HARRISBURG — A map of congressional districts drawn by Pennsylvania’s Republican-controlled Legislature helped the GOP win nearly three more of the state’s U.S. House seats than the party otherwise would have won in last year’s election, an Associated Press analysis found.

The partisan tilt was more than any other state, except for Texas, according to AP’s national analysis.

The map, drawn in 2011, was called “the worst gerrymander in modern Pennsylvania history” by Franklin & Marshall College political scientist G. Terry Madonna and is now the subject of its first court challenge, filed earlier this month by the League of Women Voters and 18 registered Democratic Party voters.

AP also found that the drawing of districts for hundreds of U.S. and state legislative districts gave Republicans a real advantage.

The news organization scrutinized the outcomes of all 435 U.S. House races and about 4,700 state House and Assembly seats up for election last year, using a new statistical method of calculating partisan advantage called the “efficiency gap.” Designed to detect cases in which one party may have secured power through political gerrymandering, it found that the GOP may have won as many as 22 additional congressional seats more than expected.

PENNSYLVANIA’S MAP

Republicans went into the map-drawing exercise — required every decade after the census — to protect their 12 incumbents in Congress, the result of a 2010 GOP wave election on a map also drawn by Republicans a decade earlier, and to try to pick up a 13th seat. The map was drawn behind closed doors, and mapmakers released no records to explain their strategy.

Districts underwent dramatic changes that broke decades of precedent: The map shifted whole counties and some of the state’s larger cities into new congressional districts, and pitted two Democratic congressmen against each other to remain in Congress. Mapmakers apparently analyzed voting patterns of individual wards. They moved Democratic-performing areas into districts that were safe for Republican or Democratic candidates. And they moved Republican-performing areas into closely divided districts held by Republican incumbents.

Ultimately, Republicans picked up a 13th district in a state where registered Democratic voters outnumber Republicans by a margin of 4 to 3. Voters again re-elected 13 Republicans to the U.S. House in the 2014 and 2016 elections.

PENNSYLVANIA’S GAP

Pennsylvania’s 16.2 percent efficiency gap favoring Republicans was the sixth highest among states last year. In 2012, the efficiency gap of Pennsylvania’s congressional districts was the largest in the nation, the lawsuit said.

The AP analysis was based on a formula developed by University of Chicago law professor Nick Stephanopoulos and Eric McGhee, a researcher at the nonpartisan Public Policy Institute of California. Their mathematical model was cited last fall as “corroborative evidence” by a federal appeals court panel that struck down Wisconsin’s state Assembly districts as an intentional partisan gerrymander. The U.S. Supreme Court has agreed to hear an appeal.

The “efficiency gap” formula creates a way to measure whether gerrymandering has helped a political party extend its power.

Stephanopoulos and McGhee computed efficiency gaps for four decades of congressional and state House races starting in 1972, concluding the pro-Republican maps enacted after the 2010 Census resulted in “the most extreme gerrymanders in modern history.”

The formula compares the statewide average share of the vote a party receives in each district with the statewide percentage of seats it wins, taking into account a common political expectation: For each 1 percentage point gain in its statewide vote share, a party normally increases its seat share by 2 percentage points. So a party that receives 55 percent of the statewide vote could expect to win 60 percent of the legislative seats.

Under the 2011 map, Republicans now fill 13 of Pennsylvania’s 18 seats in the U.S. House — or 72 percent — despite winning 54 percent of the statewide congressional vote in 2016.

CASE LAW

Court precedent says gerrymandering can be unconstitutional, although there is no definitive answer to the question of how large an efficiency gap must be to indicate an unconstitutional gerrymander.

In a recent case challenging North Carolina’s congressional districts, political scientist Simon Jackman suggested that an initial election efficiency gap of at least 7.5 percent in a state with more than 15 U.S. House districts should attract scrutiny. Pennsylvania fits that description.