Shut out of power in Washington, crestfallen about their Obama-era losses in governors’ mansions and state legislatures, Democrats have been paying more than the usual amount of attention to local races. This year, they’ve poured money into special elections in Virginia, Minnesota, Iowa, Delaware and Connecticut and pored over the results for evidence of a Trump backlash or grass-roots Democratic comeback.

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Democrats know too well that special elections can say nothing about how voters will behave in November. Last March, they celebrated a run of victories in Kentucky, which helped them keep control of the state House of Representatives. Eight months later, their candidates were buried under a wave of support for Donald Trump, turning a seven-seat Democratic majority into a 28-seat Republican supermajority.

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But with their eyes on special House races scheduled for the next few months to fill seats abandoned by Trump Cabinet picks, Democrats see hyper-local evidence that their voters are coming out again.

Virginia (Jan. 10 and Feb. 7): One of the very few states where Hillary Clinton improved on Barack Obama’s margin gave Democrats their first 2017 test. On two special-election days, they easily held the House of Delegates’ deep-blue 71st District and the state Senate’s 9th District. The race that intrigued them was in the 85th House District, where Cheryl B. Turpin came 362 votes away from victory.

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Why it mattered: The 85th, in the swingy Hampton Roads region of Virginia, had been vacated by now-U.S. Rep. Scott Taylor (R-Va.). In 2013, when Terry McAuliffe (D) was narrowly winning the governor’s race, Taylor won with 56.3 percent of 19,622 total votes. In 2015, Democrats did not field a candidate; Taylor won most of 10,053 total votes. This year, Democrats nearly took advantage of low turnout — 6,247 votes total — to hold Republican Rocky Holcomb to just 52.8 percent.

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Why it didn’t: They lost, and overall turnout was down.

Minnesota (Feb. 14): In November, as he surged across rural America, Trump won Minnesota’s House District 32B by 29 points. Due to a mix-up over candidate eligibility, there was a new election for the seat, and Democrat Laurie Warner was selected to face Republican Anne Neu.

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Why it mattered: Neu defeated Warner by just 462 votes, 3,789 to 3,327, a 6.5 percent margin. That was not just down from Trump’s margin; it was down from the 2014 race, when the Republican then-incumbent won by 10.5 points.

Why it didn’t: See above.

Delaware (Feb. 25): The highest-profile special election of the year found Democrats greatly outmatching Republicans in spending and star power. As Alexander Burns wrote for the New York Times, former vice president Joe Biden, who had represented the voters of the 10th Senate District since 1970, campaigned for Democrat Stephanie Hansen. He did so as Democrats outspent Republican John Marino by a 6-to-1 margin, in a district he’d nearly won in 2014.

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Why it mattered: Hansen won in a landslide, 58 percent to 41 percent in a district that broke by 11 points for Clinton. But what struck Democrats was that turnout spiked compared with the 2014 midterm; Hansen’s 7,314 votes marked a 1,000-plus vote improvement on now-Lt. Gov. Bethany Hall-Long’s 2014 total. After the victory, Democratic Legislative Campaign Committee spokeswoman Carolyn Fiddler noted that the attention helped Democrats pile up national support for the campaign: “Donors from all 50 states contributed to Senator-elect Hansen’s campaign. Over 1,000 volunteers knocked on nearly 90,000 doors and made over 60,000 phone calls.”

Why it didn’t: Hall-Long’s 2014 race was close largely because of a late-breaking scandal in which her husband was caught stealing campaign signs.

Connecticut (Feb. 28): In 2016, Connecticut Democrats nearly lost the state Senate; the election ended with the body in a tie. Vacancies prompted a trio of special elections, with the party defending two seats and fighting for District 32, the most conservative seat in the state. Greg Cava, the Democrat who’d lost the seat in a landslide in 2016, ran again against state Rep. Eric Berthel. Wolf PAC, a campaign-finance-focused group founded by liberal online commentator Cenk Uygur, threw $50,000 at the race, and he increasingly active Working Families Party gave Cava its ballot line. The National Rifle Association endorsed and sent mail for Berthel

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Why it mattered: Cava lost, by just 10,147 to 8,311. Months earlier, he’d lost 33,090 to 15,697. The Republican vote had fallen by two-thirds, the Democratic/WFP vote by less than half.