Without looking it up, how can an NFL game end in a 6-1 final score?

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Has never happened before and likely will never happened even though it’s possible.

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1 point safety

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A team scored a touchdown and the opponent blocks the extra point and returns it

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No, the team that scores a touchdown would have to be tackled or commit a penalty in their own endzone 98 yards away on the extra point or 2 point conversion try.

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My guess is a team blocks the extra point, returnees it but gets tackled short of the end zone and a penalty occurs on the tackling team and they elect to kick the extra point.

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No, one point safeties are most common when a team blocks an extra point, attempts to return it, and is tackled on their own endzone. But they would make the score 7-0. In the play you described, that penalty would likely be applied on the kickoff. They wouldn't give the other team a chance at a 1 point try from the spot of the foul.

Correct. It’s considered the holy grail and rarest of scorigami even though a 4-4 final score is expected to occur every 1.7 billion years.

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Most "likely" scenario, team A scores a TD, decides to go for 2. Gets several penalties and gets backed up to say the 40 yard line, they decide to kick it, the long snap sails high over the holder's and ends up going toward their goal. The kicker and holder chase after it, get possession, and inexplicably get tackled in their own endzone or commit a hold in their own endzone.

Score is 6-1.

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but I’m with ya

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1 point safety

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Did look it up and found this gem in College... LINK

Safety on the extra point try.

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Gets several penalties and gets backed up to say the 40 yard line, they decide to kick it,

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You’re allowed to change it after the fact? Honestly didn’t know that.

Once you commit to the 2PC, you should have to commit to the 2PC not an extra point kick.

(no message)

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Most "likely" scenario, team A scores a TD, decides to go for 2. Gets several penalties and gets backed up to say the 40 yard line, they decide to kick it, the long snap sails high over the holder's head and ends up going toward their goal. The kicker and holder chase after it, get possession, and inexplicably get tackled in their own endzone or commit a hold in their own endzone.

Score is 6-1

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It’s basically impossible for a snap to go that far I think unless the LS was actively trying to do it, not just a bad snap (and even then, and even factoring in the roll, I’m not sure any snapper could get the ball to travel 60 yards). I’ve never seen a bad snap on a punt travel more than 40 yards with the roll, and that’s when it’s a punt (15 yards away compared to 8 yards for a kick).

I think the “more likely” scenario (though extremely extremely extremely unlikely) is Team A is kicking an extra point or going for two. Team B blocks the kick/intercepts/returns a fumble the other way trying to score two points. Team A tackles Team B on Team A’s 5-yard line and Team B fumbles. Team A picks it up at the 1 to attempt to return it 99 yards back the other way. In doing so, Team A runs into its own end zone on the return attempt and is tackled.

ETA: Using your example, Team A could have a bad snap and Team B could start returning it and then the aforementioned paragraph happens, but I don’t see a bad snap actually being able to make it all the way to the end zone on the other side of the field.