SIGN R.D. ROSEN to a long-term contract. In his rookie season, he has delivered in the clutch with Strike Three, You're Dead (Walker, $12.95), a sprightly, entertaining sports mystery that will help baseball fans through these dreary winter months until spring training begins.

Even those unfortunate readers who are not fans and cannot share the delights of the game can enjoy a nifty mystery puzzle and the roster of colorful characters in Strike Three, You're Dead.

Is there any other amateur sleuth who plays centerfield, has a rifle arm to cut down base runners, and is hitting over .300 in the tough Eastern Division of the American League?

Ironically, Harvey Blissberg is having his best season at the plate with a losing team. The Providence Jewels, newest expansion team in baseball, are headed for the cellar. At 30, Harvey is at his baseball prime and was playing good baseball for the Boston Red Sox, a pennant contender, when he was left unprotected in the expansion draft.

So here is Harvey with the Jewels, a team nickname that comes from the owner's tacky costume-jewelry business and provides fodder for snide commentary from smart-aleck sports columnists. A college history major who knows there is life after baseball, Harvey has made the best of his roster change to a losing team. An affair with a woman TV sportscaster helps make life bearable in Providence.

Then, as if the Jewels didn't have enough troubles on the field, Rudy Furth, the team's top relief pitcher, is found in a bloody whirlpool bath, his head bludgeoned by a bat. Harvey would like to know who killed his road-trip roommate. Now, who would want to murder a relief pitcher whose recent ineffectiveness on the mound was one reason that the team had taken a nose-dive to the cellar?

Rosen knows his way around the baseball field and the clubhouse. The talk is gamey. The players are real guys, not the Robert Redford folk hero of The Natural. They worry about a hitch in their batting swing, bicker with each other, and grow moody on a losing streak.

It helps to know and like baseball to savor all the nuances of Strike Three, You're Dead. ("But extramarital affairs were as common as 6-4-3 double plays.") The vital clue does come from the statistics that dedicated baseball fans cherish.

But there is much beyond the baseball background to appease and attract nonfans. Rosen, a TV writer- producer in the Boston area, writes brightly and sharply. Providence is a little-used setting for mystery novels. Then there is a humdinger of a chase-confrontation scene in the clubhouse and on the baseball field with all the excitement of a 3-2 pitch with two out and the winning run at third base. $&%Foul Shot

DOUG HORNIG's Foul Shot (Scribners, $13.95) doesn't do for basketball what Rosen's book does for baseball. It really isn't a sports mystery. True, there are lively action scenes on the basketball court as the University of Virginia Cavaliers take on other Atlantic Coast Conference teams. But Hornig's first mystery deals with basketball only marginally. From the moment Loren Swift, the only private eye in the Charlottesville phone book, is ushered into the mansion of old Colonel Majors, you know you are in Raymond Chandler territory.

Secrets from the past fester beneath the surface. A wealthy, aristocratic family is full of hate and bitterness. Most of the characters are nasty people -- old Colonel Majors is a bigot who mixes his racial slurs with sexual leers; son John is an uptight stick; John's wife is a whore; the younger daughter, Melissa, is freaked out on drugs, sex and alcohol.

The only decent members of the family are the older daughter, Leigh, and the Colonel's former wife, who fled the fold long ago. And then there is Delmos Venable, the black basketball superstar who grew up with Leigh.

Swift, the wisecracking narrator-sleuth, is likable enough as he solves a tangle of three murders. Hornig has a nice touch with his Swift-paced action and repartee. Now that he has borrowed from earlier hard- boiled detective practioners, perhaps he will be his own man. We'll be patient because he shows promise. Dorothy Parker

IF YOU remember George Baxt for such delightfully zany mysteries as A Queer Kind of Death and Swing Low, Sweet Harriet, you are going to be sorely disappointed -- and angry -- with his latest, The Dorothy Parker Murder Case (St. Martin's, $14.95). It is tasteless, exploitive, presumptuous and precious.

Baxt has the audacity to put words into the mouths of Dorothy Parker, Alexander Woollcott and other legendary wits of the Algonquin Round Table. Not any words -- but words that make them sound like third- rate standup comics.

"Take your husband," Sara Murphy says to Dorothy Parker.

"You take him. I can't stand him," Parker retorts.

It is August 1926. Crowds of sobbing women in black have gathered to mourn Rudolph Valentino. He had been taken ill at a party while escorting Ilona Mercury, a Ziegfield Follies girl. When Ilona is found strangled in George S. Kaufman's intimate pied- a-terre Parker and Woollcott join forces with a friend on the police force to solve the crime. Murder on Mike

MORE NAME-DROPPING, this time from the late '30s and the '40s, in Murder on Mike (St. Martin's, $12.95).

There is a cameo appearance by Ed Sullivan when he was a columnist for the New York Daily News in pre-TV days. Other famous names pop up on nearly every page: Damon Runyon, Walter Winchell, Mayor LaGuardia, Prosecutor Thomas E. Dewey, Lucky Luciano, Lou Gehrig.

It is 1939 in New York City. This is the golden age of radio. Listeners arrange dinner and social schedules to hear the cascade of junk falling from Fibber McGee's closet, the thundering hoofs of the Lone Ranger, and the machine-gun bursts of Gangbusters.

For Murder on Mike, H. Paul Jeffers (Murder Most Irregular, on the Baker Street Regulars), has created a fictional Sunday night series titled "Detective Fitzroy's Casebook." Millions of listeners instantly recognize the voice of Derek Worthington as Fitzroy, that of Maggie Skeffington as the Gal Friday, Miss Molloy, and that of David Reed as the announcer.

When Worthington is shot to death in the studio between the final rehearsal and the live show, the police think they have an open-and-shut case. The shot was heard precisely at 6:05 p.m. over an open mike by a Radio City tour group. Reed is the only suspect without an alibi for that time.

Harry MacNeil, ex-cop, private eye, and sucker for a sweet Irish face, agrees to try to prove Reed's innocence on pleas from Maggie. He has to take a primer course in sound effects and radio technology before he gets a glimmer of the solution.

The problem is that the alert reader will have figured out how one of the clues could have been faked several chapters before MacNeil does.

If short on detection, Murder on Mike is long on nostalgia. It's rather nice to recall a time when Gone With the Wind was tying up traffic at two elegant Manhattan movie palaces, while Cab Calloway and Bojangles Robinson were opening the Cotton Club.