The child, whose identity, along with that of her family, is still being withheld, was struck by a line drive off the bat of Chicago Cubs outfielder Albert Almora Jr. during the Astros-Cubs game May 29.
The two-year-old suffered bleeding and swelling in her brain, as well as a seizure and a brain contusion after being hit.
"The family's foremost concern is about the health of their child, but they also wanted me to extend their thanks to the fans and the Astros for their concern", said Mithoff.
The girl will be medically examined next month and the family hopes to receive more information about the longterm effects of her injuries, Mithoff said.
Albert Almora, the Cubs player who hit the foul ball, crouched at home plate and was consoled by teammate Jason Heyward and Cubs manager Joe Maddon.
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"She is doing relatively well, but she has had seizure (s) and the abnormal EEG, and so it's going to be a matter of time" the family's attorney Richard Mithoff said in a statement Wednesday, via the Houston Chronicle. Almora appeared to be shaken after the incident and was close to tears.
What is MLB's rule for protective netting?
For more than a decade, all major league tickets have included a disclaimer that states the ticket holder is responsible for "all risk and danger incidental to the baseball game" and any resulting injuries incurred at the stadium.
Netting is required to go to at least the far ends of the dugouts. She was sitting along the third base line in Minute Maid Park when she was struck.
In 2017, a boy at Yankee Stadium was hit by a portion of Chris Carter's broken bat.
In the wake of the incident, the Chicago White Sox, Los Angeles Dodgers, Texas Rangers and Washington Nationals all agreed to extend netting in their ballparks. The girl and her family were sitting a few seats up from the field in section 111, just past the end of the netting. They are the first two teams to announce plans to extend netting that far.