The Badgers won three games in four days at the Big Ten tournament. There were even plenty of encouraging signs in the lone defeat, a 93-87 setback against Illinois with the title on the line at the Target Center.

“We’re leaving here today a much better team than when we came in on Wednesday,” Wisconsin coach Greg Gard said.

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Gard is right. Performances against Rutgers and Purdue during the final week of the regular season provided hints that the Badgers were trending back in the right direction following a horrific stretch in which they lost seven times in nine games.

These past four days confirmed that Wisconsin had indeed turned a corner just in time for the start of the NCAA Tournament.

The Badgers (22-13) earned a No. 5 seed in the South Region and will open against James Madison (31-3) at 8:40 p.m. Friday in Brooklyn, New York. Duke, which broke Wisconsin’s hearts in the 2015 NCAA final, could be waiting in the second round.

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Here’s my take on the draw for Gard’s team:

Wisconsin earning a No. 5 seed is fair.

It’s hard to say if an overtime win over top-seeded Purdue caused the selection committee to move Wisconsin from the 6 line to the 5 line, but that’s a fair assumption. Anything worse than a 6 would have been shocking, as would anything better than a 5.

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Wisconsin is the No. 19 overall seed. For as much as fans dwell on the Associated Press Top 25 rankings, what that means is the committee thought the Badgers have a top-20 resume.

And I agree with that assessment. Wisconsin played a tough schedule and had a respectable 14-13 record in Quad 1 and 2 games.

• A quick turnaround from an exhausting conference tournament run to a first-round NCAA Tournament game on Thursday would have been brutal. But the Badgers avoided that by being sent to Brooklyn.

Make no mistake, Wisconsin is banged up. The list of injured players starts with John Blackwell, Chucky Hepburn, Max Klesmit and Tyler Wahl. That’s four of the top six players in the Badgers’ rotation.

That extra day of rest is crucial.

“Everybody needs it,” Gard said. “We just played four games in four days. Even I need it.”

• There’s also something to be said for having too much rest. While an extra day off is good for the Badgers, I think it’s important that they’re riding a wave of momentum right now and probably want to get on the court as soon as possible.

James Madison won the Sun Belt Tournament on March 11, meaning the Dukes will have 11 days between games. That seems like a lot to me.

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“These guys want to play,” Gard said. “There’s nobody complaining about being banged up or anything. They were ready to go.”

• There are some big names in the South Region.

Duke and Kentucky are blue bloods. Houston, the No. 1 seed, has become a perennial contender under Kelvin Sampson.

Wahl’s eyes went right to Marquette at the bottom of Wisconsin’s portion of the bracket. A Badgers-Golden Eagles rematch in the Elite Eight would be fun even if that seems like a pipe dream right now.

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“You don’t know who you’re going to play,” Wahl said, “but I think a really good team is going to come out of our side.”

I don’t hate the Badgers’ first-round draw. But I don’t love it, either.

It took CBS analyst Seth Davis about two seconds to pick James Madison over Wisconsin in a 12-5 upset. I’m guessing that will be a popular opinion the next couple of days.

The Dukes are experienced and can put a lot of points on the board. They’re red-hot right now, too: James Madison’s 13-game winning streak is the longest in the nation.

Are the Dukes battle tested? Sort of. They opened the season with an overtime win at Michigan State, but Wisconsin won handily at the Breslin Center a month later.

James Madison only played a combined three games in Quad 1 and Quad 2. Twenty-two of its wins came in Quad 4 and another win — vs. Keystone College — doesn’t even count in the NCAA Net Rankings.

It’s a scary first-round opponent for the Badgers, but it’s not as bad as the one they drew as a No. 5 seed in 2019. Oregon was the No. 12 seed in that matchup and was coming off a run to the Pac-12 Tournament title.

• I don’t have to tell you that Wisconsin’s defense has been awful at times this season.

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It was again Sunday, when Illinois averaged 1.37 points per possession. That number after halftime was a whopping 1.58, with Terrence Shannon Jr. and Marcus Domask scoring at will against the Badgers.

Wisconsin has the offensive punch to make a run to the Final Four. But I don’t trust its defense to get stops when needed.

This region includes two of the top 10 offenses in the nation — Kentucky is at No. 5 in adjusted offensive efficiency while Duke is at No. 7 — and James Madison averages 84.4 points per game.

The Badgers played well on defense against Maryland and Northwestern this week. They had good moments on that end of the court vs. Purdue, too, at least when they weren’t getting called for fouls.

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They still need to buckle down and stop opponents from getting such easy access to the rim. That could be the difference between Wisconsin’s season ending at the Barclays Center or continuing to Dallas next week.

The Badgers were upbeat following the loss to Illinois.

“I like where we’re sitting right now,” Klesmit said. “I’m proud of the all the dudes in here and how we responded when stuff kind of hit the fan earlier in February.”

The vibes with this team feel good right now. Hepburn had a great Big Ten Tournament, and AJ Storr and Steven Crowl were really good as well.

My bracket will include wins over James Madison and Duke before a loss to Houston in the Sweet 16.