DETROIT — C. C. Sabathia has been a boon to the Yankees since he arrived in New York, going 59-23 with a 3.18 earned run average in three seasons, and leading the team, both on and off the field. In 2009, he repaid his huge contract by leading the Yankees all the way to a World Series championship.

Paul Sancya/Associated Press

Sabathia says he loves pitching for the Yankees, but there is a small chance he threw his last pitch for them Monday night. In Game 3 of this American League division series, he started as the Yankees lost to the Detroit Tigers, 5-4, leaving them on the verge of elimination heading into Game 4 on Tuesday night.

Sabathia can opt out of his seven-year, $161 million contract after the season and become a free agent. Most players who have those options in their contracts tend to exercise them. That does not necessarily mean they want to leave, though. Sometimes, as in the case of Alex Rodriguez in 2007, opt-outs are used as a way to secure a longer, more lucrative contract with the same team.

Sabathia, for his part, has expressed only happiness during his time in New York. As recently as Sunday, he said there was no better place to play.

“It’s the Bronx,” he said. “It’s the Yankees, with all the history and tradition. It’s just unbelievable, especially around this time. I always will say this is the best place to play.”

Those are encouraging words for the Yankees. But the front office will still have to assess how much more of a commitment it is willing to make to Sabathia, who has four years and $92 million on his current contract.

Sabathia turned 31 on July 21, and although he has been a durable and dogged pitcher since he arrived, there were signs that fatigue might have caused a downturn in his effectiveness in the second half of the season. The Yankees need to determine if that is the beginning of a trend, or an anomaly.

In the first half of the season, Sabathia was 13-4 with a 2.72 earned run average, and was possibly on his way to the Cy Young Award. But in the second half of the season he slowed, going only 6-4 with a 3.44 E.R.A. Always willing to throw deep into games, Sabathia finished fourth in innings pitched with 2371/3.

Perhaps all those pitches took their toll as the season wound down. In Game 3 on Monday, Sabathia struggled with the strike zone, which the Yankees felt was abnormally small, and battled his command all game.

“He hasn’t thrown the ball bad,” Manager Joe Girardi said of Sabathia’s last two months of the season. “He set such a high expectation when he was on that roll. Probably impossible to keep that up or he probably would have won 25 games. Teams have made him work a little bit more, and maybe he hasn’t been quite as sharp.”

Whatever turning point there may have been from Sabathia’s dominant first half to his merely good second half might have come July 26 against the Seattle Mariners. That was when Sabathia was working on a perfect game and came back after two short rain delays, one 30 minutes, the other 14. Sabathia ultimately allowed only one hit and one run in seven innings and struck out 14.

Since that game, however, his numbers went into a steeper decline. In 10 starts since that soggy night, Sabathia went 4-3 with a 4.06 E.R.A.

There was also the issue of the six-man rotation. Sabathia likes to pitch every five days, but was unable to do so for most of August and September. But Girardi felt any connection between his small downturn and the expanded rotation did not affect Sabathia. In fact, Girardi felt it helped him.

“With the innings that he logged, yeah, I think he did,” Girardi said.

JETER’S STRUGGLES Derek Jeter went 4 for 15 in the first three games of the division series, and had a tone-setting hit off of Justin Verlander in the first inning of Game 3. But he also struck out in three key late-inning situations in Games 2 and 3, leaving runners in scoring position all three times. But Joe Girardi said there was nothing alarming about that since Jeter struck out twice against closer Jose Valverde and once against Al Alburquerque.

“That’s why they get paid the big bucks,” Girardi said, “to get those big outs.”

TOO MUCH MONEY? A spoof of the movie “Moneyball” that makes fun of the Yankees’ ability to spend huge amounts of money on players has been making the rounds on YouTube. The central character in the faux trailer is Brian Cashman, the Yankees’ general manager, who wonders what to do with all the money the Yankees have.

The real Brian Cashman said he saw the clip and thought it was very good.

“I liked it,” he said. “I thought it was really funny.”

Speaking two hours before the start of Game 4, Cashman said he felt good about his team’s chances, not only to win that game, but a potential Game 5 as well.

“I’m looking forward to the next 18 innings,” he said.