The baseball bat is a common melee weapon found in the Wasteland. The United States was stereotyped as a patriotic country, so it's very logical to find them everywhere. While useful for close combat with raiders, they are not particularly effective against the more durable foes found throughout the Wasteland.
All things considered, Fallout 3's baseball bat is a decent melee weapon for early use and helps to preserve ammunition when starting out in the wasteland. Later, much more powerful melee weapons become available, such as the Ripper and Shishkebab.
The bat is branded on one side with a machine-caligraphed "B" in an ovoid shape. Beneath the logo are the words "Since 1879," suggesting the bat's manufacturer has been producing sporting goods since the 19th century.