KANSAS CITY, Mo. — Right-hander Zack Greinke and the Kansas City Royals agreed Monday to a $38 million, four-year contract that avoided a salary arbitration hearing next month.

Greinke went 13-10 with a 3.47 ERA in 32 starts for Kansas City last season, setting career highs in strikeouts (183) and innings (202 1-3). His 3.47 ERA was the best by a Royals starter in 11 years.

After earning $1,475,000 last season, Greinke had asked for $4.4 million when he exchanged proposed arbitration salaries with the Royals last week. The team offered $3.4 million.

He gets $3.75 million this year, $7.25 million in 2010, and $13.5 million in each of the final two seasons.

Greinke would have been eligible for free agency after the 2010 season.

Often moody and uncommunicative early in his career, Greinke left Kansas City's spring training camp in 2006 and returned to his home in Orlando, Fla. The Royals had been worried for more than a year that the pitcher, the No. 6 overall pick in the 2002 amateur draft, might quit baseball.

Since finishing treatment for social anxiety late in the 2006 season, Greinke has steadily improved his on-field performance and admitted baseball had become fun for him.

Kansas City has three more players scheduled for arbitration hearings: outfielder-infielder Mark Teahen, first baseman Mike Jacobs and right-hander Brian Bannister.