With the conclusion of primary season, we can now consider how the November elections will alter women’s representation in government.

The House

Women stand to make their greatest gains in the House. As always, I’m continually updating http://www.morewomeninthehouse.com/ to reflect the current ratings from Cook Political Report.

Historically, the largest gain from one Congress to the next came between the 102nd and 103rd Congress, when the count of Congresswomen jumped from 30 to 48 due to broad victories in 1992’s Year of the Woman. No other election has produced more than a single digit gain in the number of Congresswomen.

As it stands, the expected number of women in the next House is 99.34. There were 83 women in the House at the start of the current (115th) Congress, though 84 are now serving. So, to make an apples to apples comparison: the expected gain from start of the 115th to the start of the 116th Congress is currently 16.34 Congresswomen, just shy of the record.

But of course, this is an expected value, not a projection. If we were to make the (wrong) assumption that the races were independent, then the distribution of the number of women in the next Congress would follow my favorite distribution, the Poisson Binomial. If we then approximate via a normal distribution, a 95% (Wald) confidence interval would encompass outcomes from 94 women in the next Congress to 105 women.

In reality, the race outcomes are mostly positively correlated with one another, because the vast majority of the female candidates are Democrats. If existing measures are generally over-estimating Democrats’ chances, then many fewer women will land in Congress; if they’re under-estimating them, then many more women will be elected. These (mostly) positive correlations induce larger variance in the total number of female-held seats, so a true 95% interval is probably quite a bit wider than (94, 105).

A final point: the expected number of newly elected Congresswomen in the next House is 31. This is well above the record of 24 set in 1992. The reason next year won’t easily set the record for the greatest gain in Congresswomen is the high number of incumbent Congresswomen (13) not seeking reelection. But this “cannibalization” has some benefits for women’s representation: six of these women are now nominees for governorships or Senate seats.

The Senate

Things look less rosy in the Senate. There are currently a record 23 female Senators, but thirteen of them (57%) are up for reelection this year, including two highly vulnerable red state Democrats: Claire McCaskill (MO) and Heidi Heitkamp (ND). Early handicapping also identified Democrats Debbie Stabenow (MI), Tammy Baldwin (WI), and appointed Senator Tina Smith (MN) as potentially vulnerable, but recent polling has seemed to favor all three women. Ditto for appointed Republican Senator Cindy Hyde-Smith (MS), who could theoretically fail to advance to a runoff from Mississippi’s nonpartisan blanket primary, or even lose a head-to-head match-up against Democrat Mike Espy, but I wouldn’t bet on it.

Women do stand to pick up a few seats. Arizona will gain a female Senator in 2019, as Democrat Kyrsten Sinema is facing Republican Martha McSally in a toss-up race for retiring Senator Jeff Flake’s seat. And women could conceivably pick up seats in Nevada — where Congresswoman Jacky Rosen is taking on incumbent Republican Dean Heller — and Tennessee, where Congresswoman Marsha Blackburn is taking on Phil Bredesen, a moderate Democrat and former Governor. All three races, along with McCaskill’s and Heitkamp’s, are rated as Toss-Ups by Cook.

Again, women’s gains are closely tied to outcomes for Democrats. If they have a great night on November 6, then women could conceivably hold 25 seats in January (the incumbent Senators, plus Rosen and Sinema). If Democrats underperform, we might see Heitkamp and McCaskill lose but McSally and Blackburn win, yielding no change in the total number of female Senators. And of course, weirder outcomes are possible that might yield a net loss in female Senators.

Governor’s Mansions

The greatest uncertainty lies in the number of female Governors. As I’ve discussed in previous posts, governorships are unique in that they are the one office where women have actually lost ground in recent years (there are currently six female governors, as opposed to nine at their peak). Governorships are also much more idiosyncratic than federal elections. Case in point: Democrats are almost certain to lose the Massachusetts Governor race, but are competitive in gubernatorial races in Oklahoma and Kansas.

As it stands, six women are favored to win by Cook: incumbents Kay Ivey (R-AL), Gina Raimondo (D-RI), and Kate Brown (D-OR), as well as Kristi Noem (R-SD), Michelle Lujan Grisham (D-NM) and Gretchen Whitmer (D-MI). Polling has continued to be a mixed bag for both Raimondo and Brown, who are the only incumbent Democratic female governors and have middling approval ratings. These races could conceivably move into Toss-Up territory. Things seem to be moving in the other direction for Whitmer, who faced early doubters, but has led all polls since winning the nomination.

Four women are also in Toss-Up races. The buzziest candidate is Democrat Stacey Abrams in Georgia, who is tied in the polls as she vies to become the first black female governor. Democrats also have competitive female candidates in Janet Mills of Maine and Laura Kelly of Kansas. And appointed incumbent Republican Kim Reynolds of Iowa is also in a competitive race against Democrat Fred Hubbell. Five additional Democratic women are gubernatorial candidates, but none are currently considered competitive.

More so than in the House and Senate, it’s plausible that competitive races won’t disproportionately break for one party or the other. In more statistical terms: the covariance between the race outcomes is probably lower. So it’s possible we could end up with a record ten female governors next year, if all the Toss-Up races go to the female candidates. More likely is that we see an increase in the number of female governors, but fall short of or tie the record of nine.