The hand-to-hand political combat in House elections on Tuesday in Georgia and last week in Kansas had the feel of the first rounds of an epic battle next year for control of the House of Representatives and the direction of national politics as the Trump presidency unfolds.

But for all the zeal on the ground, none of it may matter as much as a case heading to the Supreme Court, one that could transform political maps from City Hall to Congress — often to Democrats’ benefit.

A bipartisan group of voting rights advocates says the lower house of the Wisconsin Legislature, the State Assembly, was gerrymandered by its Republican majority before the 2012 election — so artfully, in fact, that Democrats won a third fewer Assembly seats than Republicans despite prevailing in the popular vote. In November, in a 2-to-1 ruling, a panel of federal judges agreed.

Now the Wisconsin case is headed to a Supreme Court that has repeatedly said that extreme partisan gerrymanders are unconstitutional, but has never found a way to decide which ones cross the line.

Some legal scholars believe this could be the year that changes that. If that happens, they say, an emphatic ruling against partisan gerrymanders would rank with another redistricting decision: Baker v. Carr, the historic 1962 case that led to the principle of one person, one vote.

 “My feeling is that there is increasing concern within the court about the extent of partisan gerrymandering over the last 10 or 15 years,” said Richard H. Pildes, a constitutional law professor at the New York University School of Law. “I do think this is a pivotal moment — a big, big moment.”

Gerrymandering has always been contentious. But the extraordinary success of a Republican strategy to control redistricting by capturing majorities in state legislatures in the 2010 elections has lent urgency to the debate.

Today, at a time of hyperpartisan politics and computer technology that can measure political leanings almost house by house, Republicans control legislatures in 33 states, 25 with Republican governors. They have unfettered command over the boundaries of at least 204 congressional districts — amounting to nearly half the 435-seat House.

In contrast, Democrats’ share of state legislature seats has shrunk to a level not seen since Warren G. Harding was president, according to the National Conference of State Legislatures. And in recent years, their numbers in the House of Representatives have hovered near levels last seen during the Truman administration.

Partly because of the Voting Rights Act, gerrymanders based on race are flatly illegal, but ones based on partisan intent remain in limbo.

The Wisconsin case heads four legal actions on partisan gerrymanders that the Supreme Court could consider and, perhaps, consolidate. In Maryland, another three-judge panel will hear arguments over whether a Democratic legislature gerrymandered House districts in 2011 to oust a 10-term Republican congressman.

In North Carolina, a June hearing is scheduled in a suit over the unabashedly partisan carving of the state into 10 Republican and three Democratic House seats — this in a state with more registered Democrats than Republicans.

The state representative who drew that map said he had engineered 10 safely Republican seats only “because I do not believe it’s possible to draw a map with 11 Republicans and two Democrats.”

Experts disagree over how much gerrymandering has hurt Democrats. One prominent 2013 study mostly blamed geography, not partisanship, because Democrats tend to cluster in cities. But the most recent study, by a Princeton professor, Samuel S. H. Wang, concluded that gerrymanders had cost Democrats as many as 22 House seats in the 2012 election — nearly enough to flip the chamber’s control.

Politicians, on the other hand, appear certain of their electoral potency. Former President Barack Obama and his attorney general, Eric H. Holder Jr., are spearheading an initiative to undo Republicans’ redistricting triumphs. Arnold Schwarzenegger, a Republican and the former governor of California, is leading a movement to outlaw gerrymanders of any political stripe.

Wisconsin Republican leaders say they dominate the Legislature because they have both a better strategy and vision of governing, not because of illegal gerrymandering.

“In a year when people want change, even in a district that favors one party over another, a good candidate with a good message wins,” said Robin Vos, Wisconsin’s Assembly speaker.

But the court said in November that the redistricting clearly aimed to entrench Republican control of the Assembly. The party took 60 of the Assembly’s 99 seats in 2012 despite losing the popular vote, and has since added three more.

As in all gerrymanders, Wisconsin’s mapmakers hobbled their opponents in two ways. One was to pack as many Democrats as possible into a few districts, leaving fewer Democrats for potentially competitive ones. In 2012, 21 of the 39 Assembly districts that Democrats won were so lopsided that Republicans did not even field candidates. In two more, Democrats captured at least 94 percent of the vote.

The other method was to fracture unwinnable Democratic districts, salting their Democrats among Republican-majority districts so that races there became closer yet remained out of Democrats’ reach.

“They just busted my district and put it into four or five others,” said Mark Radcliffe, a 45-year-old Democrat and former state representative, whose district encompassed Alma Center, in rural western Wisconsin. Mr. Radcliffe, who wound up in the district of another Democrat, chose to resign rather than run against a popular member of his own party.

John Steinbrink, another Democrat, had represented southeastern Wisconsin in the Assembly since 1996, supported by a Democratic base in Kenosha, six miles from where he farms corn and soybeans. After redistricting, Kenosha became a safe Democratic district, and Mr. Steinbrink was exiled to an adjoining district populated by rural conservatives. In 2012, his Republican opponent won with 55 percent of the vote.

“I could have moved to Kenosha” and sought re-election there, Mr. Steinbrink said. “But I don’t know how you farm in the city.”

The legal argument against such maps is akin to the one used for decades to outlaw ethnic and racial gerrymanders. Gerrymanders dilute a minority group’s votes, muffling its voice in the political process. The Wisconsin plaintiffs argue that whether the minority group is African-Americans or members of a political party makes no difference.

“When you’re talking about the opportunity to turn your vote into a policy or change, the 14th Amendment says you should have an equal chance, whether you’re a Democrat or a Republican,” said Ruth Greenwood, the deputy director for redistricting at the Campaign Legal Center, which is representing plaintiffs in Wisconsin and North Carolina. “But if you’re a Republican in Wisconsin, you get an outsized say with your vote. And if you’re a Democrat in Rhode Island, you get an outsized say.’’

But while racial or ethnic gerrymanders can be statistically measured — a Latino remains a Latino from election to election — judges have struggled to identify overly partisan districts, knowing voter sentiments can quickly change.

In Supreme Court cases in 1986, 2004 and 2006, justices variously called partisan gerrymanders illegitimate, seriously harmful, incompatible with democratic principles and “manipulation of the electorate.” But they have never struck one down. And in 2004, they came within a single vote of ruling them impossible to judge, because nobody could draw the line between unavoidable political influence in redistricting and an unconstitutional rigging of the vote.

The Maryland lawsuit proposes a solution that some justices have pondered: an argument that gerrymanders violate the First Amendment, not the 14th, by retaliating against opponents who express contrary views. Under that standard, any partisanship-inspired district would be unconstitutional if it hobbled a minority party.

The Wisconsin plaintiffs’ attempt to break the logjam is a new standard, the efficiency gap. It is a numerical rating of parties’ “wasted” votes: those above the 50-percent-plus-1 needed to win a seat, and all votes cast in a loss. When the gap between the parties’ ratings exceeds a limit based on ratings from hundreds of past elections, the plaintiffs argue, the majority party should have to justify the boundaries it drew. Even then, plaintiffs would have to prove the party aimed to weaken the opposition.

The Wisconsin case underscores how modern gerrymanders, using computers and political and behavioral data, have become increasingly effective. Measured by the efficiency gap, four of the five most partisan state legislature maps in the last 45 years were drawn after 2010, said Nicholas O. Stephanopoulos, a University of Chicago law professor and lawyer for the plaintiffs.

In the House of Representatives, eight of the 10 most partisan maps were created after 2010, including Wisconsin’s and two in North Carolina.

One participant in the 2004 decision, Justice Anthony M. Kennedy, may prove the fulcrum in the court’s deliberations. In that case, he held out hope that the court could find a solution to extreme gerrymanders that political leaders were unable or unwilling to address.

“The ordered working of our Republic, and of the democratic process, depends on a sense of decorum and restraint in all branches of government, and in the citizenry itself,” he wrote then.

At a time of soaring concern over hyperpartisanship, those words could resonate. That sentence “is the most important line” in the court’s decision, said Edward B. Foley, director of the Election Law Project at the Ohio State University Moritz College of Law.

If the Wisconsin statistical standards do not persuade the justices, other proposals are waiting in the wings. But some worry that the debate may be close to hitting the brick wall it avoided in 2004.

“If the court doesn’t endorse some version of what the three-judge panel decided” in Wisconsin, said Ellen D. Katz, a University of Michigan scholar of election law, “then it may be they’re never going to find a standard they’re comfortable applying.”