Neither has had a smooth path to this point, and there are clubs that appear to see their signings as bigger risks than the usual big-ticket free agents. Still, there are a sufficient number of clubs that see the positives outweighing the negatives to suggest that Greinke and Hamilton are going to land huge deals.
First, there's Hamilton. He appears to be the bigger question mark because his issues are so complex. At his best, he's easily one of the three best players in the game, a guy who sometimes makes the game look easy.
In his last three seasons with the Rangers, he has averaged 34 doubles, 33 home runs and a .952 OPS. He has also averaged just 134 games a season, so the team that signs him must understand he's going to miss some time.
Here's the other part of the deal. At times, he appears to lose focus. He seems disinterested at the plate and in the outfield. His at-bats seem half-hearted, his play in the outfield just short of embarrassing.
For instance, in a May 26 game against the Blue Jays, Hamilton played despite suffering from a flu bug. His body language that day was terrible. He looked overmatched at the plate and seemed about to collapse in the outfield.
But with the Rangers trailing by a run in the bottom of the 13th inning, he drove a two-run home run over the center-field wall to win it.
There were times last season when he looked like the American Leaguer most likely to win the Triple Crown. On the morning of June 1, he was hitting .368 with 21 home runs and 57 RBIs.
He hadn't been just good. He'd been scary good. The Rangers were running away with the AL West, leading by 5 1/2 games.
But then Hamilton hit .223 in June and struck out 35 times in 94 at-bats. He suddenly seemed lost and never really got his complete game back. His final numbers were terrific, but they came in bursts.
He hit just .245 after Aug. 31. When the A's were sweeping the final series of the year to win the division, Hamilton was 2-for-13 with no home runs and six strikeouts. He played a fly ball nonchalantly and dropped it in the 161st game of the season.
When the Rangers most needed him, he simply wasn't there for them. In the days after the season, the Rangers seemed unlikely to offer him a single dollar, much less $100 million.
Emotions seem to have cooled in the weeks since. The Rangers have taken a deep breath and attempted to look at the whole package, at both the incredibly productive player as well as the guy who misses some games and doesn't always seem to have his head in others.
Some executives have wondered if the years of substance abuse will end up shortening Hamilton's career. While that question can't be answered, the basics can be: Even with all the negatives, Hamilton is the most electrifying offensive player available in this year's market.
The Red Sox are thought to be kicking the tires. The Phillies have at least taken a look. The Rangers would like to sign him if the dollars and years don't get outrageous.
Likewise, Greinke comes with a bit of baggage, although certainly less than Hamilton. He's two years younger, but he missed most of the 2006 season with social anxiety disorder and depression.
Since his return, he has missed no more time. And in the last five seasons, he has been terrific, averaging 32 starts and 207 innings a season with a 3.39 ERA. He has pitched more than 200 innings in four of the last five seasons.
His history has led some to speculate that the big-market clubs will shy away from him. But Greinke has laughed at such a notion, telling friends he can do just fine in any environment.
At the moment, he appears to be the most sought-after of the big-ticket free agents. The Angels would love to keep him. The Rangers would like to steal him away. And some executives believe the free-spending Dodgers will end up landing him.
It's probably not too simple to say that those three teams believe Greinke would make them good enough to win the 2013 World Series. They might all be at that level anyway, but they all see him as one of, if not the, final piece to the puzzle.
For both Greinke and Hamilton, there were times when it seemed neither would get to this point, and that probably makes them appreciate their accomplishments even more. This offseason is their time.