4.58%. So out of every £100 wagered across both sides of an NBA spread market, the book expects to keep about £4.58 long-run.
That number has been creeping up. Average hold percentage at US sportsbooks rose from 6.7% in 2018 to over 9% by 2024-2025. UK retail books have moved in similar directions, though the regulatory framework – the UK’s online segment captured 78.47% of the sports betting market revenue share in 2024 – keeps competition meaningful enough that NBA spread holds in the UK haven’t quite reached the US peaks. But the trend is upward and the punter’s defence is to know which book is charging what.
Hold differs market by market. NBA spread is generally one of the more competitive markets – books fight for spread action because it’s high-volume and predictable. Player props carry much higher hold, often 8-12% on individual prop markets. Live spreads carry higher hold than pre-match because the volatility justifies – from the book’s view – a wider margin. Knowing the hold on the market you’re betting helps you understand which markets are actually fair-ish and which are taxing the punter heavily.
The other practical consequence: converting fractional odds to decimal makes the implied probability calculation a one-step exercise rather than a two-step one. Most regulars I know who track CLV or compare books work in decimal exclusively for this reason.
The No-Vig Fair Line and What It Tells You
The no-vig fair line is what the spread price would look like if the bookmaker took no margin. The calculation strips the overround and rebalances the implied probabilities so they sum to exactly 100%.
Here’s the maths. Take a two-way spread priced at 10/11 (52.4%) and 10/11 (52.4%). Total = 104.8%. To strip the vig, divide each side by the total: 52.4 / 104.8 = 50.0% on each side. The no-vig fair line for both sides is exactly 50%, which is the decimal equivalent of 2.00, or fractional 1/1 (evens). So the bookmaker is “charging” you about 4.5 cents on each side in juice to convert a fair 50/50 proposition into the 52.4%/52.4% they actually offer.
Now apply the same maths to a non-symmetric spread. Imagine an NBA -7.5 line where the favourite is priced at 5/6 (54.5%) and the underdog at 21/20 (48.8%). Total = 103.3%. To strip the vig: favourite no-vig = 54.5 / 103.3 = 52.8%. Underdog no-vig = 48.8 / 103.3 = 47.2%. Sum is 100%. So the bookmaker thinks the favourite has roughly a 52.8% chance to cover -7.5, even though the displayed price implies 54.5%. The difference is the margin.
That 52.8% number is the no-vig fair line. It’s what the market – collectively – believes is the true probability of the favourite covering. If your own analysis disagrees with the no-vig fair line by enough to matter, you have a potential bet. If your analysis broadly agrees with the no-vig fair line, you don’t have an edge – you’re just paying juice to express the same view the market already has.
Comparing Two UK Books on the Same Spread
Take a Lakers -7.5 line priced two different ways. Book A: -7.5 at 10/11 (52.4%) and +7.5 at 10/11 (52.4%). Total 104.8%, hold 4.58%, no-vig fair on both sides = 50%. Book B: -7.5 at 5/6 (54.5%) and +7.5 at 8/11 (57.9%). Total 112.4%, hold 11.0%, no-vig fair = 48.5% on Lakers, 51.5% on the dog.
The displayed prices on Book B look “safer” because both numbers are shorter than 10/11. To a casual eye, that means lower risk. To anyone reading the implied probabilities, Book B is charging more than double the margin for the same fundamental bet. The no-vig fair line on Book B’s market is also tilted away from symmetry, suggesting the book has shaded the line for reasons that may or may not reflect genuine information.
Which side is genuinely the better bet depends on your own view. But on margin alone, Book A is dramatically more punter-friendly. Across a season of betting one or the other, Book A’s lower hold compounds into significantly more retained value for the same betting performance. UK NBA bettors who don’t shop the implied probabilities – instead reading “shorter odds = stronger team” – frequently pay these higher margins without realising.
The other thing to look for: when one book has a meaningfully different no-vig fair line from another book, the market is split. If Book A’s no-vig is 50/50 and Book B’s no-vig is 52/48, one of them disagrees with consensus and the other is closer to it. Sharp punters will lean toward the book whose no-vig is closer to broader market consensus, because the outlier is more likely to be either an information asymmetry (rare) or a pricing mistake (sometimes worth attacking).
When the Fair Line Is Still Wrong
The no-vig fair line is the market’s best collective guess at the true probability. It’s not necessarily right. Markets can be wrong, especially on smaller sports, niche markets, or events with information asymmetries. NBA spread markets are heavily traded and broadly efficient, but they’re not infallible.
Where the no-vig fair line is most likely to be wrong: pre-season games, where the market hasn’t seen the teams play yet and the line is built largely on prior-season carryover. Late-night UK betting on West Coast NBA games, where major late-breaking news might have just happened on the US side and the UK book lags. Games involving teams in unusual circumstances – long road trips, schedule oddities, players in personal situations – where the public model doesn’t have a clean read.
The reverse case: when the no-vig is more right than your own analysis. This is the more common situation, painful as it is to admit. Most punters most of the time disagree with the market and are wrong about it. The fair line absorbs the work of thousands of other people’s analysis, the bookmaker’s risk team, sharp money, and pricing models. Disagreeing with it requires either a genuinely new piece of information or a genuinely better model. Most of us, most of the time, have neither.
The discipline is humility. Read the fair line, decide whether your view differs by enough to matter, and accept that “differs by 1%” is rarely an edge once juice is factored in. Differences of 3-4% in implied probability, with a clear reason for the difference, are where the actual edges live. The smaller disagreements are usually you talking yourself into a flat market.
The other discipline is self-honesty about which markets are efficient and which aren’t. NBA prime-time spreads on major UK books are very efficient. Pre-season alternate lines on a Tuesday morning are not. Knowing where the no-vig fair line is informative – and where it’s just an aggregation of guesses – separates the punters who use the metric well from the ones who treat it as gospel.
Should I always bet the side with higher no-vig probability?
No. The no-vig fair line tells you the market’s view of probability after stripping out margin, but it doesn’t tell you whether your own view differs from it. Betting the side with higher no-vig probability is just betting the market favourite, which after juice is rarely a profitable strategy on its own.
Does the hold change in-play on NBA spreads?
Yes. Live spreads almost always carry higher hold than pre-match. The bookmaker pads the margin during in-play to manage the higher volatility and shorter pricing windows. Expect 6-9% overround on live NBA spreads versus 4-5% pre-match. The increase is structural rather than punter-targeted.
Created by the ”nba Handicap Betting” editorial team.
