They've played some of their best basketball over the years with their collective backs against the wall.

While the UConn Huskies are not quite there yet this season, they're a few steps away.

During a shaky start to American Athletic Conference play, they've looked more like last year's NIT team than one on course to qualify for the NCAA tournament.

It's hard to predict which UConn (11-5, 2-2) team will show up Sunday afternoon against Houston at Hofheinz Pavilion (2 p.m., CBS Sports Network).

Will it be the offensively-challenged Huskies who shot a season-low 30.9 percent and scored a season-low in an ugly 60-51 loss at Tulsa on Thursday?

Or the UConn that played with a sense of desperation and earned a home win over Memphis on Jan. 9 before departing on a two-game road trip?

It better be the latter for the Huskies to be able to pull off an upset.

Yes, upset.

Given the current state of the Huskies, a win over much-improved Houston (13-3, 3-1), which has already equaled last year's overall win total, would fall in that category.

Especially considering that a few key players are mired in major shooting funks, contributing to the Huskies averaging 65 points and shooting 36.7 percent in the AAC.

Sound familiar?

Their offensive output also dipped last season after entering conference play. They finished averaging a paltry 63.2 points and shooting 43 percent in league games.

But this year's team has more weapons, so the big dropoff is unexpected.

Only two UConn starters — forwards Shonn Miller and Kentan Facey — are shooting higher than 40 percent from the field in the last four games. Bench production also has dried up.

Sophomore Daniel Hamilton is suffering from a confidence crisis, converting an icy 20.8 percent (10-for-48) during that span. Even the normally reliable Rodney Purvis is searching to regain his aim, sinking 39 percent (16-for-41). The pair combined to go 3-for-21 versus Tulsa.

Raising their scoring output will be vital for the Huskies to chase down the Cougars, who are led former junior college star Rob Gray, Jr. the conference's leading scorer at 17.7 points per game. He's one of three transfers that helped revive a program that went 13-19 last season.

A good place to start is for the Huskies to attack the basket. They settled for too many 3-pointers — 29 of 55 field goal attempts from beyond the arc — against Tulsa and took only 13 free throws. That approach led them blowing an eight-point second half lead.

Sterling Gibbs and Shonn Miller, who combined for 34 points, acted as life preservers, keeping a struggling UConn's offense afloat. There's just been too many anchors dragging the Huskies down.

Coach Kevin Ollie accepted his share of the blame after the Tulsa game and then again Saturday in Houston.

"My job is to make players great," Ollie told reporters in Houston. "They haven't been playing great."

On the plus side, UConn's defense remains a rock despite the absence of shot-blocking center Amida Brimah.

Hofheinz Pavilion has been a House of Horrors for the Huskies. In their brief history there, they've lost both meetings. The Cougars also are tough to beat at home, sitting at 10-0 this season.

So, it may take UConn's best shot to score the knockout.

g.keefe@theday.com

Twitter: @GavinKeefe