LAS VEGAS — For the sake of argument, let’s say former USC coach Tim Floyd never put himself in position to get in trouble with the NCAA and his former school. Nobody has proven that he gave $1,000 in cash to O.J. Mayo’s handler, but the bottom line is Floyd is no longer in Los Angeles.

Know this: The NCAA, which put the USC football program on probation for two years and reduced its scholarships significantly, took no further action against the school’s basketball team. The Trojans’ basketball program had already banned itself from postseason play last spring and vacated its wins from Mayo’s only season with the Trojans. Floyd, now the UTEP head coach, continues to deny he gave money to anybody.

Let’s say Floyd was genuinely interested in Jim Livengood’s sales pitch on April Fool’s Day 2009 and not just used the impromptu meeting with the former Arizona athletic director as a way to boost his contract status at USC.

Let’s say Floyd accepted the Arizona head coaching job and was wearing a UA polo shirt — not Sean Miller — during all these evaluation tournaments throughout the country this month.

If a coach is to be measured by the amount of NBA talent he produces, Floyd would have been a welcome sight in Tucson (again, only without the baggage). USC, much more of an NFL factory than NBA, is in the same conversation as Kentucky and North Carolina in terms of talent at the NBA Summer League here in Las Vegas.

The list: Mayo with Memphis; Dwight Lewis, Houston; Marcus Johnson, Phoenix; DeMar DeRozan, Toronto; and Davon Jefferson, Miami. Moreover, former USC center Taj Gibson of Chicago was on the NBA’s All-Rookie team.

If Floyd never got himself in trouble, he would have continued to produce NBA talent at a fast rate, similar to his first four years at USC. But Floyd put himself in a position to be judged at USC, fair or not. Arizona followers are grateful he only used the meeting with Livengood last year as a way to sweeten his contract at USC.

Miller does not have a long list of alumni in the NBA, but he does not have baggage, either. Most importantly, he does has Solomon Hill, Lamont “MoMo” Jones and Derrick Williams — all Floyd recruits who fled to Arizona after the fiasco that led to Floyd’s resignation.

Budinger improving. In the Rockets 100-91 loss to Toronto on Tuesday, former UA wing player Chase Budinger finished with 13 points, making only 4 of 13 shots, including 0 for 5 from three-point range. He was scoreless in the first half. DeRozan had 23 points in 20 minutes, many when Budinger was matched against him.

Budinger scored 24 points in an 82-75 victory over Denver. He scored Houston’s first 12 points, including a thunderous dunk following a steal three minutes into the game.Jordan Hill added 14 points and 13 rebounds for the Rockets.

Budinger finished Houston’s five-game schedule in the NBA Summer League averaging 15 points and four rebounds a game. He made 42.2 percent of his field goals and 33.3 percent of his three-pointers, which pales in comparison to his percentages last year (68 from the field and 72.7 percent from beyond the arc). Shooting that well again would be asking too much.

A testament to his turnaround: After head coach Rick Adelman told him to be more aggressive Saturday, Budinger went to the free-throw line often. He was 13-of-17 from the line in the three games after Adelman offered his advice. He was 1-of-2 from the line in the first two games.

Hill’s averages in Houston’s five games: 13.6 points, 7.8 rebounds and 54.5 percent field-goal shooting. He finally had two blocked shots in the last game against Denver on Wednesday after going through the first four games without a block. His foul total in three of the games was equal of more than his rebound total.

Imagine that you are drifting off to a sound sleep …

Breaking News: USC has announced self-imposed sanctions that will ban it from postseason play this season and place restrictions on recruiting — including the loss of a scholarship — before the 2010-11 season. …

Arizona interim coach Phil Johnson opted to not face the Tucson media regarding USC’s decision today, noting that he is “focused on leading the Arizona program with my undivided attention and undying effort,” according to a UA press release.

Former USC coach Tim Floyd interviewed for the Arizona job on April 2. Four days later, Sean Miller was hired.

Johnson, who accompanied Tim Floyd to Arizona from USC, is in the midst of a 4-10 season after agreeing to remain in Tucson as the interim coach following Floyd’s abrupt resignation when news of alleged infractions surfaced in Los Angeles involving the recruitment of former USC standout O.J. Mayo.

Floyd’s hiring at Arizona on April 3 by former UA athletic director Jim Livengood ultimately rocked both programs. A month after Floyd’s arrival in Tucson, Yahoo! Sports reported that Louis Johnson, a former associate of O.J. Mayo’s, told federal and NCAA investigators that Floyd paid cash to have Mayo sign with the Trojans. On June 10, Floyd stepped down as Arizona’s coach before coaching a game with the Wildcats amid growing scrutiny from the UA administration and members of the Arizona Board of Regents.

Livengood, whose contract was set to expire at the end of this school year, was fired within a week of Floyd’s resignation, setting up a dubious distinction for the Arizona athletic department. UA president Robert Shelton was forced to search for an athletic director and head men’s basketball coach at the same time less than a month before Arizona’s basketball players were to report for summer school.

Shelton asked Johnson to remain as interim coach. Johnson, citing his respect for Lute Olson (his former boss at Arizona) and the Wildcat program, decided to stay for at least one season. He is the third consecutive interim coach at Arizona, following Kevin O’Neill (who is now the head coach at USC) and Russ Pennell.

Sheldon hired Xavier athletic director Mike Bobinksi in late June to fill Arizona’s AD position. Bobinksi attempted to bring Sean Miller with him, but Miller said the timing was not right in terms of the recruiting calendar and that “he wants to coach at Xavier for as long as Xavier wants him.”

Miller, 41, is considered a top candidate for the permanent job in 2010-11 because of his affiliation with Bobinski, but Miller continues to deny any interest in the UA post. His Musketeers are ranked No. 12 and primed for another deep NCAA tournament run. Miller enhanced his image as a recruiter earlier this summer when high-profile recruit Lance Stephenson agreed to play for Xavier. The Musketeers also feature touted recruits Kyryl Natyazhko of Ukraine and Kevin Parrom of New York.

One of Arizona’s top recruits, Derrick Williams, who followed Floyd from USC, changed his mind and is playing at Memphis under former UA player and assistant coach Josh Pastner. Another recruit, Renardo Sidney, contemplated joining Floyd at Arizona after committing to him at USC, but he opted for Mississippi State.

Johnson was able to keep Solomon Hill and Lamont “MoMo” Jones on the Arizona roster after they also left USC for Arizona. UA senior guard Nic Wise decided to stay in Tucson after flirting with the NBA or playing professionally overseas. Jamelle Horne is also back with the Wildcats as a junior forward. The last permanent coach for Wise and Horne was Lute Olson in 2006-07.

Highly-rated recruit Dwayne Polee of Los Angeles Westchester committed to Arizona after Floyd was hired, but he re-opened his recruitment after Floyd resigned.

Arizona’s recruitment of top-notch talent figured to be restored after Floyd’s hiring but now the Wildcats are mired in three consecutive years of uncertainty. Because of the turmoil and lack of consistent influx of talent, the UA’s NCAA tournament streak of 25 consecutive years is in serious jeopardy.

As it stand right now, Johnson and the Wildcats would be hard-pressed to get to .500. That is the goal now for the once-proud Arizona program, which in past years set its sights on a Final Four and potential national championship.

The best possibile scenario in the UA coach search occurred when Jim Livengood hired Sean Miller from Xavier (Tucson Citizen file photo)

… you now awake from your deep sleep, shaking off the nightmare. You come to your senses that what you dreamed is not true, and you have never been more relieved.

Arizona is still feeling the effects of Olson’s turbulent retirement phase with Miller trying to coach a program that for two years put recruiting on hold. The Wildcats are 7-7 and figure to be better than a .500 team with Williams a potential Pac-10 Freshman of the Year performer. Miller’s recruiting agenda is in full swing as talented Class of 2010 point guard Josh Selby of Baltimore takes an official visit this weekend to Tucson. Doron Lamb, a shooting guard from Mouth of Wilson (Va.) Oak Hill Academy, is also expected to visit Tucson.

The UA’s replacement for Livengood, who fortunately for him was hired by UNLV last month, is still to be decided with Xavier’s Bobinksi a possibility.

USC’s offseason was tumultuous following the departure of underclassmen DeMar DeRozan, Taj Gibson and Daniel Hackett to the NBA and Floyd’s forced resignation during the offseason. O’Neill’s hire, Floyd’s staff staying at the school with O’Neill, and the addition of transfers Mike Gerrity (North Carolina-Charlotte) and Alex Stepheson (North Carolina) seemed to right the ship.

The Trojans, however, are now stuck in a nightmare Arizona avoided.