Imprecise disclosures to the FEC. FEC spending disclosures are broken down by purpose, such as “Advertising-TV Placement,” “Web Ads” or “Voter Contact Phones.” But these designations are not uniform between groups, and sometimes are so imprecise that they do not clearly describe how money is being spent. For example, as we noted in our graphic, the pro-Romney super PAC Restore Our Future has spent $75.1 million on “Media Buys.” This is a separate category from Internet ads and print ads, but we cannot be fully certain that it is all dedicated to television and none of it goes to radio.

Genuine misconduct. The litany of discrepancies and imprecisions above opens the door for real misconduct. If the reason the FEC was showing higher TV spending than Kantar for Priorities USA was, in fact, that Priorities USA was misreporting the purpose of their expenditures, or if Kantar was actually showing higher TV ad spending for Americans For Prosperity because AFP had failed to report relevant material to the FEC, we would be none the wiser.

Watchdog reporting on the ad wars depends upon a simple concept that has recently returned to fashion: arithmetic. It loses its teeth when the numbers don’t add up.

Related stories:

“The Ad Wars: How do we cover them?”

“For TV, campaigns create big winners and (relative) losers”

“Where to Turn When Tackling Money-in-Politics Stories”

“The Top Campaign Finance Tools for Local News Sites”

Sasha Chavkin covers political money and influence for CJR's United States Project, our politics and policy desk. He has written for ProPublica, the Center for Public Integrity, and The New York World. Follow him on Twitter @sashachavkin.