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Adam Vinatieri is, at age 43, the NFL’s oldest player, and he’s heading into his 21st season. He has now been with the Colts longer than he was with the Patriots, but it was in New England that he developed a reputation for big kicks in big games, a reputation that could get him into the Hall of Fame some day.

And his entire career almost ended just as it was beginning.

That’s the word from New York sports radio fixture Mike Francessa, who has long been close with former Patriots coach Bill Parcells. Francessa said on the air on Monday that Parcells nearly cut Vinatieri after Week Three of Vinatieri’s rookie season.

Vinatieri missed three field goals in Week Two of his rookie season, and in Week Three he missed his first field goal attempt and an extra point attempt. And so, late in the fourth quarter of a game the Patriots were winning 28-0, Parcells went to Vinatieri on the sideline with a little test to see how much intestinal fortitude he had: Parcells told Vinatieri that he was going to go into the game to attempt a 31-yard field goal with his job on the line. If Vinatieri missed, Parcells told him, he was getting cut. Vinatieri made the kick.

“I’ve had it with that kicker,” Parcells said, according to Francessa. “If he had missed it I would have cut him. And I told him, ‘You better make this kick’ before I sent him out there. And he made the kick, and he gained confidence little by little, and look who he became.”

What he became is one of the best kickers in NFL history. If he had missed that kick, it probably would have ended his career right there: Undrafted rookie kickers who miss five field goals and an extra point in their first three games usually don’t get a second chance. Two decades later, it’s a good thing for the Patriots, and the Colts, that Vinatieri made it.