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by PokerJoeTwo Plus Two Magazine, Vol. 12, No. 9

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Chapter 11: Line grinding and the juice-free line

The core idea of line grinding is to use the sharp market to estimate an offer’s proper odds, and then to find a sufficiently off-market line to bet into. If the sharp market line is +/- 125, figuring out which lines have value relative to that number is easy.

But generally the two sides of a betting offer aren’t equal, they are separated by the juice, so a little math needs to be done to get the juice-free line, that is, the midpoint of an offer’s two sides.

The general habit among line grinders is to use Pinnacle’s line on a game if it’s a sport Pinny is very active with. If Pinnacle has a baseball game lined -173/+159, the vig-free line is -164 (math to follow). That’s the simplest version.

A higher level approach is to use the line parameters from all the biggest, sharpest, most open books for the sport in which you’re interested.

If, on that same game Pinny lined -173/+159, you could find +167 at another major book, and you considered that book to be part of the world market for MLB, you could then use their dog price to reduce the market range to -173/+167, and then calculate the vig-free line to be -169. This is a sharper sharp line.

Using the best lines from the broad market to establish the range available to sharps is better than using the line from only one house because sharps have access to the major houses. That’s part of what they do. They bet anywhere as long as they’re confident they can get paid, as long as they haven’t been booted or crippled, at the shop with the best line on the offer they like.

If CRIS has 7 on a game and The Greek has it at 6.5, any sharp looking to bet the dog is going to bet it at CRIS, any sharp looking to bet the fave is going to bet it at The Greek. The weight of the betting will close the discrepancy between the books’ lines until the difference is within the width of the juice. This has the market effect of massaging the lines at all the sharp books into place, creating relative pricing efficiency.

The market can then be said to be estimating the game to somewhere between the parameters of the best lines on both sides. Exactly where isn’t knowable. It can’t be further reduced. But to find the midpoint is fairly easy.

Here’s how to do it, in horrible language-form: convert the US-style numbers to decimal-style, take the reciprocal of those, divide the larger of those two reciprocals by the total of the two reciprocals, take the reciprocal of that number, subtract 1, take the reciprocal of that, and you have the market estimated US-style odds on the offer.

The above sentence explains why math is best explained using formulas and would-be sharps should learn a little about spreadsheets.

To find an offer’s juice-free line:
In A1, put the road team’s price, US-style.
In A2, put the home team’s price, US-style.
In A3, to find the fair line on the favorite, put:


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In a fourth cell, to translate this hopefully sharp line into an estimated win rate, put: =A3/(A3-100)

That formula in A3 may look monstrous to someone who doesn’t work with spreadsheets (it may look inelegant to someone who does), but in truth you don’t need to understand how it works, just type it in or copy it exactly as it appears and then when you change the prices in cells A1 and A2, the juice-free line and win rate will change accordingly. Spreadsheets are cool like that.

It is possible to sharpen your sharp line further by considering the line movements.

Square-inspired line movement makes the trailing end of line movement the most accurate; sharp-driven line movement makes the leading edge the most accurate.

Consider a game lined -7 -110 in a sport where a half point equals the juice (that is, ten cents), and assume that line is accurate by the generalized opinion of sharps.

If the favorite is the most popular side for squares and is attracting lots of action, the book will move the number to -7.5 -110. This has the effect of doubling the juice on the side getting the action (because the squares will be paying, in addition to the -110, ten cents in push frequency value), yet does not open the book up to sharp action on the other side because, though the line should be 7 (as we’re hypothesizing), the advantage of getting +7.5 is exactly negated by having to pay -110. There’s still no +EV here for sharps, so they can’t bet. The books here will happily take unbalanced action because their hold is higher.

Therefore the line, having moved to -7.5 -110 on square action, is less sharp than the earlier line of -7 -110, if you were to go by the no-vig calculation on the new line.

Generally, in such a game, you’ll see the market offering lines of -7 and -7.5 both. The -7 is the trailing line, the -7.5 is the leading line. If a line is being moved by square action, use the trailing line as your sharp, juice-free number. Even if the entire market settles on -7.5, there was a trailing line of -7, which may still be the sharper line.

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If Pinnacle has a game’s moneyline -130/+120, and sharps are comfortable with that number and thus on the sidelines, then the no-vig line is +/- 124.

If the favorite is a public side and Pinny gets hit with action there (and, yes, Pinny gets square action, too; all the best books still do, even if it’s only by locals laying off action), they will move it up. Sharps, watching, will let it move until it crosses +124, at which point they will have incentive to counter the line move. The line settles at -134/+124, yet the new no-vig line is less accurate than the old one. The trailing, bottom side of the new line, the +124 part of the new line of -134/+124, is more accurate.

Now expand this idea to include the world’s sports betting market as a whole and you understand why the trailing side of the line, in the face of public, square betting action, can be sharper than the new line itself.

Conversely, where sharp action is driving the line movements, the leading edge of the market is the more accurate no-vig line.

If a game is lined -130/+120 but sharps like the favorite, they’ll bet and move the line approximately until there’s no EV left in betting the favorite. If they move the line to -140/+130 and stop, it’s because -140 leaves them ambivalent. The leading edge of that line, the -140, is, essentially, the truer no-vig line, not the no-vig line traditionally calculated on the -140/+130.

How can you know whether the market drivers are sharps or squares? By the books leading the charge, to some extent, and by the nature of the teams involved, and by the betting percentages available, and by experience watching lines move. It will always be a matter of opinion; one of many, many factors in sports betting that are matters of opinion even among sharps.

In truth, you don’t even have to go to this much trouble to line grind. Here’s the “line grinding for dummies” version: take the best prices from both sides of an offer at whichever shops you consider sharp. If you can find a line on the favorite that would allow you to arbitrage with the sharp market, bet it without arbing.

If the sharp market, for example, has a best price on the favorite of -120 and a best price on the dog of +115, if you can find a favorite priced lower than -115 or a dog priced better than +120, you can bet.

Easy, huh? Line grinding is hard because of the work needed to accrue a lot of outs and the time needed to look for off-numbers, but it isn’t hard to learn how to know what an off-number is.

A caveat:
This is a market we’re talking about, so there is never anything more than a generalized consensus, an average price view, settled upon by bet-wars up until the game starts, and only relatively efficient, not absolutely so.



Even though the juice-free sharp line is considered the gold standard of odds estimation, in reality the sharp line cannot be reduced beyond the width of the market juice.

If the sharp range is +115/-120, the no-vig line on that makes for a break-even win rate of 54%. If you find a line of -115, that line in decimal odds is 1.87, and 54% times 1.87 is 1.01, for an estimated edge of 1%.

But the market isn’t that precise, and there may be systemic biases in its movements. You do not definitelyhave a 1% edge in the above situation. You may have no edge. In fact the sharp market may not have been much formed yet, or may not be much involved, or may flat out be wrong, so it’s possible you are making a negative EV wager. The risk of error in edge estimation is important when bet sizing.

Sharper: A Guide to Modern Sports Betting by Pokerjoe can be purchased on Amazon.

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