“I was really proud of the way we played that day,” Smith said. “A week after we had such a major celebration when we beat Wisconsin, to go on the road and play that well proved that we really have improved, that Wisconsin wasn’t just a one-day thing.”

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At about 10 o’clock, Smith looked up from his early work for this week’s game against Rutgers, when he heard what sounded like music outside his window. He wasn’t hearing things.

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“It was our band,” he said Monday afternoon, clearly enjoying the memory. “They had been at a band competition earlier in the day, and they came to the house, stood outside and played the school fight song.”

He paused for a moment and added, “That doesn’t happen in the NFL.”

Smith is four years removed from his last NFL job, returning to the college game after a 20-year absence to try to rebuild Illinois’ program. The journey, as coaches nowadays like to call it, hasn’t been easy.

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Illinois was reeling from the firing, just before the start of the 2015 season, of Tim Beckman, who had been accused of abusing players, most notably forcing them to play through injuries. Bill Cubit served as interim coach that season and went 5-7, including 2-6 in the Big Ten. When Smith arrived, Illinois had last won more than two Big Ten games in 2010, when it went 4-4 under Ron Zook.

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Smith, 61, had spent 13 seasons as an assistant at six schools before being hired by Tony Dungy to be the linebackers coach in Tampa Bay in 1996. Smith got his first crack at being a head coach in the NFL in 2004, when the Chicago Bears hired him to replace Dick Jauron. In Smith’s second season, the Bears went 11-5, and he was the NFL’s coach of the year. A year later the Bears reached the Super Bowl, making Smith the first African American coach to reach the NFL’s ultimate game — barely.

“Not a lot of people remember that I was the first,” he laughed. “I beat Tony [Dungy] by about ­3 1/ 2 hours.”

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Hours after the Bears’ win, Dungy’s Indianapolis Colts came back to beat the New England Patriots in the AFC championship game to set up a coach-vs.-pupil Super Bowl matchup that the Colts won, 29-17.

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“It would have been unfair if Tony hadn’t won a Super Bowl,” Smith said. “I just wish he’d been coaching against someone else on the day he got that win.”

Smith coached in Chicago through 2012, when he was fired after going 10-6. A year later he signed a five-year contract in Tampa Bay, only to be fired after going from 2-14 in his first season to 6-10 in his second. The given excuse from the organization was that they wanted Dirk Koetter — yes, the Dirk Koetter — to tutor Jameis Winston. Everyone knows how that has worked out.

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“What can I possibly say about that?” Smith said. “I’ll just say this: Most of the time when you go 10-6 in the NFL you don’t get fired; you get a contract extension. And, sure, I thought I’d have more time in Tampa than two years. But you know what? When a door closes, another one opens. I’ve been very lucky.”

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Two months after Smith was fired in Tampa, the next door opened — at Illinois. Smith never worried about returning to coaching at the college level after a 20-year absence.

“There are certainly differences you have to adapt to again,” he said. “In the NFL you have the players all day. In college, it’s four hours a day. Time management becomes more important. You can’t cut players or make trades at the college level. Your roster is your roster.

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“But you also get the players when they’re younger, more impressionable, maybe a little more teachable. To me a big part of coaching has always been teaching — high school, college or pro.”

He paused for a moment. “Of course, no matter how much you enjoy teaching, 9-27 is never fun.”

That was Smith’s combined record in his first three seasons at Illinois. Even so, Athletic Director Josh Whitman liked the progress he saw and extended Smith’s contract through 2023 at the end of last season. By then, Smith had recruited players he thought had a chance to take a major step forward this season. And he had grown the beard.

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“I never shaved much during the summer, before seasons started,” he said. “Two summers ago, I let it grow out for a while, and my wife said to me: ‘I love it. Don’t ever shave it.’ So I guess I won’t.”

The beard, Santa Claus long and gray, was the talk of the Big Ten entering the 2018 season. Two weeks ago, the Illini became the talk of the conference for a much better reason: their stunning victory over a then-undefeated Wisconsin team that had hammered Michigan and hadn’t trailed all season.

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“I felt like it was coming,” Smith said. “We were up two touchdowns on Nebraska and lost by four. We were down to Michigan 28-25 in the fourth quarter. It felt close.”

When senior James McCourt drilled a 39-yard field goal as time expired, “it” arrived.

“We were meant to win that game,” he said. “Our kids had earned it.”

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The Illini still have a lot of season left. If they can win their two remaining home games — against Rutgers on Saturday and Northwestern to end the season — they will be in a bowl game for the first time in five years. If they can win at Michigan State or Iowa then . . . wow.

“I told the players when we were 2-4 that we had a six-game season to play,” Smith said. “We’re now 2-0. Our only goal this week is 3-0.”

One goal — the “signature win,” as Smith called it — has been met. And the marching band showing up in the front yard was a really nice bonus.