All week, Doug Kyed — the Boston Herald’s New England Patriots beat writer — has flipped my phone into a seismograph. Every few minutes, Kyed issues a new update on the Patriots’ free-agency signings. After decades of Old Man Bill Belichick’s austerity, it’s disorienting to witness New England pay premiums for proven talents and retain rising stars. 

Besides Rob Gronkowski, Belichick rarely paid the market price. If a player wouldn’t take a discount, they were often banished from Foxborough. But with Executive Vice President of Player Personnel Eliot Wolf now directing the front office, the Patriots are dealing for playmakers.  

So, with New England discontinuing its typical offseason dormancy, I’ve been mulling over methods to maximize the free (NFL) market. Naturally, this thinking has infiltrated my studies. You see, I’m not quite the counter-cappie I claim to be — I’m enrolled in a financial markets course. And the other day, my professor challenged the class to come up with real-life examples of arbitrage.

In this conjectural actualization of the efficient market hypothesis, arbitrage was defined as the simultaneous purchase and sale of the same asset to profit from differences in the asset’s mismatched listed prices. 

Of course, being the only one who failed to recognize the tricky nature of the ask, I threw out an example: Say, what if Matt Millen traded the Lions’ 2007 No. 2 draft pick in exchange for the Cleveland Browns’ No. 22 draft pick. Foolish? Yes. But also arbitrage.  

To my disappointment, my case was rejected. There are almost-arbitrage instances, like the Minnesota Vikings’ 2016 trade for Sam Bradford, where they gave up a first- and fourth-round pick to add Mister Mediocre — a quarterback the Eagles didn’t even want. Or in 2004, when the Washington Redskins traded Hall of Famer Champ Bailey to the Denver Broncos for an okay running back in Clinton Portis. While these are terrible trades, they still carried uncertainty; any player could have unexpected success, and any draft pick could be a bust.

The point is that it’s almost impossible to pull off true arbitrage in the NFL. Luckily, you’re likely not a general manager, so let’s hit the books and take a punt.

I’ve never gambled before, but I can tell you how to make a buck. It’s time to hedge away; here’s a guide to sure betting the NFL.

At brief moments, different books may set inconsistent point spreads, money lines, over/under or props. Alongside these discrepancies arise arbitrage opportunities, as you may be able to bet both sides of a game and guarantee profit, regardless of which team wins or loses. 

In the simplest scenario, you find two sportsbooks with opposing odds. For example, Bookdude A has the Patriots at -6.5 (-110), whereas Bookdude B has the Jaguars disproportionately at +7.5 (+120). 

To determine if this is a viable arbitrage opportunity, calculate the implied probability of Bookdude A’s Patriots and Bookdude B’s Jaguars by dividing each of the odds by its sum with 100. This yields 52.38% and 45.45%, respectively. The combined percentage is less than 100%, meaning the total implied probability guarantees profit if stakes are allocated rationally.

Multiplying your bet, in this case, $500, by the quotient of each implied probability and the total implied probability suggests a $267.11 stake should be placed on the Patriots and the remaining $232.89 on the Jaguars. No matter which team covers, you will profit.

This works because, unlike negotiating between front offices, sports betting operates in a closed probability space, where numbers react to wager volume, injuries and public sentiment, and initially, different sportsbooks set their lines independently. 

Finding miraculous holes in the market is demanding because discrepancies are narrow, often correcting within seconds or minutes as oddsmakers adjust. But a locked-in bettor can lock in a sure profit by exploiting incongruent spreads just like a financial trader capitalizes on price differences between exchanges. 

For the average gambler, sure betting won’t lead to massive gains, but one low-margin bet can probably get you a Chipotle bowl (sadly without guac) to watch the game. Come to think of it, I’m getting a little hungry, I should probably go find my calculator.

Leila MacKenzie is a junior writing about minor details in sports in her column, “Little Things,” which runs every other Wednesday. She is also the data editor at the Daily Trojan.