Would they really be better off without him? Are the Rangers prepared to look elsewhere? There are likely to be interesting free-agent options out there, especially Michael Bourn and B.J. Upton.
Still, that's a huge step for a club that has made three straight playoff appearances. Rangers fans are disappointed about how the season finished, and Hamilton appears to be the player they'd most like to show the door.
During five seasons with the Rangers, he averaged 129 games a season along with 31 doubles, 28 home runs and 101 RBIs. He had a .912 OPS during those five seasons, which is actually lower than his .930 OPS this season.
He's only 31 years old. He may not be worth a 10-year commitment, or even a five-year commitment.
But the Rangers could easily justify a three-year deal. If some team steps up and makes a wild offer, the Rangers might have an easier decision.
Once the emotions of the last few days calm down, Rangers president Nolan Ryan and general manager Jon Daniels will be faced with the tough decision to assign a value to Hamilton. Are the fans who booed Hamilton during Friday's 5-1 Wild Card loss to the Orioles sure they're done with him?
He was lousy at the end. There's no arguing that. He was also wildly inconsistent throughout. At his best, he was one of the five best players in baseball. At his worst, he was an embarrassingly easy out.
He batted .368 and had a ridiculous 1.184 OPS in April and May. And then he disappeared for two months. He hit .202 in June and July and had an equally ridiculous .687 OPS during those two months.
The Rangers were 31-20 and averaged 5.7 runs per game in April and May. They were 28-23 and averaged 4.2 runs per game in June and July.
He was all over the place after that, combining some terrific stretches with some awful ones. But the Rangers were 84-62 when he started and 9-7 when he didn't. Third baseman Adrian Beltre was by far the most valuable Ranger, but every hitter almost certainly benefited by having Hamilton's bat in the lineup.
There were stretches when huge holes in his swing were exposed, but he still had an enormously productive season. Despite everything, he finished the season second in the American League in home runs and RBIs, fifth in OPS and 21st in batting average. Fangraphs.com ranked him 15th in the American League in Wins Above Replacement.
That's way below Mike Trout and Miguel Cabrera, but allowing him to leave via free agency would create a huge hole in the lineup. That's the thing the Rangers will get back to once the emotions of the last few days fade away.
Daniels is smart and tough and will make a decision based on the whole of Hamilton's season rather than the last couple of weeks.
When the Rangers analyze the last few weeks, the team's problems began with a lack of quality starting pitching. Texas starters failed to last six innings in six of their last 10 regular-season games and had a 5.84 ERA in the last 18.
Still, great players are supposed to be at their best when the lights are the brightest. When the Rangers most needed him these last few weeks, he wasn't there for them.
He was casual in his pursuit of a fly ball on the final day of the regular season in Oakland and unproductive at the plate. Actually, he was staggeringly unproductive. In the last nine games, he batted .205 with 18 strikeouts in 39 at-bats. He went his final 52 at-bats without a home run.
With their season on the line Friday night in the American League Wild Card Game, Hamilton saw just eight pitches in four at-bats, striking out twice and grounding out weakly.
He was booed loudly after his final two at-bats, but offered no excuse after the game. At other times this season, he offered strange explanations for his problems, including consuming too much caffeine.
In the end, he's easily the toughest decision the Rangers will have this offseason. He's a unique figure, a survivor of a hellish battle with addiction. He has been the franchise's most popular player until recently.
He also has far more positives than negatives in his game. There's no way the Rangers will offer him a record-setting contract. They're so disappointed at this time it'll be interesting to see if they offer him anything.
Together, they've done some pretty special things the last three years. In that stretch, they had more playoff success than their previous 37 years combined. Allowing him to walk seems like an easy call in the wake of a 4-10 finish. It's actually anything but.
Richard Justice is a columnist for MLB.com. Read his blog, Justice4U. This story was not subject to the approval of Major League Baseball or its clubs.