Former Minnesota Gov. Jesse Ventura, center, arrives at court with his wife, Terry, and others, Tuesday, July 22, 2014, in St. Paul, Minn.

Attorneys for Chris Kyle's estate are asking a judge to throw out a defamation verdict and $1.8 million award in the late Navy SEAL-turned-author's legal battle against Jesse Ventura — or send the matter back for a new trial.

In court filings Thursday, they argued that the former Minnesota governor didn't meet the high bar of proof for defamation of a public figure. The judge failed to steer the jury away from an erroneous decision, they said, and the award's dollar amount was pulled from thin air.

The Kyle estate is seeking to reverse a verdict issued in July that found the author defamed Ventura in Kyle's best-selling autobiography "American Sniper."

The book claims Kyle punched out a celebrity, dubbed "Scruff Face" but later identified as Ventura, at a Coronado, Calif., bar in 2006 after the man badmouthed fallen soldiers at a war hero's wake.

Ventura said it never happened and sued for defamation. The author was shot to death in 2013 at a Texas gun range; Ventura took the lawsuit to trial against his estate, represented by his widow Taya.

The 10 jurors hit an impasse during deliberations and came to a verdict after lawyers from both sides agreed to accept an 8-2 split decision. Neither side knew at the time where the jury stood.

In Thursday's filings, the Kyle estate argued — as it has before — that the evidence of defamation laid out at trial wasn't strong enough to support the verdict. As a public figure, Ventura had to prove that Kyle's story defamed him, that it was false and that Kyle knew as much or had serious doubts about its veracity.

The final component had to be proven by "clear and convincing evidence" — jurors had to find it very likely that Kyle knew the story wasn't true when he told it.

The testimony laid out in trial fell short of that burden, Kyle's attorneys argued. Outside of Ventura and Kyle, 11 witnesses said they heard or saw parts of Kyle's story unfold. Three from Ventura's side said they were with him and didn't see a fight.

"The testimony at trial overwhelming established that Ventura made offensive, anti-military statements" at the wake, Kyle's attorneys wrote — including the statement that "SEALs deserve to lose a few" in the war in Iraq.

They also argued that U.S. District Judge Richard H. Kyle, no relation to Chris Kyle, made numerous missteps in instructing the jury, and let in evidence that tainted the proceedings.

The judge's instructions failed to properly convey the burden of proof or clear up "obvious juror confusion" about the questions they were weighing, the estate said. Instead, the court filings said, jurors were left to cobble together a verdict that improperly mixed and matched defamatory and irrelevant details of Kyle's story.

At one point, jurors sent a note to the judge asking what the legal definition of "serious doubt" was. There was none, he told them.

Kyle's attorneys said that wasn't right — the U.S. Supreme Court has addressed the topic, calling it a "high degree" of "awareness of probable falsity," and the judge could have clarified. Instead, they argued, he "forced the jury to guess at the meaning of the crucial phrase."

The jury award Ventura $500,000 for defamation and $1.3 million for unjust enrichment. The defamation portion is covered by insurance; the unjust enrichment is not, according to the Kyle estate.

The unjust enrichment award represented a little less than 25 percent of the $6 million Ventura's attorneys claimed the estate had earned in royalties.

Kyle's attorneys said Ventura did nothing to prove the story about him drove 25 percent — or any specific percentage — of the book's sales. They also said the $6 million figure was wildly inaccurate; the estate earned $2.25 million from royalties through 2013, according to their figures.

Judge Kyle will hear arguments on the filings at a date that has yet to be set.

©2014 the (St. Paul, Minn.) Pioneer Press. Distributed by McClatchy-Tribune Information Services.