QUARTERBLACK Shattering the NFL Myth By Doug Williams with Bruce Hunter Bonus Books. 275 pp. $18.95

THROUGHOUT America's history of discrimination against its black citizens, two recurring and deliberate myths were proffered: They are not smart enough, and they are not tough enough. Phillis Wheatley's poetry in the late 1700s was assumed to be ghost-written; no black woman could have possibly penned such elegant phrases. More than 60 years later, Union generals were loath to assign combat duty to black volunteers as was so graphically depicted in the recent movie "Glory."

'Twas ever thus for black athletes as well. America's first genuine sports hero, the white boxer John L. Sullivan, the Boston Strongboy, repeatedly branded Jack Johnson as "yellow" and "a coward" before Johnson KO'd Jim Jefferies in their famous 1910 encounter. Negro League baseball players were thought to be not intelligent enough to play in the majors, according to Commissioner Kennesaw Mountain Landis in the 20 years leading up to his death in 1942. And of course even today some believe blacks don't have "the necessities" to manage sports franchises or corporations. Or play quarterback in the National Football League.

I wish I could say that at the very least Doug Williams changed this prevailing view about black quarterbacks. But in truth his record-tying Super Bowl XXII performance on Jan. 31, 1988 -- throwing four touchdown passes en route to leading the team to a 35-point second quarter -- only gave some doubters pause to think, "Well, maybe there are a handful who are up to the task." In Williams s new book, Quarterblack, he takes the reader through that winter Sunday in San Diego's Jack Murphy Stadium when he rent apart the NFL record for total passing yardage, total team yardage and number of touchdowns. The real story, however, is how Williams endured five years at Tampa Bay, and managed to keep his dignity in one piece.

I remember his years at Tampa Bay. The Buchaneers were 0-26 before Williams arrived, and after helping them to the National Football Conference championship game in his second season, he was still the 54th highest paid quarterback in the league three years later. Ridiculous by any standards.

Williams had plenty of warning about the Hugh Culverhouses (the Bucaneers

owner) of the world. He was coached by Eddie Robinson at predominantly black Grambling University in Louisiana. Robinson himself had at one time been considered for a head coaching job in the NFL, and would have been the first black to hold such a job had it materialized. Quarterbacks who play at schools like Grambling with hopes of an NFL career are forced to prepare to be switched to a position like wide receiver. The reasoning is speciously clear: Black college offensive strategies are not sophisticated enough to give serious attention to their quarterbacks.

There are other interesting stories in Quarterblack. Zachary, La., Williams s hometown, is hardly akin to the hills of western Pennsylvania where great football players can be mined like coal. Williams called his World War II-disabled father before every game, and the strong, traditionally religious black family values were reinforced over the wires. Interesting as well is a recounting of life as a married warrior in the NFL.

His first wifedied of a brain tumor, which left him with an infant daughter. Another wife became a profligate spender, as has most of the rest of America that tries to live to the limit of its credit instead of the limit of its incomes. The reader's reaction to this is almost sure to be "Ah yes, I know somebody just like that." WILLIAMS DID not singlehandedly win the Super Bowl, and his Washington Redskins teammates appear throughout the book. He gives ample credit to his supporting cast in this contemporary account of the hard work and discipline that it takes to win such events as the Super Bowl, World Series, Stanley Cup, etc. If Hugh Culverhouse of Tampa Bay is pictured as unappreciative, stingy and fearful of giving a black quarterback his full confidence, Jack Kent Cooke was sensitive and highly respected by the entire team. Tampa Bay's coach John McKay was a good person without the clout of Joe Gibbs of the Redskins who reflected the best intentions of Cooke.

Next to Culverhouse, Williams reserves the fewest nice words for Jay Schroeder, whom he initially came in to back up at quarterback. Gibbs switched to Williams as his starter for the playoffs in 1987 and Schroeder reportedly stopped talking to his erstwhile substitute. It was a potentially explosive racial situation, since Schroeder is white and was making $900,000 per season, and Williams substantially less. Apparently, however, the team felt the change was overdue all along.

It is difficult near the end of Quarterblack not to compare it with previous books by black NFL players, especially Jim Brown's Off My Chest. Both men had difficult adjustments in their professional careers, and were initially underappreciated. The three so-called "whites only" positions of center, middle linebacker and quarterback were part of orthodox coaching theory in Brown's era in the late 1950s and early 1960s. Ironically, the Redskins themselves were the last NFL team to sign a black player, Bobby Mitchell, who came from the Cleveland Browns. The 'Skins had a Southern-based radio network that former owner George Marshall didn't want imperiled.

Inevitably Art Shell, the first black NFL head coach, will write a book one day, and this next-to-last layer of the team sports onion will be peeled away. That will leave only one to be written by the first black owners of an NFL franchise. Quarterblack, meanwhile, will make our Sunday afternoons and Monday evenings a bit more informative. Arthur Ashe is the author of "A Hard Road to Glory," a three-volume history of black American athletes.

Excerpts from "Quarterblack" begin in Sports this Sunday.