The Limitations of the No-Vig Calculator
The official seeming calculators you have used before don't work as well as you think they do under certain conditions.
The no-vig calculator is one of the most commonly used tools in sports betting. The underlying concept- get the true probability of each side of the bet based on the prices the sportsbook is offering- is incredibly powerful, as it allows us to estimate probabilities for every market that has two-way action (the ability to bet both sides of the market). Our market-based projections and best bets page rely heavily on deriving true probabilities from market prices, and the ability to do these calculations accurately is a foundational element of any top-down betting approach. But like many sports betting tools, the no-vig calculator you get off the shelf at any number of places hits a sweet spot of seeming sophisticated enough that it makes you feel smart, while papering over some assumptions that have varying degrees of validity depending on its inputs. We’ll take an in depth look at these calculators and unpack exactly how they work, what might cause them to trip up, and what corrective actions are required to get their true accuracy.
Let’s start with an example of how these calculators are used. Say there’s an NBA prop at a sportsbook where the over/under for a player’s rebounds is 7.5, with -140 on the over and +120 on the under. The sportsbook thinks the true and fair price for this prop is somewhere between -140 and +120, since a sportsbook is by definition in the business of offering bets with a house edge baked in relative to what they think the fair price is. So what do they think the true fair price is? Strictly speaking, we can only say with ironclad certainty that it’s somewhere between -140 and +120. One approach would be to take a simple average, and say the fair price is -130/+130. This is a little too simplifying and breaks down under more extreme conditions, which is why most places used a little more sophisticated formula: convert each individual price to an implied probability, then divide each individual price by the sum of both prices. Using our -140/+120 example and a standard American-to-probability conversion formula, -140 converts to 58.3% and +120 converts to 45.4%, and the two probabilities add to 1.038. Our normalized probability comes out to (58.3%/1.038) = 56.3% for the over, and (45.4% / 1.038) = 43.7% for the under, or -128.33 for the fair price for the over, a slightly different value than our simple average approach to get us to -130.
There are plenty of online calculators and Excel sheets that will do this formula for you, and as mentioned above, they do have a way of making you feel smart. But those formulas, as are literally all approaches in sports betting, are an estimate. Put another way: there is nothing according to the laws of physics that guarantees a sportsbook’s true probability must be the number this formula spits out. Using our -140/+120 example, they could believe the true line for the over is -138, -135, -130, or -125, and if their pricing is accurate, they would still make money over the long term with their pricing. Granted, they probably wouldn’t want their true price to be super close to the edges of their actual prices offered, since they’ll want some safety factor built in. But it’s not as though they’re required to follow the exact letter of the formula to the law when they set their prices. In fact, they have a strong risk management incentive to have a slight bias towards the favorite than the underdog, because the cost of being wrong in one direction is much more costly than being wrong in the other direction. And this becomes even more relevant when the no-vig calculators are applied to markets with more juice.
Let’s take another example, maybe from the alternate spreads market, where the line is home team -5.5 points, and the prices for the home team -10.5 are -270/+190 instead of the standard -110 on each side. The standard no-vig formula will tell you the true line is -212/+212, which is a decent estimate, but again, an estimate. The sportsbook’s true line for this market could be -260, -240, -220, -200, or virtually any value between 270 and 190 (or put another way, the home team’s probability for this market can be anywhere between 65.5% and 73%- a full 7.5% range!) and they would still expect this market to make them a profit- a much wider range than our -140 to -120 range from the earlier example. This illustrates a key point: the larger the house edge, the more unreliable the estimates of the no-vig calculator become. These errors matter immensely in a market where the best sports bettors in the world live off of 2-3% ROI for their margins. If your estimate is off by 4%, your bets that you think are winners can actually be losers. And if the top-down probabilities are your source of truth for estimating true probabilities, you need to make sure any errors in your method for generating sources of truth are properly accounted for.
So how can we improve on the basic approaches to no-vig probabilities and obtain something more reliable? The best way is to calibrate your probabilities, which is a fancy way of saying compare estimated actual probabilities against observed probabilities and seeing how they stack up against one another. This is a pretty painful process: it requires to constantly log sportsbook data and derive no-vig probabilities, compare them against the actual bet results, and adjusting the estimated probabilities to reflect their true occurrences. It requires logging a lot of bets to get sufficient sample size, as well as constantly refit your calibrations, since each sportsbook is also constantly changing their approach, so last year’s calibrations may not be the same as this year’s calibrations. Calibrations will also differ by market type and sportsbook, as each sportsbook will have their own individual preferences on where they want to be within the range of their vig.
If this sounds like a lot of work to do on your own, I agree- which is why we do this work at Betscope so you don’t have to. All of our market-derived projections and Best Bets recommendations have a healthy dose of calibration and empiricism baked in, moving beyond the standard no-vig approaches and leveraging actual observed results to refine our accuracy. We take pains to collect a lot of sportsbook data to measure our estimates and refine them over time, so that when we produce bet recommendations, we’re eliminating as much known sources of error as possible. We’ll have more to say on this as we roll out additional features that formally capture and illustrate this concept, but for now, you can rest easy knowing that the top-down estimates in our Best Bets pages account for this known flaw in standard no-vig approaches, putting it a step ahead of the standard top-down sports betting tools.