The fight over whether Democrats should choose Rep. Nancy Pelosi to be the speaker of the House again is really a fight over what Democrats should want in a speaker. Do they need someone skilled at the inside game — tucking small-but-significant provisions into appropriations bills or convincing other House Democrats to campaign on health care a lot and impeachment almost never? Or do they need a master of the outside game — an articulate, engaging spokesperson for the party who can appeal to the party’s liberal base as well as Obama-Trump voters in the Midwest?

Of course, that’s not what the Pelosi debate on Twitter and in op-ed columns has revolved around; instead, Pelosi’s advocates and critics are going around and around about her age and gender. But that debate is different than the one taking place on Capitol Hill, where this decision will actually be made. There, the Pelosi fight is not really about gender — some of Pelosi’s critics are women, and virtually all of them, I think, would accept a female speaker not named Pelosi. It’s not really about ideology either — some of Pelosi’s critics are pretty liberal, as are some of her supporters; opinion about her also seems to be mixed among more conservative Democrats. It’s also not solely about age — Pelosi’s critics are suggesting that the party needs a new generation of leaders, but some were recently touting 66-year-old Marcia Fudge of Ohio for speaker. Fudge is 12 years younger than Pelosi but hardly represents a generational shift. (Fudge on Tuesday announced that she was backing Pelosi and ending her own brief flirtation with running for speaker.)

Instead, based on my conversations on Capital Hill, the case Pelosi’s critics are making is that Democrats, particularly those in competitive districts, would be better off electorally without her as their leader. Yes, other congressional leaders, such as Sen. Mitch McConnell, are unpopular. But there has been an organized push by Republicans to press Democratic House candidates into either aligning themselves with or distancing themselves from Pelosi. The media usually plays along, asking Democratic candidates if they will back her for Democratic leader or speaker. And Pelosi is controversial enough and sufficiently well-known that some House Democratic candidates think it helps to say they won’t back her. Not many Senate Republicans felt the need to distance themselves from McConnell during the midterm campaign.

The case Pelosi’s defenders are making on Capitol Hill is that the California Democrat is skilled legislatively — when she was speaker from 2007 to 2011, Democrats pushed through a ton of legislation, most notably the Affordable Care Act. Her defenders make an electoral argument too: Democrats just won the House by a huge margin, with a political strategy (talking about pre-existing conditions, not impeachment) that Pelosi helped craft.

I would argue that both sides are overstating their cases. The strongest argument about Pelosi’s electoral effect is that she is not having much of one — positive or negative. The Democrats won the House under Pelosi’s leadership the three times there was an unpopular Republican president in the White House (2006, 2008, 2018) and lost it the rest of the time. Structural forces like the economy and the president’s popularity exert far, far more influence over election results than the speaker of the House.

“It is likely that any Democratic leader would have won seats in 2006, 2008 and 2018 while losing seats in 2010 and 2014,” said Gregory Koger, a University of Miami political science professor who studies Congress.

He added, “Yes, Pelosi raises a lot of money. But here the key question is, how much money would a different person with the same position raise? Quite likely a similar amount.”

Could Democrats have won more with another leader? Hard to say.

“There’s not much evidence that minority leaders in the House can change election outcomes,” said Matthew Green, a political science professor at Catholic University and author of a 2010 book on House speakers. “In this past election, Republicans ran more anti-Pelosi campaign ads than ads about almost anything else, and it didn’t protect their majority.”

“On the other hand, it’s unclear whether a party leader’s reputation is irrelevant to election outcomes, especially in individual races,” he added. “Yes, House Democrats did well on Election Day, but it’s simply impossible to know whether Pelosi’s negative image kept some Democrats from winning close elections in conservative districts.”

What about Pelosi’s effect in terms of legislation? It’s true, Democrats passed a lot of major legislation in 2009 and 2010. But by far the most important factor in that success was that Democrats had total control of government — they had the presidency, a clear majority in the House and either 59 or 60 seats in the Senate. Pelosi is considered a liberal hero for one specific move: imploring Democrats to keep trying to push through the Affordable Care Act, even after the election of Republican Scott Brown in Massachusetts in early 2010 opened the door to GOP filibusters and was viewed as a signal that voters might be leery of the health care proposal. But Barack Obama, the sitting president, was also in favor of the pushing-ahead strategy. And so was much of the Democratic Party.

Was Pelosi a central figure in stopping the repeal of Obamacare once Republicans won the House (and eventually the Senate and presidency)? Maybe. But remember that repeal actually passed the House, because ultimately, it was a party-line vote and Republicans had the majority. Pelosi couldn’t stop them.

Pelosi kept her party unified while it was in the minority, said Green. “I also think her role in passing the ACA was truly significant, and it would have been difficult for others to replicate it.”

But, Green added, “while Pelosi did exercise some remarkable leadership on passing the ACA, she had a lot of help — and she was hardly the first speaker to accomplish significant legislative leadership.”

“She is a formidable legislator and negotiator, no question, but Steny Hoyer” — the No. 2 Democrat in the House — “would be too,” said Gisela Sin, a political science professor and congressional expert at the University of Illinois.

I’m not saying that Pelosi has been a bad speaker, or that the speaker doesn’t matter. I think the best way to think about this debate is that the speaker matters at the margins, and the question for Democrats is which margin they want to improve. At least for the next few months, Pelosi is probably their best potential speaker to negotiate budget bills with Trump — she’s been doing this for 16 years. She might also be the best at dealing with tensions between various factions within the party. She has already, in the Bush years, figured out how to placate liberal activists who want to see the president impeached without fully going down that road and potentially annoying swing voters.

At the same time, she will not be a fresh face for the party. She won’t become the kind of dynamic public speaker that, say, Stacey Abrams and Beto O’Rourke are. She probably won’t get more popular in competitive congressional districts — and she could become even more toxic.

“Leaders in Congress are expected to excel at both their public and private responsibilities,” said Green. “Pelosi is a tough bargainer and excellent vote counter, but her communication skills are poor, and she does not appeal to many voters outside of Democratic circles.”

So my bottom line is this: Democrats, both in and out of Congress, and the media should probably depersonalize this process a tad. It’s not really about whether or not the party wants Nancy Pelosi, the 78-year-old Democrat from San Francisco. It’s about whether they want a master of the House or someone they can bring to their districts to campaign for them. There are few Democrats who can match her legislative experience — but she is not going to become a wildly popular public figure.