Discrete aurora at Mars, characterized by their small spatial scale and tendency to form near strong crustal magnetic fields, are emissions produced by particle precipitation into the Martian upper atmosphere. Since 2014, Mars Atmosphere and Volatile EvolutioN’s (MAVEN’s) Imaging Ultraviolet Spectrograph (IUVS) has obtained a large collection of nightside UV discrete aurora observations. Initial analysis of these observations has shown that, near the strong crustal field region (SCFR) in the southern hemisphere, the aurora detection frequency is highly sensitive to the interplanetary magnetic field (IMF) clock angle. However, the role of other solar wind properties in controlling the aurora detection frequency has not yet been determined. In this work, we use IUVS discrete aurora observations, and MAVEN solar wind observations, to determine how the discrete aurora detection frequency varies with solar wind dynamic pressure, IMF strength, and IMF cone angle. We find that, outside of the SCFR, the detection frequency is relatively insensitive to the IMF orientation, but significantly increases with solar wind dynamic pressure and moderately increases with IMF strength. Interestingly, the auroral emission brightness outside the SCFR is insensitive to the dynamic pressure. Inside the SCFR, the detection frequency is moderately dependent on the dynamic pressure and is much more sensitive to the IMF clock and cone angles. In the SCFR, aurora are unlikely to occur when the IMF points near the radial or anti-radial directions. Together, these results provide the first comprehensive characterization of how upstream solar wind conditions affect the formation of discrete aurora at Mars.