Per ESPN --
The suit seeks to vacate Horowitz' ruling, based on the arbitrator's "manifest disregard for the law,'' his "evident partiality,'' and refusal "to entertain evidence that was pertinent and material to the outcome."
Manifest disregard for the law was abandoned as a grounds for overturning an arbitration award in 2010. Even under the old standard, you needed an arbitrator to say, 'I know the law means A-Rod wins, but I don't care...." Strike one.
"Evident partiality" does not mean that the guy hated you and liked the other side. It generally means that he has a clear and undisclosed conflict of interest that would have made him obviously have to decide for one side or the other (for example, he was A-Rod or Bud Selig's business partner or he was taking bribes from one side and not the other). This argument was probably already waived by A-Rod way back when the arbitrator was appointed. Strike two.
"Refusal to entertain evidence" is almost certainly a reference to the fact that the arbitrator did not require the Commissioner (whose opinion was being appealed) to testify at the arbitration. A-Rod seems to think that had Selig testified that it would have become apparent that Selig was biased against A-Rod and the suspension overturned by the arbitrator. This argument, of course, overlooks the fact that the arbitrator, by reducing the suspension, actually DID ALREADY FIND that Selig's conduct was unfair to A-Rod. Effectively, the arbitrator found that Selig was biased against A-Rod and gave him too long of a suspension. So, A-Rod wanted more testimony to prove a fact he already won on? Strike three.
Frankly, I am not sure that any of these three primary arguments even passes the threshold of "non-frivolous". Just this summer (2013) the U.S. Supreme Court stated in Oxford Health v. Sutter that so long as an arbitrator attempts to find some contractual or legal basis for his decision that the court must accept that decision, "good, bad or ugly." Given that the law is so pro-arbitration and the law was settled by the USSCt less than a year ago, I would not want to be defending a Rule 11 motion if I were A-Rod's attorneys.