What FBI head Robert Mueller and the NSA really need this week is simple. They need a terror attack they can point to and say: "Our surveillance tools, the ones everyone is complaining about, stopped that."

Otherwise, they're in an uncomfortable position. They argue that the surveillance tools they're using (or, depending on your point of view, abusing) get the job done but (given that at least one major attack wasn't prevented and a number of others failed due to ineptitude) are having trouble coming up with a time that happened. (With an exception, that we'll get to.) The usual fall-back position ("Trust us, we can't tell you about when this stuff works because it's classified") won't get the messaging job done when the whole question is can we trust the NSA. The conundrum leads to verbal gymnastics like Mueller telling the House Judiciary Committee this afternoon that national security tools aided the Boston investigation — it helped them find Ibragim Todashev, the man FBI agents shot to death in Florida under questionable circumstances.

They get points for trying, however. The government's intelligence agencies have constructed an elegant, informal mental map of terror attacks and attempted attacks since 2000. In their formulation, nearly every terror attack is or was preventable, via some combination of surveillance law and luck.

We built a highly subjective, New York-style approval matrix, plotting the incidents in the categories listed below. There are two axes: How preventable the attacks were or might have been versus how they could have been stopped, either through luck or use of expanded surveillance laws. How we positioned each incident is explained in its category. As you can see, the government has had trouble placing many incidents we know about in that top right quadrant.

The golden child: Zazi versus the subways

What happened: Najibullah Zazi was arrested in September 2009 for his role in a plot that would have detonated bombs on the New York City subway. He pled guilty and is now in prison.

What the government has said: After the NSA revelations came out, Rep. Mike Rogers of Michigan referred obliquely to a time when the government's surveillance tools broke up a high-profile plot. In short order, the details of that plot were released, indicating that it was Zazi. According to Reuters:

U.S. authorities had discovered the Zazi plot after running across an email sent to a rarely used al Qaeda address that was associated with a notorious bomb-maker based in Pakistan.

[CBS News' John] Miller said authorities traced the sender of the email to a suburb of Denver. At the time of Zazi's arrest, U.S. authorities revealed that he had been tracked from Denver to New York, where, after a brief interlude during which U.S. investigators lost track of him, he was arrested by the FBI.

Counterpoint: In very short order, a lot of other sources called this claim into question, as we reported on Wednesday. That email, one AP reporter pointed out, came from an operation in UK. Nor were the NSA's secret tools necessary; Zazi's existing links to terror organizations would have allowed the FBI to use its standard tools.

Surveillance Matrix: The attack was clearly very preventable, since it was prevented. The extent to which the NSA surveillance laws played a role is under contention but there's a case out there they were useful.

The if-only: September 11

What happened: You know what happened.

What the government has said: Testifying before Congress today, Mueller suggested that the 9/11 attacks could have been stopped if one existing tool — the phone records provision of the PATRIOT Act — had been in place. Politico reports:

Monitoring calls between a Yemen safe house and an organizer in San Diego, “could have derailed the plan, in any case, the opportunity was not there,” Mueller told the House Judicary Committee. “If we had this program that opportunity would have been there.”

Counterpoint: After the 9/11 Commission concluded its investigation into the attacks, its chairman, Thomas Kean, stated categorically that the attacks were preventable. Not if the government had the PATRIOT Act in place, but simply through better investigative work.

Mueller, who took over as head of the FBI a week before the attacks, is right. It's possible they could have been prevented. Even without the phone records tool.

Surveillance Matrix: It's hard to say the 9/11 attacks were very preventable, since they occurred. But it appears safe to assume that, had a lot gone right, they might have been stopped. How much the NSA's laws would have helped isn't clear, especially since it's all hypothetical, but "preventing another 9/11" was the guiding spirit of these new programs.

The one where it helped a little, they promise: Boston

What happened: Tamerlan and Dzhokhar Tsarnaev planted pressure cooker bombs along the finish line of the Boston Marathon on April 15 of this year.

What the government has said: In his testimony today — which was scheduled before last week's leaks — Mueller was asked about the FBI's failure to stop the attack. As we mentioned above, he indicated that the PATRIOT Act provision had helped, by identifying a person with unclear ties to the bombers and no apparent tie to the bombings.

Counterpoint: Tamerlan Tsarnaev was on the FBI's radar screen prior to the bombings. Despite that, the NSA and FBI's tools failed to identify and prevent the incipient plot. Mueller couldn't not mention the Boston attacks, since it was a large part of why he was on Capitol Hill. But it's hard to see how the death of Todashev is much of a victory for the government's surveillance tools.

Surveillance Matrix: No one appears to be claiming that the Boston bombings themselves were preventable, nor is a strong case being made that the law could have helped.

The ones they don't talk about: Underwear and shoe bombings, Fort Hood, and Times Square

What happened: In four separate incidents since 9/11, terror plots either failed or were executed without disruption. Those examples are the shoe bomber in December 2001, the Fort Hood shooting in November 2009, the underwear bomber that December, and the attempted Times Square bombing in May 2010.

What the government has said: In the context of the NSA revelations, nothing.

Counterpoint: It's not clear what could have been done in the Fort Hood incident, which bears more similarity to a mass killing by a deranged shooter than the other terror attacks. But in the other three cases, it was incompetence that interfered: Richard Reid's failure to take his shoe to the restroom before trying to light the fuse or the Times Square bomber's inability to construct a working bomb. Three of these incidents occurred within the timeframe during which the NSA's tools were in effect, yet, as in Boston, law enforcement did not intervene prior to the incidents.

Surveillance Matrix: Four different cases here. The shoe and underwear bombings were apparently preventable — but only through sheer, dumb luck. The Fort Hood shooting wasn't preventable, nor does it appear that the law played any role in stopping it. The Times Square bombing was prevented, again largely through luck, but the perpetrator may have been identified in part through phone records so we moved that one to the right.

The ones they can't talk about: the "dozens"

What happened: That is classified.

What the government has said: In his testimony before the Senate Appropriations Commitee onWednesday, NSA head Keith Alexander declared that the government had disrupted "dozens" of terror attacks in the United States and abroad thanks to the tools provided under the PATRIOT Act and the expansion of the Foreign Intelligence Surveillance Act. Alexander insisted that he couldn't talk specifically about those dozens of incidents, except, perhaps in a classified session with Congress. (Why these must be kept secret while the Zazi details weren't isn't clear.)

Mueller similarly made vague references to disrupted plots during his testimony.

Update, 3:14 p.m.: That number has apparently fallen.

Counterpoint: It is very possible that a terror plot was halted through the use of these tools. If it exists, though, they're the only ones who know about it. Congress and the American people haven't been told.

Mueller and Alexander should be pushing hard to release as many details about that plot as possible. Somewhere in this group — represented by that little clot of orange bubbles on the matrix — may be the smoking gun that proves the utility of their interpretation of the surveillance rules. If it exists, the public should be told. If it doesn't, the FBI and the NSA may just keep saying it does, until everyone stops paying so much attention.

Surveillance Matrix: Since these unidentified cases were only mentioned because they represent the government's ideal, they get the ideal position: preventable, thanks to the law.

Photo: Robert Mueller on Capitol Hill. (AP)