It is a measure of Muhammad Ali's greatness that a book this frustrating can be this good. It should be simple. You have the greatest sportsman of the century, about whom some of the sharpest American writers of the century have written. The only difficulty lies in the editing, in what to leave in or out. Yet Gerald Early begins from the wrong premise; his introduction serves as a meditation on Ali the black icon, not on Ali the boxer. He quotes Garry Wills' observation that "modern Pindars sing the weirdest songs about Ali. They cluster around him, trying to probe non-existent mysteries." The irony is that Early spends much of his introduction probing for non-existent mysteries; but the mystery of Ali lay not in his blackness or politics, but in his boxing.
Ali himself cleverly played with the prejudices and uncertainties of the white establishment, especially when burdening his black opponents with stereotypes - Frazier is a gorilla, Shavers "shiftless". But you cannot say, as Norman Mailer does here, that his encounters with black fighters can be read as the beginnings of a "psychology of the blacks".
Still, the politics do matter. There is the remarkable transition from draft dodger in the 1960s to national icon; there is the craven, terrified reaction of the boxing authorities when, at the height of his powers in 1966, Ali announced, "No Vietcong ever called me nigger". It was only in the late 1970s that the establishment started rooting for Ali, once his powers had waned and he had turned his back on the followers of Louis Farrakhan.
Ali needs great writing - indeed can cope with great writing - because of the special demands of boxing. To those of us who have never stepped inside a ring, it is almost impossible to understand the stamina, speed and pain of the fight game. Mailer captures something of this when he writes that Ali "played with punches, was tender with them, laid them on as delicately as you put a postage stamp on an envelope, then cracked them in like a riding crop across your face".
Some of the best writing here comes from Hunter S Thompson. He is the ideal ring-side companion for the wild-eyed appetites of Vegas '78, and that first contest with Leon Spinks (the pre-fight entertainment included Isaac Hayes performing a disco version of "America the Beautiful", and Joe Frazier singing "The Star Spangled Banner".). And how can you resist this verbal flourish from Thompson: "Now Frazier disappears from view/The crowd is getting frantic/Our radar stations have picked him up/He's somewhere over the Atlantic".
When he is not being hysterical, Thompson is thoughtful; the fascination of Ali, he says, is that unlike most celebrities, he has a "ring of moats around him"; what's more, he has learnt the subtle art of making each one seem like the last you need to leap over to get to the essence of the man.
Ali's decline, from superb athlete to the shambling wreck that he became, is poignant. The circus of public adoration continues even as his voice becomes ever quieter, his eyes glaze over, and his body trembles. The portraits here of Ali in the last two decades are affectionate, devastating. They are also satisfying because they carry the fewest expectations in the book; they don't attempt to over-intellectualise boxing in the manner of Gerald Early, who too often searches for complexity where there is none.
There would have been no shame, for instance, in straight talking, in saying that no other fighter has regained the heavyweight championship twice, as Ali did; no shame in including a detailed "fightography". Better still, it would have been good to read accounts of the "Rumble in the Jungle", Ali's monumental clash with George Foreman in Zaire; of the anticlimax of the second encounter with Sonny Liston; of the rematch with Spinks (which brought Ali, at the age of 36, the heavyweight title for the third time); of the indignity of the final defeat against Larry Holmes. But all this is missing. So I'm a Little Special is an anthology for those who have read everything about Ali before.
Tim Franks is the home political correspondent of the BBC World Service