She is expected to survive the injuries, which were originally called life-threatening, The Associated Press reported Saturday.
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After the third out, the game was delayed while the fan was tended to in the stands between home plate and the third base dugout. Carpenter was wheeled off on a stretcher and rushed to the hospital. Witnesses told WFXT that the president of the Red Sox ran down from the boxes to try and help.
>> Click here to watch a video report from Boston's WFXT
Another fan who was at the ballpark said, "She slumped down after she was hit, and the crowd of paramedics shielded her after."
A source told WFXT that Carpenter was at the game with her husband and son.
Red Sox player Mookie Betts spoke to WFXT after the game Friday night, saying, "It's definitely scary, it's scary for anybody."
The Red Sox released a statement Saturday that read, in part: "All of us offer our prayers and our thoughts as we wish her a speedy recovery."
>> Click here to see photos from WFXT
Boston police say Carpenter had surgery Friday night at Beth Israel Deaconess Medical Center and her injuries were life-threatening. On Saturday, she was upgraded to serious condition.
Also on Saturday, Beth Israel released a statement, saying Carpenter's "family and loved ones are grateful to all who have reached out with thoughts and prayers but are requesting privacy at this time as Tonya recovers."
Fans headed to Saturday's game were a bit nervous given what happened to Carpenter.
"Excited to go to the game, but a little cautious," fan Sean Allen said.
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"I don't really think there is anything else they could do. If you are going to be close down on the field you have to be careful and paying attention but that is just a freak accident."
Broken bat injuries are down considerably, especially since 2008 when the MLB researched record numbers because players were using bats made out of maple wood. The switch back to other wooden bats has cut bat breakage averages in half.
And as most people know, on the back of game tickets there is fine print, which warns fans about foul balls and broken bats.
The Associated Press contributed to this report.
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