This paper presents a method to recover quadrotor UAV from a throw, when no control parameters are known before the throw. We leverage the availability of high-frequency rotor speed feedback available in racing drone hardware and software to find control effectiveness values and fit a motor model using recursive least squares (RLS) estimation. Furthermore, we propose an excitation sequence that provides large actuation commands while guaranteeing to stay within gyroscope sensing limits. After 450ms of excitation, an INDI attitude controller uses the 52 fitted parameters to arrest rotational motion and recover an upright attitude. Finally, a NDI position controller drives the craft to a position setpoint. The proposed algorithm runs efficiently on microcontrollers found in common UAV flight controllers, and was shown to recover an agile quadrotor every time in 57 live experiments with as low as 3.5m throw height, demonstrating robustness against initial rotations and noise. We also demonstrate control of randomized quadrotors in simulated throws, where the parameter fitting RMS error is typically within 10% of the true value.