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It’s hard to think of Paul Soglin, who has served as Madison mayor for a combined 22 years, as an underdog in the April general election. But that could be just what he is. Soglin narrowly won the primary last week, but he did so with only 28 percent of the vote. For an incumbent who is as well-known as Soglin, that’s not good news. It suggests that 72 percent of voters are ready to move on to somebody else. So, it seems a safe bet that his general election opponent, former Ald. Satya Rhodes-Conway, will pick up the lion’s share of primary votes that went to Ald. Mo Cheeks and nonprofit director Raj Shukla.

When you add in Soglin’s poor showing in the gubernatorial primary last August, when he finished sixth in Madison and didn’t win a single ward with more than a handful of votes, Rhodes-Conway could be justified for asking if she could get some measurements for drapes in the mayor’s office. (This is only a figure of speech. The mayor’s office has blinds, but no drapes.)

Just as significant as the percentages is the geography of the race. Rhodes-Conway won overwhelmingly on the high-voting isthmus. Soglin actually placed fourth in the important second and sixth aldermanic districts, the Tenney-Lapham and Marquette neighborhoods, respectively. As a rule, nobody loses a Madison mayoral race by running to the left of her opponent and these are the city’s most liberal districts. A candidate popular there has a leg up.

In fact, I can’t think of a mayoral race where the more centrist candidate won since Joe Sensenbrenner beat Toby Reynolds back in 1983. I beat Soglin running to his left in 2003 and he came back and beat me running from my left in 2011. I still won the isthmus in 2011 but not by the margins of eight years earlier.

But it’s not like this is a slam dunk for Rhodes-Conway. First, she has to secure the votes of those who wanted Cheeks or Shukla to face Soglin in the general election. That might be harder than it initially appears. She was probably the furthest left of Soglin’s three most serious challengers and it’s not a given that their supporters will all come her way. She doesn’t need them all, but she needs a strong majority of them.

Then there are the new voters to contend with. There will probably be another 20,000 voters in April who didn’t show up in February. She has to introduce herself to them and, as the old saying goes, you only get one chance to make a first impression. The downside for Soglin is that, because he’s such a known entity, it’s all but impossible to change voters’ perceptions of him if they’re negative. But the risk for Rhodes-Conway is that she makes a bad first impression and those voters flee back to the candidate they know.

In this case, if Rhodes-Conway pursues what has become the standard operating procedure of American politics — doubling down on your base rather than trying to build on it — she may well lose. That’s because her most ardent supporters probably already showed up in February, but she’ll need to grow the roughly 10,000 votes she got then into about 30,000 in April.

It’s a tricky formula. Yes, a Madison mayoral candidate generally wins running to the left of her opponent, but not too far left. I narrowly defeated Soglin in the primary in 2003 in a similar race with four serious candidates and my electoral map looked almost identical to hers. But I hardly ran away with the general election. Six weeks later I squeaked out a victory by less than two points. The lesson I took from that is that Soglin may be a known entity and he may not be universally loved, but his opponents still need to make a case for why voters should pick them over him.

Paul Soglin has been mayor of this city off and on for more than two decades. He is not likely to be unseated easily. There’s an old saying in politics that you can’t beat somebody with nobody. Like him or not, there’s no arguing that Paul Soglin is somebody. The next six weeks will be crucial for Satya Rhodes-Conway to show that she is somebody too.

[Editor's note: This article was corrected to note that Paul Soglin finished sixth in Madison in the gubernatorial primary.]