Allonzo Trier and the Wildcats are having a most unusual season. (Christian Petersen/Getty Images)

TUCSON, Ariz. — If No. 9 Arizona, nationally and oddly overlooked for much of this college basketball season, were to turn up by bus in Greater Phoenix for the 2017 Final Four, it will have hurdled a motley collection of oddities. Those include a months-long mystery, a delicate coaching puzzle and an obliteration from an inhospitable batch of Ducks.

First came the weird November, the weird December and the weird half-January through which Arizona’s best returning player, 6-foot-5 guard Allonzo Trier, spent the first 19 games cheering from the sideline for reasons few knew and nobody announced. That’s how the basketball-gripped brains in this desert hoop kingdom of four Final Fours and the 1997 national title spent months trying to read the cactus-tea leaves about the sophomore Trier, the 2014 first-team Washington Post All-Met guard who played high school in three time zones and four schools, including Montrose Christian as a junior.

Fans parsed Coach Sean Miller’s vague sentences for clues. They went to fan websites and opined even without knowledge. They sought meaning once or twice from Trier’s shoes as he sat serially in plain sight: Might certain sneakers indicate reinstatement? News conferences began with reminders of no forthcoming news about Trier, such that it became almost a ritual like sunny weather reports.

“Kind of a helpless feeling, but I stayed strong through it,” Trier finally said on Jan. 26, after three months of either silence or cryptic tweeting.

Arizona, depleted through various injuries, life choices and a Trier storyline local sages deemed unprecedented, willed itself to 17-2 without Trier as a little engine with seven mainstay players and cemented roles. It brandished the futuristic 7-foot freshman Finnish marksman Lauri Markkanen, Trier’s roommate, amid its typical cluster of talent. On Dec. 19, Trier tweeted: “Everybody talking and guessing trying to be right first rather than actually correct knowing there’s no repercussions for being wrong.” On Jan. 8: “Remain a mystery.” Everybody knew. Everybody didn’t know.

“Disappointment turning into frustration turning into, almost at the end, anger,” said Zach Clark, who hosts a Tucson radio show on ESPN. “Anger at this invisible thing you don’t understand. It almost became like this — and I was guilty of it, too — this droning. It wouldn’t go away . . . The level of bizarre that it reached, it said so much about who we’ve become as sports fans.”

Come Jan. 18, there came a statement from Trier, shortly after a report from ESPN’s Jeff Goodman: “Earlier this season, I was notified that I tested positive for a trace amount of a banned performance-enhancing drug following an NCAA random test and I was shocked. I have never knowingly taken a banned substance. After finding out that I was given a banned substance by a well-intentioned but misguided person not associated with the University after an injury, I presented this information to the NCAA.

“The NCAA agreed that I had no knowledge of receiving the substance and my eligibility was restored. Although I can practice and travel with the team, I am not allowed to resume playing in games until the substance completely leaves my body even at a trace amount. Unfortunately, I am unsure of when that time will be, but I hope it is soon.”

It was soon, days-later soon. Trier played on Jan. 21 in a 96-85 win at UCLA that stamped Arizona as a serious, serious matter and maybe even, to hear Miller tell it, saddled Arizona with an onerous glob of cockiness. Meanwhile, as the mystery mostly fizzled while all officialdom cited Trier’s privacy concerns, people googled to learn which drugs might take their sweet time leaving human systems.

A horde of drugs do that, said Charles Yesalis, the Penn State epidemiologist who has studied athletic performance enhancement, among other matters, through five decades. Their length of stay hinges on many factors and can require many months. “They’re metabolized,” he said. “You have to keep saying and adding that, because the vast majority of the time, you don’t find the drugs [in the system] per se. It’s just the breakdown products of the drug.”

On Jan. 26 against Washington State, with 15:19 left in the first half, Trier entered his first home game of the season at McKale Center, and the ovation was standing. Forty-seven seconds later, the sleek workaholic with the daily 500-shot practice ritual since age 8, banged in a three-point shot from the top, and the roar was full.

For two home games, he reminded the Wildcat congregation that he is a thrilling basketball player, wreaking mass gasps at least twice. Off the bench in five games, he has had 15 assists and four turnovers, although the assists dried up on the two-game swing through Oregon, and he has scored unfailingly in double figures, including a team-leading 17 against Washington State. To the surprise of all who had followed this murk, he then emerged around the corner into the press-conference room to speak publicly, alongside Markkanen. He spoke with such savvy that one might have wondered why he didn’t speak all along. He said he had sobbed upon reinstatement.

“It was tough, but I love the game of basketball, so even though I couldn’t play, I stayed around the game as much as I could, so I was working in the gym,” he said. “I could see my teammates every day [for practice]. And I tried to make an impact in any way I could, so even though I couldn’t play I tried to be there for my teammates and cheer them on, and then in practice I tried to do my part, practicing hard and helping these guys, you know, to get prepared for the games.” He thought the whole, strange thing “really solidified [Miller] as coach of the year this year.”

To a question from the Arizona Daily Star’s veteran writer Bruce Pascoe about what injury he might have suffered last summer, Trier said, “I’m not getting into that.”

From there, Miller delved into a ticklish puzzle. Adding another player 20 games into a season certainly helps everyone’s late-game lungs but as Miller said, “Missing 19 games is an odd thing.” And: “Substitution patterns are awkward when somebody’s playing 30 minutes and they’re not even starting.” All five starters — Markkanen, Dusan Ristic, Kobi Simmons, Rawle Alkins and Kadeem Allen — also score in double figures on average.

Said the 48-year-old, 13-season head coach at Xavier and Arizona, “We’ve added a player, and it affects everybody. It affects virtually every possession of the game. It affects our substitution pattern. It affects how we attack a zone.” The kind of 2-3 zone that addled them against Washington on Jan. 29, he said, normally would have posed itself to Trier starting in November. Instead the guard was adjusting in conference play.

Still, they coped with the newness and the horror of fresh accolades, reached 21-2, reached a No. 5 ranking and became something of a hip mid-season pick for what would be, oddly, Arizona’s first Final Four berth in 16 years. Then last Saturday, they went messing around with Ducks.

The obliteration at No. 13 Oregon both snuffed out and minimized a 15-game win streak. It became the second-worst defeat of Miller’s eight Arizona seasons. It ended at 85-58 and got there via grotesque mid-game scores such as 38-11 and 64-27. Tweeted Ken Goe of the Oregonian, “I’ve seen a lot of Arizona games in 40 years in the biz, and never seen the Wildcats taken apart the way Oregon is taking them apart now.”

Afterward, Miller told reporters in Eugene, “We can’t let anything from this game linger into the future.” He reminded that Arizona stands at 21-3, 10-1 in the Pac-12 Conference. He said of Oregon, which reached the final eight last year and made 16 of 24 three-point shots last Saturday, “If they have another level above that, that’s a bad thing for, I think, every team in the country.” He spoke of making 85-58 “a positive.” For a marker, he might revisit March 8, 2014, when Connecticut lost 81-48 at Louisville, only to win the national championship 30 nights later, which certainly qualified as madness.

In some quirky way in this quirky season, his curious team had just gotten a notch more curious.