ROCHESTER, N.Y. -- Even in the midst of a perpetual learning process, it never hurts to step back and take stock of what you already know. And in beating Mexico 3-1 in Wednesday's international friendly at PAETEC Park, the U.S. again saw that Abby Wambach is to its success what the Pythagorean theorem is to a geometry student's success.
The U.S. can solve problems without Wambach, and will need to be able to solve more by the time it faces stiffer tests from teams like Germany in next summer's World Cup, but Wambach is both literally and figuratively a solid foundation on which to build.
Playing in front of a vocal crowd of 6,784 that cheered every move the Rochester native made in her homecoming, Wambach came through with two first-half goals and a performance that showed off both her trademark power and the all-around skills that occasionally get overlooked as a result of her sheer size and skill in the air.
Using a quick first step to induce a whiff from a would-be tackler after a pass from Carli Lloyd in the 17th minute, Wambach drew a penalty in the box from a second defender who was left with little choice but to pull her down from behind. In the space of 10 yards, she proved to be both quicker and stronger than anything Mexico's back line could offer.
Wambach's second goal was more of the same. Taking in a pass from Leslie Osborne, she controlled the ball while turning away from a defender and drilled a hard shot off goalkeeper Sophia Perez's hands from 14 yards out.
"You've got to do whatever you can," Wambach said after the game. "I'm obviously bigger and hopefully stronger than most of the people out here. I just have to use everything I can, because I'm not necessarily the quick, slashing forward. I mean, I have some speed, but mostly I'm powerful and strong and I need to use that to my advantage."
Only a slightly errant shot after a solo run, that saw her hold off a defender for about 10 yards, prevented her from scoring a hat trick in the opening half. As it was, the two goals moved Wambach to within one of Shannon MacMillan for sixth all-time among U.S. players (in nearly 100 fewer games than MacMillan).
It was a tremendous individual performance that sent the crowd home happy and helped move the U.S. to 19-0-4 under Ryan (including a penalty shootout loss against Germany in the final of this year's Algarve Cup).
However, the story of the night isn't necessarily what will matter most in the long run for the U.S. team. After all, everyone -- from the fans in Rochester to the defenders for Germany and Brazil -- knows what Wambach is capable of when defenses don't successfully maul her. What remains to be seen on the biggest stage is what else the United States will bring to the table.
Missing Cat Whitehill, Kate Markgraf, Shannon Boxx and Heather O'Reilly -- four players who are at least strong favorites to start should the U.S. qualify for next summer's World Cup -- Greg Ryan's team had an opportunity to experiment in a few places. Before Wednesday's game, Ryan said he felt the roster was at least 90 percent set for World Cup qualifying, but that doesn't mean each role within the roster is set.
Without Whitehill (plantar fascia) and Markgraf (still coming back after giving birth to her first child), the U.S. was without its two best central defenders against a team with at least a little offensive firepower. Ryan's solution was to move Christine Rampone (and in the second half, Heather Mitts) from the outside to the middle.
Considering Mexico finished with just three shots, the results were even better than he may have hoped for.
"Fantastic, I'm really happy," Ryan said of the defense. "I mean we had four outside backs on the field for awhile. And I'm really happy, because we want out outside backs to be able to play in the middle, but Christie Rampone and Mittsie [Heather Mitts] are outside backs, and they both did a great job in the center. So I was very happy with the way the defense played."
The one goal that Mexico did score came on back-to-back mistakes by natural center back Amy LePeilbet and goalkeeper Hope Solo. When LePeilbet misplayed a pass from Solo, Mexico's Monica Ocampo pounced on the loose ball and drilled a shot past Solo, who was slow to get back on her line.
At halftime, United States goalkeeper coach Marc Dougherty could be seen indicating that Solo, who has a history of brilliant play marred by occasional glaring lapses, was a little nonchalant in getting back to her line after making the pass.
"Our goalkeeper coach addressed it with Hope," Ryan said. "You've just got to follow that up. If you play a ball out that direction, you've got to stay in that angle. There's nothing you can say to a defender when you make a mistake like that. It's one of those things that happens, you try not to do it again."
Even that mistake led to a positive for the United States, as less than a minute later an Aly Wagner pass found Lindsay Tarpley streaking down the right side, where she chipped a beautiful shot over the approaching goalkeeper to reclaim the lead for the United States.
"That's a coach's dream," Ryan said. "You give up a bad goal, and your team gets together, responds and comes down the field and scores a great goal. So yeah, really happy with the way they came back from that."
Starting at forward in place of former North Carolina teammate Heather O'Reilly -- who missed the game with an injury sustained last week playing for the Tar Heels -- Tarpley was another bright spot with her energy and aggressive play.
"Lindsay Tarpley has changed the complex of our whole starting forward lineup," Wambach said. "She gives us a total different look. She keeps the ball in possession for us like a midfielder does, she can get behind defenders and the girl can run all day."
Whether she remains in the mix at forward or returns to midfield, where she played earlier this year, Tarpley made a statement against Mexico that she can be a valuable part of the offense.
"For me, I just look at it as if I can be more versatile and get on the field -- in midfield, up front -- it really doesn't matter," she said after the game.
Wednesday's win was anything but mistake-free, but this is the time of year when mistakes are permissible in pursuit of bigger goals. And in getting productive minutes from new faces like Megan Rapinoe and Stephanie Lopez, and from old faces in new places, the United States continued a learning process that ultimately is more important than one win on a Wednesday night in Rochester.
Of course, on this night, even the big picture somehow comes back to Wambach.
"You talk about leadership and leading off the field, but you see her leadership on the field," Ryan said. "You can just see she's helping the young players, she's talking to them, she's directing people. And it's all good stuff. With the direction she's giving them, it's like having another coach on the field. I thought she just gave so much to this game tonight: her effort, her intensity, her focus and big heart on the field tonight."
Standing on the field in a parka after the game (she may be from Rochester, but the California resident admitted her internal thermometer is no longer set according to upstate New York weather), Wambach was the center of attention and the star of the night. But the smile on her face was likely due in part to feeling more and more comfortable that she won't always have to play that role for this team to win.
Graham Hays is a regular contributor to ESPN.com's soccer coverage. E-mail him at Graham.Hays@espn3.com