The private pilot was flying multiple visual patterns on a 40-foot wide asphalt runway. Winds were reported by the pilot as variable and gusting. The pilot stated that during the third touch-and-go, the wind shifted to a crosswind with a tailwind component. While reconfiguring for takeoff, the pilot perceived a faster than normal groundspeed. A gust of wind contacted the airplane's tail pushing the nose to the left. The pilot attempted to correct back to centerline but was hesitant to input an aggressive correction due to the faster than normal groundspeed. The left main gear ran off the runway onto the grass and the airplane departed the left side of the runway. The nose gear sank into mud and was separated. The nose gear strut dug into the muddy terrain and the airplane nosed over coming to rest in the inverted position. On a NTSB Form 6120.1, the pilot reported that the accident could have been prevented with a more aggressive rudder input.