“I thought she was going to die in front of me,” Barrett said. “I started saying, ‘Stay with me, stay with me.’ ”

Her daughter survived, but medical expenses exceeded $100,000. Barrett, a human resources executive who lives in Pound Ridge, N.Y., is now among a group of people pushing for more safety at minor league parks. They believe sharing their stories could spark clubs to extend netting and prevent such accidents.

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This summer has induced a renewed awareness of the threat of foul balls, after a 4-year-old girl was struck at a major league game in Houston, leading to calls for teams to do more. This season, there have been 16 reported cases of fans being injured at major league games from foul balls or flying bats and six at minor league games.

Five major league teams and seven minor league clubs have extended their netting beyond the dugouts, while six major league teams and 11 minor league clubs have announced plans to do the same for the 2020 season. Three teams in the majors and 11 in the minors said they are studying the issue. Fans who have witnessed or suffered injuries at minor league parks believe more of the 159 minor league stadiums nationwide should follow the example of the majors, where more than a third of the teams have addressed foul ball risks or plan to do so.

Minor league teams enter the offseason in September, when they usually make ballpark improvements. And because the parks are smaller than major league stadiums, fans are closer to the action. In many cases, they’re more prone to foul balls, which are increasingly common in the velocity era: With pitchers throwing harder, batters have less time to make solid contact, leading to more foul balls reaching the seats.

Many who oppose extended netting say it obstructs fans’ views and interferes with their ability to mingle with players. There also are financial barriers at the minor league level: While major league teams have large budgets, minor league clubs have less to allocate for additions such as netting.

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The cost depends on ballpark size and dimensions, but extending netting down the foul lines often runs between $75,000 and $200,000, according to minor league general managers who have done so.

The Iowa Cubs, the Class AAA affiliate for the Chicago Cubs, will be one of the first teams in the minors to extend to the foul poles before next season. The team spent about $155,000 to extend netting from behind home plate to the end of each dugout.

“Most of us in minor league baseball don’t work under unlimited budgets,” Iowa General Manager Sam Bernabe said. “But it’s a great thing to protect the fans.”

The Washington Nationals’ Class AAA affiliate, the Fresno Grizzlies, will extend netting to each foul pole, as well. Once the Nationals announced in June that they would extend netting after the all-star break, Grizzlies President Derek Franks said “it made us feel more eager” to do the same for 2020. The team plans to make the netting “invisible” and retractable so fans can still mingle with players and request autographs. Over two-plus years, the extensions will cost more than $100,000, Franks said.

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Closer to Washington, the Frederick Keys, the Class A affiliate of the Baltimore Orioles, have extended netting twice in the past three years. In 2017, they expanded to adhere to the leaguewide recommendation, which suggested teams cover seats between each dugout. This year, the Keys went farther, covering 95 percent of the ballpark’s seats, according to General Manager Dave Ziedelis.

But there are many minor league parks, particularly below Class AAA, where thousands of seats aren’t covered. Whether they eventually mirror what the higher levels of baseball have done remains to be seen, largely because of budgets.

“We have about $35,000 per year budgeted for ballpark improvements,” said Travis Painter, general manager of the Hagerstown Suns, whose netting covers dugout to dugout. “We haven’t had concrete discussions about extending netting as of yet.”

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Foul ball victims at minor league games encourage others to write to their local minor league team. In some cases, they themselves have written, explaining the physical damage and emotional trauma they experienced. That includes Dina Simpson of Chardon, Ohio, who attended a May 2017 Lake County Captains game with her husband and three children.

In the ninth inning, a hard line drive hit her directly in the right eye, breaking her nose and causing “bleeding everywhere.” The eye swelled shut, she said, and she permanently lost vision in the eye. The injury cost her $4,000 in out-of-pocket medical expenses.

“I didn’t mean to make this a cause,” said Simpson, a netting advocate who writes about fan safety. “I went to a baseball game and came home blind.”

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There are dozens of cases in which fans experienced a life-changing accident while watching a minor league baseball game. Dana Mattay, a school counselor in Frisco, Tex., was at a Frisco RoughRiders game in 2014 when, as she reached for her popcorn, she was struck by a line drive. The ball’s seams left a mark between her eyes. Mattay was rushed to the hospital, and doctors told her it was a miracle that she survived. She suffered nerve damage and has since dealt with memory loss, confusion and headaches.

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“The trauma,” she said, “has been a ripple effect.”

Barrett, the mother whose 7-year-old daughter was struck in 2005, did not attend a baseball game for several years after the incident. The incident occurred 14 years ago, but Barrett said it was life-altering. Her daughter was left with scars across her head. Her older daughter, also present at the game, suffered from post-traumatic stress disorder, Barrett said.

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Finally, in 2009, she attended a game at Yankee Stadium. When she pulled into the parking lot, Barrett said, she had an anxiety attack.

“It is very simple,” Barrett said. “Extend the netting so nobody has to go through what I did.”