In recent years, urban bicycle networks have expanded globally, accompanied by a rise in bicycle commuting. Despite this growth, cyclists remain disproportionately affected by traffic crashes involving motor vehicles, resulting in significant fatalities and injuries. Bikeway designs vary widely, influenced by factors such as geometry, positioning relative to traffic, and shared use with other modes. While infrastructure design is known to impact cycling safety, few studies have comprehensively analyzed entire city networks or compared bikeway typologies. This study uses multivariate linear regression to test whether bikeway design contributes to bicycle-motor vehicle crashes. Analyzing geolocated 38,917 bicycling crashes in Berlin, along the 5,350 km of the city's road network, this study found that bikeway-type extension, motor and bicycle trip volumes per observation unit are statistically significant predictors at the 99% confidence level of crash rates, with independent variable p-value well below 0.01. Resulting models simulate that replacing 50 km of mixed-traffic roads with dedicated bike lanes could prevent 2,631 crashes annually. Furthermore, converting 50 km of mixed-traffic roads to shared-use lanes between bicycles and buses could reduce crashes by 82%.