Ah, January. A time when a new year comes, when winter is at its peak and when the rumor mills around the NBA churn madly as time moves closer to the February mid-season trade deadline.

For some players, it's a chance to move out of a frustrating situation and begin anew, sometimes on a team that is destined to win a title that year. For teams, it's a time to wipe the slate clean and begin rebuilding, or to hunt for that one critical missing piece that can complete the championship puzzle. And for other players, it's a hard time—a time when they must part with dear friends and teammates and cities that they have come to call home as one of the hardest parts of the business is enacted despite their wishes.

There are a lot of big names—names that can instantaneously impact whatever team acquires them—being thrown about this time around on the NBA trade market. Names like Jeremy Lin. Carmelo Anthony. Rajon Rondo. Pau Gasol. And that's just for starters. For some of these players, they cannot get out of their current situation soon enough, and a change of scenery could be just what the doctor ordered. But some of them may not be looking for a change of scenery. Some like where they are just fine, and could be disrupted by the idea of moving to another team. The fact is, however, there is a strong chance that some of these players may not be wearing the current jerseys they are wearing now after the Feb. 20 NBA trade deadline comes and goes.

But which of these players are most affected by trade rumors? Who is playing better? Who is starting to slide in the stats column? And who might be better off finding a new home? Let's take a look. 

Jeremy Lin

Lin bolted from New York, the city where he became practically a household name in a matter of weeks, for Houston in the summer of 2012 for a bigger paycheck than what Knicks owner Jim Dolan was willing to offer the fan-favorite point guard that helped turn the Knicks' season around. But he found life in Houston to be a greater challenge than he anticipated in his first year. His play was inconsistent and splotched with flashes of both good and bad. One season later, Lin seems to have found his groove as the sixth man for the Rockets, at one point averaging 15 or more points per game on 49.3 percent shooting from the field in November. Yet, rumors have been buzzing for more than a month that the Rockets might seek to part with Lin in a trade—perhaps as a package deal with disgruntled center Omer Asik—as a way to shave off their combined salaries, which approach $30 million for next season, and to bring in another key player in their NBA title quest.

CHECK OUT MORE OFJEAN PAUL'S JEREMY LIN/NBA STORIES HERE

During the last five games since he returned from a back injury, Lin has struggled, particularly with his shot—his shooting percentage has dipped to 40.7 percent. A lot of that may have to do with the back injury and Lin readjusting to the game after time off. However, it's doubtful that Lin hasn't heard the rumors about potentially being traded. It's no secret that Lin is close with a lot of the players in Houston, and they love having him around. But are the whispers of a trade starting to impact Lin at a critical time when he will have to step up to fill in for the injured Patrick Beverley as the starting point guard of the Rockets again? It's hard to say, but it's a theory that should not be dismissed. But with Beverley out, James Harden coming off injuries of his own and Houston's backcourt looking thin just as they are starting to chase San Antonio for the Southwest Division lead, it might not be the best time for the Rockets to pull the trigger on a Lin trade now.

Luol Deng

Luol Deng loves Chicago and Chicago Bulls fans love Luol Deng.

There's a reason for that. After two back-to-back All-Star Game selections, Deng has emerged as one of the best forwards in the league. But that hasn't stopped the Bulls from looking into shopping Deng, who becomes a free agent after the season. Already making over $14 million, retaining Deng won't be cheap and after losing Derrick Rose for the season—and perhaps longer—the Bulls look to be more into rebuilding and getting under the salary cap than they are about chasing the Miami Heat for the Eastern Conference crown. Deng has gone on record stating that he doesn't want to leave Chicago, but the South Sudan-born star may not have a say in the matter, especially if the Bulls shift in their optimistic stance that Deng will re-sign with them after the season.

Deng is coming off an Achilles injury and put up decent numbers in Chicago's Tuesday 85-79 loss to Toronto, hitting 6-of-15 from the field for 16 points, and averaged 22.3 points for the month of December. The only thing slowing Deng down so far is injury, and even that won't be enough to keep him from what is likely to be a third-straight NBA All-Star Game, whether it's in a Bulls uniform or not.

Zach Randolph

Randolph has a great thing going on in Memphis, so it's not hard to understand why he wouldn't want to leave.

His arrival in 2009 marked a turnaround for the franchise that has since made the playoffs in three of the four seasons Randolph has been there, the prize season being last year, when the Grizzlies reached the Western Conference Finals. Unfortunately, while Memphis has a winning team, their small market status has made Grizzlies ownership very cost-conscious, as evidenced by their willingness to trade star player Rudy Gay to Toronto last season. Randolph has not been above trade rumors himself, his name having been thrown around fairly often in the last month—something that he admitted "bothers" him on a personal level.

So far, that hasn't been bothering him on the court, as far as the eye can see. Over his last 10 games, Randolph has looked as strong as ever, averaging 18.2 points and 11.3 rebounds. Randolph is a pro right down to the bone, and the Grizzlies, though always looking for ways to save due to their market constraints, would not be wise in trading Randolph just to try and save a buck. Still, if that is what they ultimately go for, Randolph is dangerous enough to go out there and make some lucky team very happy.

Pau Gasol

It's hard to think that after years of being a cornerstone of the Los Angeles Lakers—years that yielded two world titles for L.A.—Gasol would be looking for a change of scenery. But injuries and a shift in his role thanks to a different offensive scheme employed by Lakers coach Mike D'Antoni have caused the four-time All-Star and former NBA Rookie of the Year (2002) to decline in stats and effectiveness. However, over the last month, Gasol has shown flashes and signs that there might be more left in his tank than people realize. Over his last seven games, Gasol has averaged 17.3 points on 50.5 percent shooting for the Lakers.

If he remains healthy, Gasol can be very potent for any team that he is a part of. While he thrived in Phil Jackson's triangle offense, Gasol's made no secret that he hasn't been able to fit in well in D'Antoni's fast-paced offensive system. And with the Lakers starting to look toward rebuilding, it looks like Gasol might be on his way out of L.A. for greener pastures elsewhere. If he lands on a decent team, he could make them good. If he lands on a good team, he could make them great. And if he lands on a title contender, then the balance of power might shift greatly. Gasol is still that good.