Shore is the average durometer [hardness] reading of the tire compound. A lower number is a softer tire and, roughly, more grip.
There are times where the softest tire you can get will chunk if the track surface is grippy [foam tires] or grease up from overheating [rubber tires], causing a loss of overall grip.
Too hard a tire for your purposes/track won't generate enough grip to take corners at a decent speed [foam] or won't generate enough heat to reach optimum grip [rubber].
Finding the "perfect" tire is finding the middle ground between a tire that gives up trying to grip too hard, and a tire that doesn't grip enough to go fast.
Privateer racing lots of stuff.
Remember kids, racing isn't fair!