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One of the most fascinating parts of the Utah-BYU matchup in Saturday's Las Vegas Bowl is figuring which team has the advantage when it comes to the coaches. Who gives his team the better chance of winning — Bronco Mendenhall or Kyle Whittingham?

Both of them took over as head coaches the same season (2005), with Whittingham holding the head-to-head edge, 6-3.

Apocryphal or not, it is said that at some point en route to those totals, Whittingham rather emphatically told his players they would never again lose to BYU, his alma mater, not as long as he was mentoring them. Well … the Utes have won four straight, before not playing the Cougars last season, nor heretofore this year.

Their annual games resume next season, without Mendenhall, and appear to be in the cards at least for the coming fistful of years, and, as mentioned, the rivalry is freshened now in a bowl game — for the first time.

The chronological run pitting Mendenhall against Whittingham includes scores of 41-34 (OT), Utah; 33-31, BYU; 17-10, BYU; 48-24, Utah; 26-23 (OT), BYU; 17-16, Utah; 54-10, Utah; 24-21, Utah; 20-13, Utah.

If Whittingham could script a formula for winning in Vegas, he probably would scratch out something similar to that last Ute victory, in which his team played strong defense, allowing a single BYU touchdown, and not getting crazy on offense, not turning the ball over.

Outside of the two blowouts, when things got loose for BYU, the margins between the teams have been extraordinarily tight. It's reasonable to believe it will go that way again this time around. Still, the Utes have found a way to stay on the favorable side of the recent numbers.

Those numbers suggest one of two things, or maybe it's a two-fer: Either the Utes have had better players than the Cougars since 2009, or/and Whittingham has ever-so-slightly better prepared those players schematically and emotionally to beat BYU, better motivated them.

Add to those conclusions the fact that, in bowl settings, Whittingham is 8-1 over his time as lead dog, while Mendenhall is 6-4, and that not only tilts the coaching disadvantage toward Bronco, it points a guilty finger at him. In his matter-of-fact, humdrum, all-opponents-are-the-same manner, Mendenhall hasn't quite stirred the necessary fire to give his side the burn required to get past the Utes.

There are added coaching wild cards in this game that could lean the whole nasty thing steeper toward Mendenhall — or finally tip it back the other way.

One is the mystery of whether the BYU coach's departure to Virginia, along with six of his assistants, has grabbed the attention of the Cougars, more urgently focusing their efforts and execution in this rivalry match, in the run-up to the game, or will it disintegrate all of the above, making the players less committed, more fragile in their practices and in the face of possible adversity, especially in the game's early going.

Just as significantly, how dialed in are Mendenhall and his staff as they have half a mind to prepare for the Utes and half a mind to take care of their business in Charlottesville? No matter how much those coaches claim they are all about the immediate matter at hand, it would be only human for them to let their eyes wander a bit — toward recruiting and rebuilding a Cavalier program in bad need of both.

But the uncertainties, the vagaries of circumstances as they pertain to coaching and preparation, also hover over the Utes. Nobody is sure how Utah will react to its severe drop from Rose Bowl contention just a few weeks ago to being shunned by other Pac-12-affiliated bowls, tumbling into the fear and loathing of Las Vegas.

"Kyle might do a good job of coaching," said former Utah coach Ron McBride, "but it won't make a big difference if the guys don't buy in and get ready. If they're disappointed about the way the season ended, and aren't excited about playing in this bowl game, that could be a problem."

It is Whittingham's job to make sure that doesn't happen.

Just as it is Mendenhall's to ensure his players don't give short effort on account of his bailing toward his new $17 million-plus deal at Virginia. Rather, making sure that they energize themselves to get Mendenhall his 100th — and last — win at BYU. More importantly, they must find good reasons to win the thing for themselves.

Controlling and directing players' powers of concentration, their drive and emotions, then, will be the biggest factor is who wins this game. The money here, although it's far from sure, is on the guy with the better track record — Whittingham.

GORDON MONSON hosts "The Big Show" with Spence Checketts weekdays from 3-7 p.m. on 97.5 FM and 1280 AM The Zone. Twitter: @GordonMonson.