Republican presidential candidates John Kasich, Jeb Bush, Marco Rubio, Donald Trump, Ben Carson, Ted Cruz, Carly Fiorina and Rand Paul appear during the Republican presidential debate at the Milwaukee Theatre, Tuesday, Nov. 10, 2015, in Milwaukee. (AP Photo/Jeffrey Phelps)

Tuesday night’s two Republican presidential debates produced some familiar policy-related sparring. Ohio Gov. John Kasich attacked businessman Donald Trump on immigration. Sens. Rand Paul and Marco Rubio argued over national defense. Louisiana Gov. Bobby Jindal criticized Mike Huckabee’s spending as governor of Arkansas. The candidates all used their time to proclaim their ideological or partisan loyalty.

Rhetorical red meat like that is a reliable way for candidates to attract energetic applause in the debate hall and enthusiastic nods among viewers at home. And in this election, with conservatives’ nemesis Hillary Rodham Clinton looming as the probable Democratic nominee, you’d expect her to be attacked frequently as Republican presidential contenders try to display their partisan bona fides to a friendly audience.

Some of them did repeatedly bash Clinton. But not all. Who did, and why?

I counted, so that you don’t have to. Here are each candidate’s total number of mentions of Hillary Clinton (by first name, last name, or both) in the transcripts of both debates:

You might have expected the more purist or insurgent candidates like Cruz, Paul, Trump, and retired neurosurgeon Ben Carson to denounce Clinton more often than relatively moderate or “establishment” candidates, such as Christie, former Florida governor Jeb Bush and Kasich. But the opposite was true.

No other candidate came close to Christie’s 13 separate invocations of Clinton’s name. Cruz and Rubio, in contrast, only mentioned Clinton in response to moderator Maria Bartiromo’s specific question about the Democratic presidential front-runner’s relatively extensive experience in public office.

Establishment candidates bashed Hillary — for a reason. 

This pattern reflects the distinct strategic calculations of the various candidates. For more moderate contenders like Christie and Bush, repeatedly criticizing Clinton serves two purposes.

First, candidates whose ideological principles have been questioned can attack Clinton to defend their own reputations as conservatives in good standing, in order to counteract challenges from the right. For example, Bush promoted his pledge to create 4 percent annual economic growth by simultaneously criticizing Clinton’s endorsement of Obama’s economic record. The current state of the economy “may be the best that Hillary Clinton can do,” quipped Bush, “but it’s not the best America can do.”

Second, pragmatic candidates try to portray a Clinton presidency as a frightening but very plausible possibility, which requires the Republican Party to select a nominee who would run strongly in the general election in order to forestall such a calamity. They’re implicitly urging the Republican faithful not to distract themselves with ideological litmus tests that might screen out the impure but electable candidates like themselves.

For example, Kasich argued Tuesday night that it would be “a disaster if [Clinton] got elected [because] I have two 16-year-old girls, and I want this country to be strong.”

Christie warned that “Hillary Clinton’s coming for your wallet, everybody.”

Outsider candidates don’t want to mention Hillary. And didn’t. 

Other candidates are more concerned with positioning themselves as defenders of conservative doctrine against the co-opted Republican establishment — and so had less incentive to invoke Clinton than to spend time distinguishing themselves ideologically from their Republican rivals.

For example, Jindal mentioned Clinton six times in the first debate. But he only did so when responding directly to Christie’s arguments that Republicans should put aside their own differences in order to focus on defeating her. Jindal disagreed with Christie’s assertion that Clinton was a formidable opponent, claiming instead that her political flaws “gift-wrapped the election” for the Republican Party. His message: Republicans shouldn’t worry too much about electability in 2016 but should nominate an unswerving conservative like himself.

And in the second debate, Cruz suggested that Ronald Reagan’s 1980 election demonstrated that Republicans win when they magnify ideological differences between the parties instead of eliding them. In doing so, he rejected the implication that a less conservative candidate like Bush or Christie would do better against Clinton than Cruz himself would.

The Democratic candidates used the same strategies in their debates. 

In fact, Christie, Bush, and Kasich’s strategies mirrored Clinton’s approach in the Oct. 13 Democratic presidential debate. Facing a tenacious primary challenge from Bernie Sanders on her ideological left, Clinton tried to serve up some partisan red meat of her own, repeatedly warning of dangers to the nation if a Republican became president and claiming she was proud to count Republicans among her enemies.

In his closing statement Tuesday night, Chris Christie referred to these remarks as “the most disgraceful thing I’ve seen in this entire campaign,” getting in one final lick at Clinton before pledging to “bring this entire country together for a better future for our children and grandchildren.”

Intentionally or not, Christie’s words almost perfectly echoed Clinton’s opening statement in last month’s Democratic debate. She had described her campaign as dedicated most of all to “bringing our country together again” — just before boasting about how much Republicans hate her.

Denounce your opposition. Then appeal to national unity. 

In our age, it seems, American politicians perceive that harsh denunciations of one’s partisan opponents should be balanced, sometimes in the very same breath, with the occasional rhetorical tribute to the appealing but elusive ideal of national unity. They can bring America together, they tell us — they just need to vanquish the other party first.

David A. Hopkins is assistant professor of political science at Boston College and blogs about American politics at Honest Graft.