But even Rios, who posted slightly better numbers in Texas than he did with the White Sox in 2013, understands the value of a full season with the same club -- at least from the standpoint of his own psyche.
"It's a lot easier to start with a team from Spring Training," Rios said. "When you get traded, you feel like you have to contribute right away. It's not that you put pressure on yourself, but you know that they wanted you for a reason, and your expectations grow for yourself. Sometimes it can be a hazard."
Rios is already off to a hot start this spring. After going 1-for-2 with a walk on Tuesday against the Angels, he's hitting .400. He's also swiped two bases and has earned praise from manager Ron Washington for his shrewd baserunning.
Rios believes -- quite accurately -- that it's too early to have any clue what kind of offensive season he'll put up. But he feels healthy and at ease, which at this point is all a ballplayer can ask.
"It's going to be even better," Rangers third baseman Adrian Beltre said of what he expects from Rios. "After a year passes, you get to know your teammates, and you've been around them more often. He's more comfortable. I think he can be more loose."
Beltre and Rios are two of the Rangers' elder statesmen. Their respect is mutual, and an experienced player like Beltre can appreciate what a peer like Rios brings to a lineup and a clubhouse.
"He's a veteran who knows what he needs to do to get ready every day," Beltre said. "He comes to play, and obviously his speed, power and knowledge on the field is what we need from our right fielder."
The Rangers have a team option of $13.5 million on Rios for the 2015 season, with a $1 million buyout. That buyout increased by $500,000 once he was traded.
With the two clubs combined last season, Rios batted .278 (also his career average) with 18 homers and a career-high 42 steals. He played 47 of his 156 games for Texas, where he hit .280.
Washington says there isn't much of a noticeable difference in the way Rios has carried himself this spring. But he's eager to see what Rios can achieve in his 11th big league season.
"He looks very relaxed, but he was relaxed and having fun when he joined us last year," Washington said. "He's in camp, and he looks like he belongs. I'm looking forward to watching him for a whole year, because the guy has a complete game. He can play defense, he can hit, he can run and he can run the bases."
Rios has switched teams midseason once before. In 2009, he went from the Blue Jays to the White Sox on a waiver claim in August.
The results were noticeably different that time around, as Rios hit a woeful .199 with only nine extra-base hits in 41 games.
"It does help to start with a team from the get-go," Rios said. "You've gotten to know everybody, and you've got a better feeling of how they do things."
So will his numbers get a boost this season, when he'll get the chance to spend a full year in Texas?
"I couldn't tell you, I've just taken  at-bats, so if I said so, I'd be lying," Rios said. "My physical feel -- I feel good, and that's the only thing I can ask for."