We present photometry of four transits of the planetary system HAT-P-13, obtained using defocused telescopes. We analyse these, plus nine data sets from the literature, in order to determine the physical properties of the system. The mass and radius of the star are MA= 1.320 ± 0.048 ± 0.039 M⊙ and RA= 1.756 ± 0.043 ± 0.017 R⊙ (statistical and systematic error bars). We find the equivalent quantities for the transiting planet to be Mb= 0.906 ± 0.024 ± 0.018 MJup and Rb= 1.487 ± 0.038 ± 0.015 RJup, with an equilibrium temperature of K. Compared to previous results, which were based on much sparser photometric data, we find the star to be more massive and evolved, and the planet to be larger, hotter and more rarefied. The properties of the planet are not matched by standard models of irradiated gas giants. Its large radius anomaly is in line with the observation that the hottest planets are the most inflated, but at odds with the suggestion of inverse proportionality to the [Fe/H] of the parent star. We assemble all available times of transit mid-point and determine a new linear ephemeris. Previous findings of transit timing variations in the HAT-P-13 system are shown to disagree with these measurements, and can be attributed to small-number statistics.