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The network housed databases that were built by the team and contained "internal discussions about trades, proprietary statistics and scouting reports," according to investigators.
Law-enforcement officials have already served subpoenas to the Cardinals and to Major League Baseball seeking electronic correspondence.
A spokesperson for MLB told the Times that MLB "has been aware of and has fully cooperated with the federal investigation into the illegal breach of the Astros' baseball operations database."
The attack is believed to have been carried out by "vengeful" front office employees of the Cardinals against Astros general manager Jeff Luhnow.
Luhnow had previously worked ion the Cardinals front office before being hired by the Astros in 2011. According to the report, the network hacked with the Astros was similar to one built by Luhnow during his time with the Cardinals.
It is believed the hackers gained access to the network by using passwords used by Luhnow and other former members of the Cardinals front office who joined Luhnow with the Astros. The FBI reportedly traced the hack to a home used by some members of the Cardinals front office.
The investigation appears to have originated after documents believed to be from the Astros database were posted online and obtained by Deadspin. Those documents revealed nearly a year of internal discussions on potential trades by the Astros.