It’s unlikely that the Ds will take back the House, but the question, of course, is how unlikely? Here’s a stab at answering that question.
First, the basics: There are 435 Congressional seats with voting rights, though 1 of these seats is currently empty. There are also 6 seats (from the U.S. territories, commonwealths, and the District of Columbia) without voting rights. Since the question is about control over the House, I’ll ignore the seats without voting rights. (Sorry, folks. You really should have voting rights, but I can’t fix that here.) So, in lieu of further vacancies, a party needs at least 218 seats to control the House. (I ignore here the complications raised by the election of third-party candidates, as this is unlikely to be relevant in 2016.) At the moment, the Rs have 246 seats, and the Ds have 188. So the Ds would have to win a net of 30 seats from the Rs to gain control of the House.
That’s a lot of seats! But it’s not like we’ve never seen such a thing. As recently as 2010, Rs picked up 63 seats in a single election cycle. A smart thing to do would be to look through all of the recent elections, and see what the average amount of change has been. But I’ve been struggling to find these data in a digestible form. I ended up working with a data set that had the virtue of going back to the beginning of our Republic but which also had a number of annoying typos in it, which I think I’ve managed to correct. I limited my number crunching to all of the elections following 1921, the first year in which the number of Congressional Representatives was fixed at 435. In the average House election (whatever that means), Ds lose 2 seats, and Rs pick up 2.33. Why aren’t these numbers symmetrical, you ask? Third-party candidates. More importantly, there’s is a ton of variance. The standard deviation for the Ds is 36.23 and for the R is 37.07. On no less than 18 occasions (out of 51 possibilities), one party picked up at least 30 seats.
- 1914 election: R Pres (Taft) in office during election, Rs pick up 66 seats
- 1920 election: D Pres (Wilson) in office during election, Ds lose 59 seats
- 1922 election: R Pres (Harding) in office during election, Rs lose 75 seats
- 1928 election: R Pres (Harding) in office during election, Rs pick up 30 seats
- 1930 election: R Pres (Hoover) in office during election, Rs lose 53 seats
- 1932 election: R Pres (Hoover) in office during election, Rs lose 101 seats
- 1938 election: D Pres (Roosevelt) in office during election, Ds lose 71 seats
- 1942 election: D Pres (Roosevelt) in office during election, Ds lose 45 seats
- 1946 election: D Pres (Truman) in office during election, Ds lose 55 seats
- 1948 election: D Pres (Truman) in office during election, Ds pick up 75 seats
- 1958 election: R Pres (Ike) in office during election, Rs lose 48 seats
- 1964 election: D Pres (LBJ) in office during election, Ds pick up 36 seats
- 1966 election: D Pres (LBJ) in office during election, Ds lose 47 seats
- 1974 election: R Pres (Ford) in office during election, Rs lose 48 seats
- 1980 election: D Pres (Carter) in office during election, Ds lose 36 seats
- 1994 election: D Pres (Clinton) in office during election, Ds lose 54 seats
- 2006 election: R Pres (Bush II) in office during election, Rs lose 33 seats
- 2010 election: D Pres (Obama) in office during election, Ds lose 63 seats
Bad news for the Ds: The majority (78%) of the time, the party that loses 30 or more seats in the House is the party with the sitting president at the time of the election. Worse news for Ds: The party with a sitting president loses on average 13.3 seats per House election. Slightly better news for the Ds: Given the high level of variance, there is a 0.123 probability of picking up 30 or more seats if your party holds the White House. (I haven’t shown my work here because it was tedious to do and, I reckon, would be even more so to look at.)
So far, so good. But foxes are supposed to have more than one trick up their furry little sleeves. So let’s try it from another angle. According to the Cook Political Report, there are 65 district races that are to at least some degree competitive. 19 of these are currently held by Ds, and the remaining 46 are held by Rs. That leaves 169 safe seats for the Ds and 200 safe seats for the Rs. The question, then, is this: How likely is it that the Ds can win 49 of the 65 (or more) of the competitive seat?
Glad you asked. CPR ranks these races as Solid R, Likely R, Leans R, Tossup, Leans D, Likely D, and Solid D. On the basis of CPR’s own assessment of their levels of accuracy and a little bit of body English, I’m translating these qualitative judgments into quantitative judgments as follows:
- Solid R: 0.997 probability of an R victory, 0.003 probability of a D victory
- Likely R: 0.95 probability of an R victory, 0.05 probability of a D victory
- Leans R: 0.85 probability of an R victory, 0.15 probability of a D victory
- Tossup: 0.50 probability of an R victory, 0.50 probability of a D victory
- Leans D: 0.15 probability of an R victory, 0.85 probability of a D victory
- Likely D: 0.05 probability of an R victory, 0.95 probability of a D victory
- Solid D: 0.003 probability of an R victory, 0.997 probability of a D victory
The average expected outcome is that Ds win 29 (rounding up from 28.79) of the 65 contested seats. That gets them to 197 total seats in the House, a nice outcome with their party holding the White House but far short of a majority. I ran a 1,000 round Monte Carlo simulation, and not once did Ds win more than 40 of these 65 seats (though they did hit 39 on a few occasions). Since Ds need to win 49 of the 65 competitive seats to take control of the House, I’m pretty damn pessimistic about their chances.
“Unless…unless it’s 1964 all over again,” you might say. As we saw above, in 1964 LBJ ran as an unelected incumbent against an extremely unpopular R candidate, Barry Goldwater, who won the nomination after a highly contentious convention. Sound familiar? LBJ won the presidency in a landslide, and the Ds netted themselves 36 seats, 6 more than they need in 2016.
But I’d urge caution about betting the farm on another 1964. Marx’s line about history repeating itself “the first time as tragedy, the second time as farce” has to be taken with a grain of salt. He was, after all, referring to “all great world-historic facts and personages”. Honestly I don’t think either Barry Goldwater or Donald Trump count as great world-historic personages, and I don’t their runs for office are great world-historic facts. And Marx was at a point in his career where the pithy phrase was sometimes more important than the carefully reasoned analysis.
Anyway, it’s unwise to become fixated on a single data point when so much data is available. In 2003, we were obsessed with Munich, and anyone who voiced doubts about going to war with Iraq was an Attlee-esque appeaser, never mind the many, many dis-analogies. Sure, Mr. Trump could bomb as a general election candidate and drag down a lot of R House Representatives with him; I don’t deny that for a second. But Rs running for House seats have been running away from Mr. Trump for some time now, and there are reports that the Koch brothers are shifting their considerable financial resources away from the presidential race (where they don’t like what’s on the menu) to Congressional and state-level races where money makes a bigger difference. If we can see the risk to Rs in the House, it’s no surprise that they can too and that they’re acting tactically to try to counter the risk.
TL;DR: The historical data suggests something like a 12% chance that the Ds will retake the House, while the race-by-race data suggests a lot less, probably less than 1%. I’ll blend these odds a nock it up 3% because treating the House races as if they were independent from one another (or, more properly, as if they were independent of common factors like who’s at the top of the ticket) is obviously inadequate. So, for the moment at least, the Ds have a 10% of taking the House, while the Rs have a 90% of keeping it.
 Brookings has the numbers since 1946, but they’re in PDF format and not easily importable to a spreadsheet: http://www.brookings.edu/~/media/Research/Files/Reports/2013/07/vital-statistics-congress-mann-ornstein/Vital-Statistics-Chapter-2–Congressional-Elections.pdf
 That is to say, they need to win 19 of the 65 to break even and another 30 of the remaining 46 to take control.
 Suggested in, for example, http://www.vox.com/2016/3/18/11265196/can-democrats-win-the-house
 Karl Marx (1952) “The Eighteenth Brumaire of Louis Napoleon,” quoted from https://www.marxists.org/archive/marx/works/1852/18th-brumaire/
 Somewhere in a New Yorker interview with Jane Mayer that I can’t find at the moment.