According to the American Veterinary Medical Association: "While some study authors suggest limiting ownership of specific breeds might reduce injuries (e.g., pit bull type, German Shepherd Dog) it has not been demonstrated that introducing a breed-specific ban will reduce the rate or severity of bite injuries occurring in the community. Strategies known to result in decreased bite incidents include active enforcement of dog control ordinances, and these may include ordinances relating to breed."

https://www.avma.org/KB/Resources/LiteratureReviews/Pages/The-Role-of-Breed-in-Dog-Bite-Risk-and-Prevention.aspx

"Pit bull"-type dogs (pit bull is not a breed, ironically for BSL supporters) are often trained for dogfighting, but there is no scientific evidence that violence is innate to the type. It's more plausible that dogs trained for aggression and fighting are skewing the stats.