With closely-watched primaries in Kentucky, Pennsylvania, and Arkansas set today, and more on the horizon, there’s been a surge of horse-race coverage in the media lately—and much of it has been pretty good. But a close look at some recent stories suggests some pitfalls for the press to be aware of as it tries to make sense of the results. Here are a few:

Even in a “nationalized” campaign, how useful are the pre-set national narratives?: The Arkansas Senate race is clearly nationalized, as the Democratic primary between incumbent Blanche Lincoln and challenger Bill Halter has become a proxy war between business and labor interests. But it may not be telling the full story to say, as Fox News does in the headline of its dispatch, that the “Arkansas primaries shape up as a test of anti-incumbency sentiment.”

Anti-incumbent sentiment seems to be, in addition to a reflection of the still-weak economy, anti-bailout sentiment. Halter, who has benefited from the fact that he was not in Congress when TARP was introduced, has indeed hit Lincoln for her vote and claimed the “outsider” mantle more broadly, and those tactics may help him in today’s vote.

But the bailout was not the key factor that gave rise to his candidacy. Instead, he’s been supported by national liberal groups that didn’t like the moderate Lincoln’s equivocations on health care, and by labor unions that don’t like her longstanding coolness to some of their priorities. In other words, Lincoln wasn’t targeted only as a result of inchoate “anti-incumbent” sentiment, or as a function of her misfortune in being in Congress when some unpopular votes had to be cast. She was targeted over specific policy choices she’s made that put her to the right of the Democratic mainstream.

On the Republican side, meanwhile, there’s no “incumbent”—but there is an establishment candidate, and he’s doing pretty well. The Fox story notes that that candidate, Rep. John Boozman, “has been targeted as a Washington insider by the two candidates aiming for at least a spot in the June 8 runoff,” which is true. But that’s a slender reed on which to hang a claim about anti-incumbent sentiment. Despite making a late entry into a crowded field, Boozman immediately claimed front-runner status. He seems likely to draw just above or just below 50 percent of the vote in an eight-way race, which could be seen as a sign of strength, not weakness. What’s more, one of the folks now targeting him as an insider, state Sen. Gilbert Baker, was until Boozman’s entry the original front-running establishment candidate. The insurgent position has never been the strongest one in this race.

Leave the hype behind: A Monday story by The Associated Press took at look at an organization called the American Future Fund, a three-year-old Iowa-based group that seems to exist to produce advertisements that advance conservative positions.

Little is known about the group’s funding sources, because its tax status does not require it to disclose individual donors. But the organization, readers are told, “has some of the best—and toughest—political talent in the nation,” including the apparatchiks behind the Willie Horton and Swift Boat Veteran campaigns, and is, per the headline, “becoming a conservative power.” And now it is using its muscle not just against Democrats but “in the middle of Republican family feuds in Kentucky and California.”

Kudos to the AP for shining a light on this group, which does merit press attention and seems to be taking advantage of lax tax laws to evade common-sense standards for disclosure in political activity. (For more background, see this March story from Politico.) But the article could have used a little more focus on whether this “power” is having an impact in the GOP primaries where it’s now being wielded.

It’s hard to show direct relationships between a given ad campaign and and a given electoral outcomes, of course. But in Kentucky, the group has backed Senate candidate Trey Grayson, who is trailing badly in the polls and seems likely to go down to defeat today. And in California, it’s come out against Tom Campbell, who, as the Los Angeles Times notes, keeps chugging along in the lead of the Republican primary despite not really capturing anyone’s imagination. It’s possible that Campbell would be doing better, and Grayson worse, if the AFF hadn’t intervened. But as evidence of the group’s sway, these examples are awfully weak.

One result, two stories: The context surrounding several of the Democratic primaries is complex. We’ve got a Democratic president whose policy agenda is, on many issues, more liberal than that of sizable bloc of Democratic senators. But with two of those senators, Lincoln and Pennsylvania’s Arlen Specter, facing challengers who are essentially pledging greater fealty to liberal elements of the president’s agenda, Obama has intervened on behalf of the incumbents, endorsing Specter and recording radio advertisements for Lincoln.

That decision is sure to aggravate Obama’s restive liberal base. But it also presents reason for caution among members of the press corps who want to interpret the results as a measure of the president’s influence.

An SFGate.com blog post listing five trends that will be “tested” (that word again) by today’s elections highlights the tension. One test will be of the “strength of [the] liberal Democratic revolt against party centrists and lawmakers seen as insufficiently partisan” (which is, as argued above, a better way to interpret events in Arkansas than pure “anti-incumbent” sentiment). Another will be of “the clout of President Obama’s endorsement in Democratic primaries.”

But despite the grumblings about Obama from the left, “insufficient partisanship,” for Democrats, is still generally manifested by failure to enthusiastically support the president’s agenda! So if Arkansas Democrats go for Halter, is that a sign that they’re punishing Lincoln for not supporting Obama? Or is it a sign that Obama’s endorsement doesn’t carry much weight? Both are plausible. Either could be true. It’s even possible both are true (if Democratic primary voters support Obama’s agenda but don’t give much weight to his endorsement). The point is, we don’t really know—and without a much more robust understanding of the factors driving voters’ choices, journalists should be wary about coming to conclusions about the broader meaning of today’s elections.

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Greg Marx is a CJR staff writer. Follow him on Twitter @gregamarx.