Down 24-10 early in the second half of their game Sunday against the New Orleans Saints, the Oakland Raiders seemed to be offering up more of the same frustration that has haunted the franchise since it last posted a winning record, in 2002. They’d just been burned on an inexcusable 98-yard touchdown pass from Drew Brees — who released the ball 6 yards deep in his own end zone — to Brandin Cooks. After the play, ESPN’s win probability model dropped Oakland’s odds of winning the game down to just 7.3 percent.

Then something amazing happened: The Raiders didn’t pack it in and accept an opening week loss for the 13th time in the past 14 seasons. They fought their way back, chipping away at the Saints’ lead and responding even when New Orleans re-took a 7-point edge with six minutes to play. So when Oakland scored a touchdown with 47 seconds left in regulation to pull within a point, Raiders coach Jack Del Rio decided to take his chances on a 2-point try that — for better or for worse — might seal the game’s outcome.

“I didn’t really ask for any feedback there,” Del Rio told reporters. “I said, ‘When we score here, we are going to go for two and win it right here.’ ”

It's Victory Monday, #RaiderNation. This two-point conversion in the game's final minute made it happen. https://t.co/XqEBzrXDXW — Oakland Raiders (@Raiders) September 12, 2016

It was only the eighth time since 2001 that a team had gone for two in the final minute of a fourth quarter or overtime after a touchdown brought them within a point of an opponent. And when Derek Carr completed his fade pass to Michael Crabtree, Oakland became the fourth team to convert in that do-or-die situation.

SEASON WEEK TEAM OPPONENT 2-PT SUCCESS? GAME RESULT 2002 15 Minnesota New Orleans ✓ W, 32-31 2005 10 Tampa Bay Washington ✓ W, 36-35 2008 2 Denver San Diego ✓ W, 39-38 2008 10 Kansas City San Diego L, 19-20 2010 14 Washington Tampa Bay L, 16-17 2011 17 Houston Tennessee L, 22-23 2013 15 Washington Atlanta L, 26-27 2016 1 Oakland New Orleans ✓ W, 35-34 Going for two while down one in the last minute In the fourth quarter or overtime, 2001-16 NFL seasons Sources: ESPN, TruMedia

The statistical wisdom of Del Rio’s choice is up for interpretation. ESPN’s Stats & Information Group crunched the numbers and found that the Raiders’ win probability would have been higher after the touchdown if they had chosen to attempt an extra point to force a likely overtime (51 percent) rather than to go for two (44 percent). Del Rio had other thoughts:

Good thing ESPN isn't coaching the Raiders https://t.co/X6tB1YlZ4d — Jack Del Rio (@coachdelrio) September 11, 2016

A simple set of conditions (a 94 percent likelihood of making the PAT, a 48 percent probability of 2-point conversion success and 50-50 odds for each team in overtime) suggests that the 2-point call was defensible. Add in extra factors such as the weakness of New Orleans’s defense, the emotional peak of the comeback, the fact that Oakland had converted a 2-pointer earlier in the quarter and the detriment to the road team if the game were extended, and you can see Del Rio’s side of things even more.

The Stats and Info model, however, accounts for something that Del Rio ignored: the 47 seconds that Brees and the Saints had to work with after the Raiders’ score. The game wouldn’t end on the basis of Oakland’s 2-point success or failure. New Orleans would have a chance to answer, with a QB who’d already shredded the Raiders’ defense for 423 yards through the air. And the Saints’ play-calling would probably be much more aggressive than usual if they were trailing by a point, rather than being tied. Things ended up working out for the Raiders, but they were taking a big risk to get a 1-point lead that wasn’t certain to hold up. This might be a case in which small, easy-to-discount factors, detectable only by a complex model like the one that Stats and Info built, can add just enough points of probability to tip the scales against the simple set of initial assumptions.

But maybe all of this win probability hair-splitting misses the forest for the trees anyway. The Raiders currently boast the franchise’s highest post-Week 1 Elo rating since the 2011 season and the second-highest since the start of its 2003 collapse. Carr played a great game Sunday and is coming off a season in which he edged out Cam Newton and Russell Wilson to project for more future Approximate Value than any other starting QB in football. The Raiders could finally — finally! — be on the verge of playing decent football again. But they needed to transform that potential into results, and it turns out that opening week outcomes have outsize importance on a team’s whole season.

It could be that by aggressively grabbing the win as a road underdog in Week 1, Oakland changed the entire complexion of its 2016 campaign and even altered the franchise’s trajectory beyond this season. In that case, Del Rio’s gambit would prove to have been a good bet, probability models be damned.