Democrats are optimistic about riding a so-called blue wave to control of the House this November, and it’s easy to see why. The president’s approval rating is in the low 40s, the Democrats have a comfortable lead in generic congressional polls, and it’s a midterm election year. Historically, it’s a setup for a wave election.

There’s no precise definition of that term, but it typically describes an election in which one party makes big gains in the national popular vote, and in seats as well. Incumbents considered safe can lose. Waves flipped control of Congress in 1994, 2006 and 2010.

Yet here’s a surprising fact: Even a wave as powerful as those in 2006 or 2010 might not give Democrats control of the House.

They need only 23 seats to make that happen, which doesn’t seem like a lot. For comparison, in 2006 Democrats picked up 31 seats, and in 2010 Republicans picked up 63.

What has changed is that the Republican caucus has fled to higher ground.

How Safe Is Each District?

Today, there are just nine Republicans who represent districts that tilt toward the Democrats, based on the districts’ voting in the last two presidential elections compared with the country as a whole. There were 24 Republicans in such a precarious position in 2006, 67 such Democrats in 2010 and 90 Democrats in 1994.

In a wave election, Republicans representing Democratic-tilting districts like these would be projected to lose their re-election bids. They are the figures farther down the slope in the accompanying illustration. (The one all by itself at the bottom, representing Pennsylvania’s Fifth, was sunk by redistricting.)

Mostly, though, the districts are above sea level. Incumbents who represent even somewhat Republican-leaning districts are generally favored to win re-election, even in a wave election. Waves aren’t necessarily as deadly as you might think.

This makes it hard to imagine huge Democratic gains, like those the Republicans made in 2010. In past elections, incumbency has been worth around seven points, although that advantage has been declining.

Republicans have so many safe seats that the Democrats would be expected to gain only 22 seats if they flipped Republican-held districts at a rate equivalent to the waves of 2006 or 2010 (without factoring in the large number of open seats). It would leave them one seat short of a majority.

Why do Republicans have such a deep structural advantage in this era? For starters, a majority of districts lean Republican in presidential elections because of gerrymandering and the tendency for Democrats to waste votes in heavily urban areas. But there’s another factor: Most Democratic-leaning districts already have Democratic representatives, and most Republican districts already have Republican representatives.

Where the Incumbent Is Not Running

One piece of good news for Democrats is that the party out of power has tended to excel in open districts, even in districts that tilt somewhat toward the president’s party. This year, 40 Republicans have decided not to seek re-election. That has meaningfully eroded the G.O.P.’s structural advantage. So has a Pennsylvania court’s decision to redraw the state’s Republican gerrymander.

The abundance of open seats (represented in this illustration by yellow, in contrast to the gray incumbents) ought to be enough to make the Democrats slight favorites to retake the House in a wave election in which the Republicans lose seats at the same rates as the incumbent party did in 1994, 2006 and 2010. The Republicans would lose a net 27 seats in such a situation, by our estimates, barely enough to flip the House.

The 2006 election, though perhaps the most similar to 2018 in terms of the number of opportunities available to Democrats, isn’t as exact a precedent as one might assume. Many Democratic gains that year were victories over incumbents facing corruption allegations in heavily Republican districts. Scandal, federal investigations or indictments helped Democrats win at least seven heavily conservative seats. Take away those seats from the 31 that the Democrats won that year, and suddenly they would have gained only 24 — just one more than the Democrats need today.

The pattern in the 2010 election, on the other hand, was quite different. Republicans wiped out Democrats in Republican-leaning districts, but made very few gains in areas that voted comfortably for President Obama.

Which Seats Flipped?

People farther down the hill are more likely to lose their seats. If this year is like the past, control of the House is going to be really close.

It’s hard, even impossible, to predict the distribution of Democratic gains at this early stage. But there are some tentative hints that the 2018 election might be a little bit more like 2006 than 2010. Democrats have done very well in special elections in conservative areas, like Pennsylvania’s 18th District. And Democrats are targeting a lot of districts in deeply conservative areas. Republicans had no need to do so in 2010, given how many Democrats represented Republican-leaning areas.

It is possible that Democrats could win more seats in 2018 than they would with a simple rerun of the 1994, 2006 and 2010 waves.

They could do so simply by winning more votes: There’s no reason 1994, 2006 and 2010 represent a ceiling for the party out of power. Democrats could gain more seats in other ways, too. For instance, if the value of incumbency declines further — and it has been declining for decades — Democrats will find it easier to knock off Republicans in districts that tilt slightly toward the G.O.P. The Democrats also have an unusually strong crop of well-funded candidates. Perhaps they can just outmuscle Republicans, even if the national political environment is no more favorable for the party out of power than it was in 2006 or 2010.

But it’s worth keeping history in mind as the fight for control of the House intensifies.