Structural Arbitrage: When Sportsbooks Contradict Themselves

Some player props are tied together by arithmetic. Receiving yards come from receptions. Completions can’t exceed pass attempts. Points, rebounds and assists add up to a combined line. When one book prices related props in a way that doesn’t fit together, one of those prices is probably wrong.

Bettors call this structural arbitrage. The name oversells it. True arbitrage guarantees a profit; this doesn’t. What it gives you is a reason to look closely at one side of a bet. Here is how to spot it, the trap that catches most people, and the check that actually works.

The quick screen: ratios

The fastest check divides one line by another and asks whether the result is realistic.

Pass attempts 35.5, completions 27.5: that implies a 77% completion rate. If the quarterback usually completes about 65%, 36 attempts means about 23 completions, so the completions under is worth checking.
Rush attempts 16.5, rushing yards 52.5: that implies 3.2 yards per carry. If the back usually averages 4.5, 16 carries is about 72 yards, so the yards over is worth checking.

For high-volume stats like these, the ratio is a reasonable screen. A quarterback is almost certain to throw 25 or more passes, so the lines behave roughly like averages.

NBA combined props

Basketball has its own version. Say a book posts a player at:

Market	Line
Points	24.5
Rebounds	7.5
Assists	5.5
Sum of the three	37.5
Points + rebounds + assists (PRA)	35.5

Because these stats are skewed toward big games, the combined line usually sits at or a little above the sum of the separate lines. A PRA line two points below the sum is the pattern worth checking: either the PRA over is cheap, or one of the separate lines is too high. Check the prices on each before you decide which.

The trap: low-volume players

Ratios break down for players who may barely touch the ball. Take a tight end at:

Receptions 1.5: over −130, under +100
Receiving yards 6.5: over −115, under −115

Divide 6.5 by 1.5 and you get 4.33 yards per catch, which looks absurdly low for a tight end. It’s tempting to call the yards line a mistake. But that division treats each line like an average, and a prop line is closer to a midpoint. For a player with a real chance of catching nothing, that zero pulls the yards line down far more than it moves the receptions line. The 4.33 number doesn’t mean the book expects 4.33 yards per catch.

The check that works: compare probabilities

Use the book’s own prices instead. Removing the vig, over 1.5 receptions at −130 against +100 prices two or more catches at 53.1%. The yards over at −115 on both sides is priced at 50%.

Now reason about the link between them. Two catches almost always add up to 7 or more yards. So the chance of 7+ yards should be at least about the chance of two catches, plus the chance of one longer catch. Using two sets of assumptions:

Assumption	Cautious	Generous
2+ catches reach 7+ yards	85%	90%
Chance of exactly 1 catch	28%	28%
1 catch reaches 7+ yards	30%	45%
Chance of 7+ yards	53.5%	60.4%

The book priced the yards over at 50%. To profit at −115 you need 53.5%. So under cautious assumptions there is no edge at all once you pay the vig, and under generous ones there are a few points. That is the honest size of this “contradiction”: real, but far smaller than “4.33 yards per catch” makes it sound.

Watch the market too

Lines like these often move fast. If the receptions under is bet from +100 to −210, two catches drop to roughly a one-in-three chance, and the yards under no longer looks out of line. When a sharp move resolves the inconsistency, the market is usually telling you which side was wrong.

Why books get this wrong

Separate pricing. Related markets can come from different models or data feeds, and they don’t always get reconciled.
Uneven updates. News moves one market before another, so for a while they disagree.
Copied lines. A book that copies another book’s line in one market but not the related one can end up inconsistent.
Less attention. Backups, tight ends and low-volume props get less scrutiny than star markets.

How to bet it

Bet one side, not both. Pairs like over receptions and under yards can both win, but they can also both lose. See why that pair isn’t arbitrage.
Price it after the vig. A gap of two or three points can disappear inside a −115 price.
Prefer high-volume stats. That is where ratios are trustworthy and gaps are easier to size.
Don’t expect a same-game parlay to escape it. Books generally price correlation into same-game parlays.

Our pricing checks page flags related props whose implied rates fall outside normal ranges. Treat each flag as a question to check with the probabilities above, not a guaranteed error.

Next: over receptions, under yardsThe prop pair that looks like it can’t lose, every outcome, and a 2025 example.

Frequently asked questions

Is structural arbitrage real arbitrage?

No. True arbitrage guarantees a profit whatever happens. Structural arbitrage means a book’s related props are priced inconsistently, which may make one side a good bet, but it is never risk-free.

Can you bet both related props to lock in a profit?

No. Pairs such as over receptions and under receiving yards can both win, but they can also both lose, and each bet carries the vig.

What is implied yards per catch?

It is the receiving yards line divided by the receptions line. It is a quick screen for high-volume players, but for players who may catch zero or one pass it is misleading, because prop lines are midpoints, not averages.

Should a points + rebounds + assists line equal the sum of the separate lines?

Roughly. Because these stats are skewed toward big games, a combined line usually sits at or a little above the sum of the individual lines. A combined line well below the sum is the pattern worth checking.

Structural Arbitrage: When a Sportsbook’s Props Contradict Each Other