
30 F.Supp.2d 1029 (1999)
NATIONAL HOCKEY LEAGUE PLAYERS' ASSOCIATION, Plaintiff,
v.
NATIONAL HOCKEY LEAGUE, Defendant.
No. 98 C 6838.
United States District Court, N.D. Illinois, Eastern Division.
January 11, 1999.
Order Supplementing Opinion January 27, 1999.
*1030 Michael P. Conway, Michael T. Donovan, Grippo & Elden, Chicago, IL, for Plaintiff.
Joseph Baumgarten, Howard Z. Robbins, Proskauer, Rose, LLP, New York City, Thomas F. Bush, Jr., Thomas A. Doyle, Saunders & Monroe, Chicago, IL, for Defendant.

MEMORANDUM OPINION AND ORDER
SHADUR, Senior District Judge.
This is the second time around the block in the ongoing dispute between National Hockey League Players' Association ("Association") and National Hockey League ("League") concerning an arbitration proceeding conducted by Arbitrator John Sands ("Sands" or the "Arbitrator" or "Impartial Arbitrator"  the latter being the term used in the parties' agreement under which the arbitration took place).[1] After this Court's July 8, 1998 memorandum opinion and order ("Opinion") had granted summary judgment in Association's favor and vacated the original arbitration award ("Award I"), the parties went back to Arbitrator Sands and obtained a second award in arbitration ("Award II").[2] Now this new action brought by Association to vacate Award II has become the subject of League's Fed.R.Civ.P. ("Rule") 12(b)(6) motion to dismiss, which is fully briefed at this point.
As the Opinion reflected, the flaw in Sands' earlier Award I lay in his having considered the parties' prior bargaining history despite their mutual agreement to the contrary. When the matter was then returned to him by the parties after issuance of the Opinion, Sands began his July 31, 1998 Award II with this set of assurances (Award II at 1-2, quoted in full because of their importance to the present controversy):
On October 10, 1997 I issued my original Opinion and Award in this case. On July 8, 1998 Senior United States District Judge Milton I. Shadur vacated my Award and returned it to me "... for resolution of the parties' contested grievance without resort to the 1994-95 bargaining history." (Memorandum Opinion and Order, p. 1029).
Pursuant to Judge Shadur's direction, I have reviewed my October 10th Opinion and Award and recall clearly the decisional process by which I reached my conclusion denying the Association's grievance as lacking merit. As Judge Shadur properly observed, "... only the judicial officer himself or herself really knows whether the same result would have been reached if it had not been for the decisionmaker's reliance on a consideration that later proves to be erroneous or impermissible." (Id., p. 1028) And, following that review, I can say with absolute certainty that I would have reached the same result.[1]
As noted on pages 20 and 21 of my original Opinion, my primary reason for my conclusion was the contract's clear and unambiguous use of the phrase, "affiliated league," in the definition of "defected player." *1031 For all practical purposes, that determination ended the inquiry; and my recitation of additional reasons provided further confirmation of the necessary result and addressed other arguments. My consideration of bargaining history  like my consideration of the parties' past dealings  did not determine the outcome but merely supported it.
I have accordingly revised my original Opinion to eliminate all references to bargaining history, based on my knowledge that the same result would have been reached without reliance on that consideration.[2]
Association's current challenges to Award II appear to have the pungent tang of sour grapes. Because Association's Response to League's motion to dismiss invokes the familiar proposition that the operative standard for testing the sufficiency of a complaint calls for crediting its allegations, another extended quotation is in order, this time from the relevant paragraphs of Association's present Complaint:
28. As noted in the July 24, 1998 NHLPA [Association] letter, Arbitrator Sands' plan to issue a revised opinion with no further proceedings was unfair and would operate to unfairly prejudice the NHLPA. Arbitrator Sands had purged his file in 1997, destroying his notes of testimony and argument and his copies of documents introduced as exhibits at the hearing. Thus, Arbitrator Sands had no record of much of the non-bargaining history evidence upon which he was required to base his decision.
29. Moreover, Arbitrator Sands' proposal to refresh his recollection using his vacated award was patently unfair and inappropriate. The vacated Opinion was prepared by Mr. Sands under a misconception about the evidence upon which the opinion could be based. The vacated Opinion, therefore, touched on only some of the relevant evidence introduced at the hearing, provided only a summary of that evidence, and did not include sufficient detail for Mr. Sands to consider and evaluate even that evidence anew. Moreover, Mr. Sands' recollection of the proceedings was likely to be influenced by his erroneous assumption during the hearing that he was permitted to consider certain 1994-95 bargaining history.
* * * * * *
35. Arbitrator Sands denied the NHLPA a fair hearing by issuing a second award without considering the evidence or hearing argument from the parties.
36. Arbitrator Sands has also acted with evident partiality in manipulating the Revised Opinion and Award to obtain the precise result he reached previously. He did not reconsider the merits of the issue before him. He also refused to consider the matter on a complete record.
37. Judge Shadur ordered reconsideration of the original decision because it was based on evidence Mr. Sands had no authority to consider. Rather than observe the limits on his authority or provide the NHLPA with a fair hearing, Mr. Sands chose instead to literally reiterate his previous decision without giving the parties a chance to present argument or provide him with testimony and documentary evidence from the 1997 hearing that he had purged from his file.
38. Arbitrator Sands' reliance on 1994-95 bargaining history, evident partiality, disregard for Judge Shadur's order, and failure to grant the NHLPA a fair hearing on this issue are evident from the manner in which he has proceeded and the text of the Revised Opinion and Award itself. Therefore, his award should be vacated.
Those argumentative assertions give no clue as to just how (or really as to just why, except that Association is obviously unhappy with the outcome) this Court should go about discrediting the express assurances by Arbitrator Sands that have been quoted earlier in this opinion. What this Court said in Opinion at 1029 is as true the second time around as it was when Award I was under review:
[T]his Court knows from its personal experience (and from comparable comments by *1032 fellow judges with whom it has sat by designation on Courts of Appeals panels) that despite the verbiage used in judicial opinions, only the judicial officer himself or herself really knows whether the same result would have been reached if it had not been for the decisionmaker's reliance on a consideration that later proves to be erroneous or impermissible. That mind-reading function is not the appropriate role for a reviewing court, other than by the possible application of the doctrine of "harmless error." And particularly given the extremely narrow scope of judicial review of arbitrators' decisions  review that does not encompass the merits of those decisions as such  in this case the soundest approach is to leave the question to a trier of fact who has been chosen in the manner on which the parties have agreed in the CBA: an Impartial Arbitrator.
Here Association really provides neither objective nor subjective support for challenging the integrity of Sands, the lawyer-arbitrator whom the litigants had jointly chosen to serve as their Impartial Arbitrator. Instead Association attempts to argue backwards from the unfavorable result  after all, the only evidence that would conceivably seem to be available to Association if League's motion were to be denied and the case then went to trial would be Award II itself and  perhaps  the testimony of Arbitrator Sands.
Association's Response memorandum is framed essentially as a cross-motion that asks this Court to decide that Award II is inherently defective, so that Association and not League is entitled to a judgment as a matter of law. But this Court is not about to accept Association's propositions, as set out in the quoted portions of its Complaint and in other portions of that document, (1) as to a decisional officer's limited powers of recollection and (2) as to the very nature of the decisional process. Those are propositions that this Court's own judging experience teaches to be unfounded. If Sands were to be called to the stand and were to reiterate his assurances quoted earlier in this opinion, this Court would have no basis in good conscience for discrediting that testimony. And once again, that is particularly so given the considerations that this opinion has quoted from Opinion at 1029.
Unless Association's argumentative conclusions quoted here from the Complaint were to be accepted as gospel, it is clear that none of the grounds for nonenforcement of an arbitration award set out in 9 U.S.C. § 10(a) can apply. Indeed, the result in this case  the upholding of Award II  would appear to follow a fortiori from decisions such as those cited in League's memorandum in support of its motion: in our Court of Appeals, Generica Ltd. v. Pharmaceutical Basics, Inc., 125 F.3d 1123, 1130-31 (7th Cir.1997) and Flender Corp. v. Techna-Quip Co., 953 F.2d 273, 280 & n. 13 (7th Cir.1992); elsewhere, see such cases as Forsythe Int'l v. Gibbs Oil Co., 915 F.2d 1017, 1023 (5th Cir.1990); Hoteles Condado Beach v. Union De Tronquistas Local 901, 763 F.2d 34, 40 (1st Cir.1985); National Post Office Mailhandlers Local 304 v. United States Postal Serv., 751 F.2d 834, 841 (6th Cir.1985); and see also Scott v. Prudential Secs., Inc., 141 F.3d 1007, 1017 (11th Cir.1998).
This opinion has already acknowledged the generous standards for judging a complaint for Rule 12(b)(6) purposes, as epitomized by Hishon v. King & Spalding, 467 U.S. 69, 73, 104 S.Ct. 2229, 81 L.Ed.2d 59 (1984):
A court may dismiss a complaint only if it is clear that no relief could be granted under any set of facts that could be proved consistent with the allegations.
But there is a reason for the qualification that a plaintiff's allegations required to be credited for such purposes must be "well-pleaded" (see, e.g., such cases as McTigue v. City of Chicago, 60 F.3d 381, 382-83 (7th Cir.1995), not only expressing that qualification but declining to give credence to a plaintiff's unsupportable allegations, and Northern Trust Co. v. Peters, 69 F.3d 123, 129 (7th Cir.1995), stating the same qualification and refusing to credit "mere unsupported conclusions of fact or mixed fact and law"). Where as here no prospect appears for Association's ability to prove its ad hominem attacks on Arbitrator Sands  for Association's argumentative contentions as to what Sands assertedly could not be able to do run counter *1033 to human experience in performing the judging function, and its attempt to rely on purported internal evidences of invalidity within Award II could not carry the day either  there appears to be no possibility at this point of salvaging the Complaint and this action. It is only because the present posture of the case is under Rule 12(b)(6) auspices that this Court will extend a brief opportunity to Association to provide some showing that might support the action's survival.

Conclusion
Because League's motion is tendered under Rule 12(b)(6), this Court holds that this opinion cannot dispatch the matter with a final order. Instead Association's counsel are ordered to file in this Court's chambers on or before January 19, 1999 (with a copy of course delivered to League's counsel) an appropriate showing of what Association would be prepared to prove in support of its Complaint and of how that evidence would sustain Association's claim in light of the principles stated in this opinion. Absent such a filing, or if such filing is inadequate as a matter of law, this Court contemplates the prompt dismissal of this action (thus permitting Award II to stand). If on the other hand Association's submission does suffice to overcome that hurdle, this Court will enter an order calling for appropriate further proceedings.

MEMORANDUM ORDER
In response to the directive contained in the Conclusion section of this Court's January 11, 1999 memorandum opinion and order ("Opinion"), counsel for National Hockey League Players' Association ("Association") have filed a Supplemental Memorandum ("Supp.Mem.") to address the question posed in the Conclusion. In doing so, counsel have demonstrated both candor and a high degree of professionalism  but Association nonetheless loses the lawsuit.
At the outset counsel describe the purpose of their current filing in these terms (Supp. Mem. at 1):
We do so to clarify our position, although we recognize that it is unlikely to resolve the concerns raised by the Court in its Order.
Then Association's counsel go on to explain the predicate for its having brought the current action, confirming that Association "did not intend to present its challenge to [the Arbitrator's] procedures as an attack on Mr. Sands' character, integrity or competence as an arbitrator" (Supp. Mem. at 2). And after having set out Association's position, counsel conclude by stating (id. at 2-3):
We agree, however, that there is no available and appropriate vehicle for testing Mr. Sands' recollection of the non-bargaining history evidence that he was required to consider. Thus, if the Court concludes that the procedures adopted on remand provided the NHLPA with an adequate opportunity to be heard, the NHLPA can make no further showing that would overcome the concerns expressed in the Court's order concerning the NHLPA's fairness challenge.
Association's counsel are correct. Their submission has not overcome the hurdle posed by the Opinion, and in accordance with Opinion at 1033 this action is dismissed, thus permitting the Arbitrator's second Award to stand.
NOTES
[1]  Association's sense of deja vu must be particularly acute: Its Notice of Filing of its just-submitted Response to League's motion to dismiss carries the 98 C 90 case number of the original lawsuit between the parties, not the current 98 C 6838 number. Fortunately, Association's Response memorandum (which accompanies the Notice of Filing) has the number right.
[2]  Opinion at 1029 had finished by stating:

This matter must be returned to an Impartial Arbitrator for resolution of the parties' contested grievance without resort to the 1994-95 bargaining history. To that end the Award is ordered vacated.
In the earlier case Association had not asked this Court to disqualify Sands  and as may be observed, this Court was deliberately neutral in its generalized reference to "an Impartial Arbitrator." Thus the parties' return to Arbitrator Sands was apparently the result of their contractual choice.
[1]  I accordingly had no need to re-open the record or solicit further argument from the parties.
[2]  I have not, however, eliminated from my recitation on pages 19-21 of the parties' arguments references to bargaining history that both made in their closing statements.
