Outlier detection: when one sportsbook is way off the market

Picture the same pair of shoes in thirty stores. Twenty-nine of them charge about $100. One charges $70. You do not need to know anything about shoes to know where to buy. Sportsbook prices work the same way: when most books have a player to score a touchdown at +200 and one has him at +260, the +260 book is paying more for the same thing.

The crowd of books is a good estimate of what the bet is really worth, because each one is trying hard not to be wrong and they mostly land close together. An outlier is the book that landed somewhere else.

• Slow to move — news broke, the market moved, one book has not caught up yet.
• Different opinion — a book's own model genuinely disagrees. Sometimes it is right.
• Boosts and promotions — a book deliberately overpays to attract bets.
• Mistakes — the sides are flipped, the line is for a different player, or the number is simply wrong.

The first three are opportunities. The fourth is a trap: a bet that looks like a huge edge because the price is not really for the thing you think it is. Good outlier detection shows you the first three and hides the fourth.

To put a number on an outlier, compare its price to the average of the market. If the average says a prop hits about half the time and one book pays as if it hits less often, that book is giving you value, and the size of the gap is its Value %. Bigger is better, up to a point: when a number looks too good, it usually is.

Convert each sportsbook's price on one side of a prop into an implied probability and average them. That average is the market's collective opinion of the side, vig included. Unlike a devigged fair price, it does not need the other side of the market, which means it works on one-sided bets too: anytime touchdowns, first goalscorer, many alternate lines.

The average still carries each book's margin, so a one-sided Value % overstates the true edge by roughly the market's vig. That is a feature, not a bug: it lets you rank mispricings on markets that cannot be devigged at all. But treat it as relative value against the market, and expect the true edge to be a few points lower. For a devigged number, use the Positive EV board on the same bet.

• More books, more trust — an average of ten books is a far better yardstick than an average of two. Check how many books went into it.
• Shorter prices drag the average — one book posting a much shorter price pulls the average up and inflates every other book's Value %. That book is never the one you would bet, so it is pure noise.
• Longer prices are the product — a book posting a much longer price is usually the best bet. Unless it is stale, flipped, or a resting exchange order nobody will fill.

A real outlier sits apart from a tight cluster of other books. A bad line sits apart because something is wrong with it. The checks worth running before you bet: are the two sides of the book's own market reversed? Is the exchange price backed by real money? Is the gap plausible for this kind of market, or is it a different bet in disguise?

• One-sided strategy — the Prop Outliers pipeline does not require a paired side. Its fair probability is the mean of the books' implied probabilities, in probability space, with no devig. One-sided markets (anytime scorer, first touchdown, deep alt ladders) are scored like any other.
• Every book votes — the default benchmark is every book that posts a price, including the outlier itself. Derived feeds (prices built from other books' prices) are excluded, and a price family (BetRivers, BallyBet and BetParX share one Kambi model) collapses to a single vote at its best price.
• Weighted blends — with a saved Compare Against blend the mean becomes Σ(wᵢ × impliedᵢ) ÷ Σwᵢ, renormalised over the books present.
• fairBookCount — the number of lines in the average, shown per row. The built-in minimum is one; the Min books filter raises it.

Each line is compared with the consensus of the plain sportsbooks on that side: the median implied probability, one vote per price family, with the line's own book removed first (leave-one-out) so no book is judged against a yardstick it helped set. A line must pass both a ratio test and a logit-distance test.

• Short side: 0.65 logits — a price shorter than consensus drags the average shorter, which inflates every other book's Value %, and it can never be the best book, so cutting it removes zero bettable inventory. The threshold sits between the widest genuine quote measured (an MLB home-run prop at +450 against a +650 to +850 board, 0.49 logits) and the closest bait (-140 against a +145 to +180 strikeout board, 0.82). The row that forced it: ProphetX -368 against -106 / -106 / -107 / -110 was only 1.52× but 1.24 logits, and it moved the average from -107 to -133 and the Value % from +0.6% to +11.0%.
• Long side: 1.8 logits — a price longer than consensus deflates Value % and is usually the best book, which is the product, so it gets room. The threshold still catches resting exchange orders at -189 sitting 1.86 to 2.07 logits off the board; one of those had shown a Sam Darnold rushing Over at +40.8% against a true −3.8%.
• Minimum voters — a sportsbook is only judged when at least three other sportsbooks vote. Below that, two books disagreeing would each gate the other and the market would eat itself.
• Exchanges are exempt from that minimum — an exchange line is judged against any non-empty sportsbook consensus. Applying the minimum to exchanges too un-flagged 419 live lines and pushed the board's net rows above the +25% alert line.
• Split board — if half or more of the voting books would be flagged, the flags are dropped: an outlier is a minority by definition.
• Exchange liquidity — an exchange line whose maximum bet is $5 or less, or unknown, is marked LOW_LIQUIDITY regardless of price.
• Exchange width — an exchange whose two sides add up to more than a 12-point overround (say -157 and -151) is marked WIDE_MARKET on both sides. On a sportsbook that gap is vig; on an exchange it is the spread between two resting orders, and a wide spread means nobody is pricing the market.

A gated line is not deleted. It stays on the row with an exclusion reason (CONSENSUS_OUTLIER, LOW_LIQUIDITY, WIDE_MARKET, SWAPPED_SIDES, or informational markers such as ONE_SIDED and DERIVED_FEED) and is simply left out of the average, the best price and any arbitrage leg. You can see what was excluded and why, and judge it yourself.

• Swap detector — for every book quoting both sides, the logit distance to consensus is measured as posted and with the sides swapped. When the swapped reading is under half the as-posted distance and the as-posted distance exceeds 0.3 logits, the book is marked SWAPPED_SIDES. It needs three clean books, runs two passes, and never swaps the price back.
• Two-sided only — an optional filter keeps a row only when the outlier book also quotes the other side. A one-sided quote has nothing holding it to the market, so its edge is the least trustworthy on the board.
• Where the gate runs — Prop Outliers, Positive EV, Auto SGP and the promo tools. The Odds Screen and Fan Favorites are deliberately raw boards and show every price as posted.