Because of all of that, Fuentes was told early in his career that he would be best-served as a left-handed specialist out of the bullpen to face strictly left-handed batters.
But Fuentes worked hard to shed that image and was rewarded by becoming a full-time closer for the first time in 2005 with the Rockies. Since then he has unquestionably made the most of his opportunities.
His 163 saves are 10th most all-time by a left-hander, his 84-percent success rate is third best by left-handed relievers with at least 100 opportunities, and, he led the Majors this season with 48 saves for the Angels.
It has been a long journey for Fuentes, who will now be called upon if the Angels have a lead in the ninth inning against the Yankees in the American League Championship Series.
"Closing was something I always saw from afar and didn't think I'd get the chance to do," Fuentes said. "As a left-hander, I was always told I'd be a specialist. But I tried to dissolve that image as quick as possible by getting lefties and righties out.
"I ended up getting fortunate to get the opportunity in Colorado, but it was one of those things where I didn't know how hard it would be until I blew a couple. But now it's something I embrace and take a lot of pride in."
Fuentes can surely take pride in his first season with the Angels. He finished the year with 48 saves in 55 opportunities, a 3.93 ERA, 46 strikeouts in 55 innings pitched and was named an All-Star for the fourth time in his career.
"He had a great year," rookie reliever Kevin Jepsen said. "All year all we've been trying to do is get the ball into his hand. We know once he gets the ball, we know he's going to close to out."
Fuentes, though, admittedly hit a few rough patches during the season, including the first two weeks of September when he had a 7.94 ERA and two blown saves in eight appearances.
But after that funk, Fuentes went on to convert his last seven save opportunities without allowing a run and kept it going in the Division Series against the Red Sox with two more saves without allowing a run.
Fuentes' success in the Division Series was not lost on Angels manager Mike Scioscia, who saw that all four teams that lost in the first round had a closer that blew a save -- the Cardinals' Ryan Franklin, the Rockies' Huston Street, the Twins' Joe Nathan and the Red Sox's Jonathan Papelbon.
"There's nothing that a closer will do that will be swept under the rug or missed," Scioscia said. "But every hitter he faced that series, he looked crisp. He made really good pitches and closed out some games against really good hitters. He's an important part of our puzzle."
Fuentes admitted that earning his first two postseason saves was exciting, but like any good closer, he's already turned the page and is focused on his next opportunity.
"It was nice," Fuentes said. "But just like when you pitch poorly, it's a short-memory thing. You have to wash it out and forget about the past. It's time to move on."
Fuentes' focus is now set on the Yankees, who led the Majors in runs this season because of their ability to get on base and hit for power.
The Yankees' lineup is as deep as they come with seven hitters in their lineup with at least 20 home runs. Center fielder Melky Cabrera hit the fewest with a respectable 13 homers while splitting time with the speedy Brett Gardner, who hit just three homers but stole 26 bases.
So if there are any weaknesses in that lineup, Fuentes hasn't seen one yet.
"It'd be nice if there was a pitcher's spot, but I guess that's not until the next round," Fuentes said with a laugh. "But you have to bear down and get through it. There's always a guy that can hurt you so you have to keep the ball down and get ahead."
Fuentes has had mixed results against New York in the past, with a 4.50 ERA in five appearances with four saves. He also blew a save in his only appearance this year at Yankee Stadium when he allowed two runs to lose a game without even recording an out on May 1.
But Fuentes says he's not worried about pitching in that hitter-friendly ballpark, because he pitched in the high altitude of Colorado for seven years before joining Los Angeles as a free agent last offseason.
"Coming from Coors Field, I'm a little used to it," Fuentes said of pitching in a hitter's park. "It's just part of the game, but our guys will have that same advantage."
Fuentes' teammates, however, won't have much of an advantage if Yankees closer Mariano Rivera comes in. Fuentes praised the all-time leader in postseason saves and ERA.
"He's the best closer of all time, and I know our hitters are aware of that," Fuentes said. "But once they get in the box, I'm sure they don't care, and they just want to scratch some runs across."
And if the Angels can scratch some runs across against Yankees pitching and take a lead into the ninth inning, Fuentes is ready for the challenge.
"I wouldn't say I'm cocky, but I'm confident in my abilities," Fuentes said. "I'm confident in my game plan, that whether I'm facing 7-8-9 or 1-2-3 in the lineup, I can get the job done."
Rhett Bollinger is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.