To improve the mileage of a BMW S1000RR, several strategies can be employed. First, consider using a well-engineered slip-on exhaust system, which can increase horsepower and torque while reducing weight, thus improving the power-to-weight ratio and acceleration. Additionally, installing a high-performance air filter can enhance the amount of air flowing into the engine, but ensure the air/fuel ratio is optimized to avoid running too lean or too rich, which can be achieved by tuning the fuel injection system by an experienced mechanic. Using synthetic oil is also beneficial as it provides better lubrication and reduces friction in the engine, directly impacting mileage by reducing drag. Regular maintenance is crucial, including checking tire pressure, changing the oil and air filter, and cleaning the fuel system. Other factors to consider include avoiding excessive weight on the motorcycle, minimizing excessive use of the clutch and brake, avoiding sudden acceleration and braking, and preventing unnecessary idling of the engine. Ensuring high-quality fuel is used and maintaining proper tire condition and chain sprocket alignment are also important. For the BMW S1000RR specifically, running the bike within the recommended rev range during the initial miles and following proper running-in tips can help in reducing oil consumption and optimizing engine performance over time.