Pilot reported landing and a tire blowing resulting in a short runway excursion.

Narrative

At XA:45 PM. Pilot and 2 passengers returning from ZZZ1 to ZZZ after lunch at ZZZ1.On landing at ZZZ airport on a normal landing (Runway XX with winds at 190 at 5 kts) the right landing gear brake was on and the right main gear first flat spotted and then lost all air. Airplane departed Runway XX to the right a short way into the grass (about 30 feet off edge of runway). No damage to airplane other than flat tire.Replaced tire with a temporary spare with the help of a A&P on the field and returned it to hanger for a new tire and tube next week.Root cause of blown tire was when I left ZZZ after a short stay I did not release the ground parking brake all the way. The left tire was a new tire and the partially released hand brake was not stopping it from rolling. The right tire was close to needing to be replaced and its brake was slightly holding. Upon normal speed landing (70 kias with 30 degree flaps) at ZZZ; the right brake held enough to first flat spot the tire and then all air was lost - not explosive; but a fairly quick leak down.When tire went flat at about 35 kias the plane started pulling to the right and I could not keep it on the runway. Steered it off to miss edge lighting and came to stop about 30 feet clear of Runway XX edge paving. No damage to aircraft other than burst tire.