In part, it's his ever-changing approach to the charges against him: one moment threatening to sue his club, baseball and anyone in sight for daring to suggest he ever touched a performance-enhancing drug, the next grovelling with contrition and swearing it would never happen again.
But it did, when Rodriguez in 2013 emerged as a prime client of Biogenesis, a Florida-based anti-ageing clinic that had a nice sideline catering for professional (and even high school) athletes who wanted a little testosterone or human growth hormone (HGH) for a chemical leg-up. Just this week Anthony Bosch, Biogenesis's owner, who boasted a fake medical degree, was sentenced to four years in jail.
Then there's the Rodriguez tin ear. Under pressure to talk, he says nothing. When you want him to be quiet, he pipes up - as with the latest instalment of the soap opera, a statement "To the Fans", in which he took "full responsibility for my mistakes... I can only say I'm sorry". To his team-mates, he's a distraction at best.
There were some novelties this time. The statement was hand-written, as if that would render contrition more genuine. And, having just a year ago threatened to go to court to clear his name of such allegations, he now seems aware his credibility is shot. "I accept," he says, "that many of you will not believe my apology or anything I say at this point."
The result has merely been to render detractors even more apoplectic. "Lying, Lying, Gone" was the headline on Juliet Macur's column that opened the sports pages of Thursday's New York Times, demanding that the Yankees simply pay off their fallen superstar.
"Hasn't everyone had enough of Alex Rodriguez by now," she began, "enough of the lies and apologies, and then the lies again and the apologies again?"
All other things being equal, the Yankees would surely be best off without him. But things are not equal.
For one thing, the team has one of the weakest offences in the majors. If A-Rod could recapture just a smidgen of the A-Rod of old, arguably the greatest pure talent of his generation, a 14-time All Star whose 654 homers rank fifth on the all-time list, it might be worth it.
Then of course there's the money. The 10-year US$275m contract he signed with the Yankees in 2007 was at the time the richest in all team sports (though it's since been overtaken by the $325m the Florida Marlins are shelling out to keep star hitter Giancarlo Stanton).
If the team dispenses with his services, Rodriguez would still be owed $61m for the remainder of the deal, a tidy sum even for the New York Yankees to swallow. That's why some unkind souls suggest the best solution might be a career-ending injury during spring training, whereby insurance would cover the outstanding three years of salary.
In the meantime, the melodrama continues. Seven more home runs would lift A-Rod past Willie Mays to fourth all-time, earning him a $6m bonus - and baseball further embarrassment at this latest steroid-fuelled inroad into its record books.
As for the player himself, he is on the backslope of a gilded career, his body no longer able to take the strain, yet still commanding the headlines as no other in his chosen sport.
-THE INDEPENDENT
