Take a look at your Connecticut phonebook for a minute. Don’t look inside, just check out the cover and tell me what you see. Yes, it’s a photograph of the University of Connecticut women’s basketball coach Geno Auriemma standing atop a ladder, holding up the net that he and his team had just cut down after winning the NCAA tournament.

For Connecticut residents like me, this isn’t such an odd thing. The year before, the phonebook had Jim Calhoun, the Connecticut men’s coach, on the cover, cutting down a net after a national title.

A lot of you are probably looking at your phonebook, wondering why a basketball coach is gracing the cover of this volume. That’s a fair enough question, but it’s not like the phonebook’s Time or anything. If there’s one thing people in this state are wild about, it’s college basketball, so why not put the coach on the cover?

Once you get past that issue, you wonder why the coach, and not the players — who do all the work on the court — gets to smile at all the Connecticut residents who need to find a good carpet cleaning service.

Another fair point.

But if following the NCAA tournament teaches us one thing, it’s that this is the time when coaches earn those six and seven figure salaries. For whatever reason, some coaches have the ability to navigate their players through the draw, giving them a chance to win a national championship.

And why is it that certain coaches always seem to be in the Final Four while others have frequent flameouts despite heaps of talent? Because as the tournament progresses and the teams are increasingly evenly matched, the importance of coaching increases.

All of this brings us to tonight’s game between Arizona and Duke. It’s impossible to say that one team is clearly better than the other. Sure, Arizona has slightly more talent on paper, but Duke will have the best player on the court (Jason Williams) as well as the best leader and the all-around exploits of Shane Battier. Arizona is a little deeper, but Duke plays with an aura of invincibility that opponents sense even when leading by 22 points (see: University of Maryland).

If you were to input these teams into a computer and have the teams play 10 times, it could very well come out with each team winning five times. The teams are so even that the coach who handles his team the best during play wins the game.

Let’s look at an example. Two years ago, Duke and Connecticut were clearly the two best teams in the country, and they met in a highly-anticipated national title game. Duke was the more talented team (though Connecticut was loaded as well), but the Huskies put Jim Calhoun on the cover of the phonebook because his adjustments during the game were superior to Mike Krzyzewski’s.

Two such adjustments stood out in particular: the use of Ricky Moore as an offensive weapon in the first half — while Duke focused on stopping Khalid El-Amin and Richard Hamilton — and double-teaming Elton Brand every time he touched the ball in the post.

Brand struggled the few times that the Huskies doubled in the first half, so Calhoun sent his big men to attack relentlessly in the final 20 minutes. On the other bench, Krzyzewski could not come up with an offensive wrinkle to free up his best player in the second half.

As a result, Connecticut ruined the “Duke Invitational” with a 77-74 win thanks to a couple of seemingly small tweaks that Calhoun made. This certainly does not mean that Krzyzewski is a bad coach — nine Final Fours and two national titles are evidence of that. Two years ago, Calhoun was a little cagier and helped his team to the victory.

Looking back through NCAA history, you see a lot of teams winning close games because of great coaching jobs — Rollie Massimino in 1985, Jim Valvano in 1983 and Al McGuire in 1977, to name three from the last 25 years. But those were evidence of a different sort of brilliance, with the mentor leading his overmatched team to victory.

Tonight, Duke and Arizona are both tough and talented, and their coaches have each won previous national titles. So pay attention to the seemingly minor strategic wrinkles that each coach employs throughout the game. The one who puts his chess pieces in the right places will land himself on the cover of a phonebook next year.