My current records show 154 drops in 2648 battles, which is very close to 1 in 17.5.
If you do decide to note your explore drops and get some hard data, heres how I record my arcane drops from explore. When I start exploring, I make a note of how many battles I have played for my current hero class and record it in a text document. When I get an arcane drop, I note the amount of battles I have fought. When I switch back to PvP or something else, I note that. When I switch classes, I note that. If you only care about the arcane drops, this is a fairly low time cost way to get some data. For me, the very act of recording the data has helped to insulate me against negativity bias and thus the bad streaks don’t feel as bad, since I know exactly how many stones I’ve gotten and when.
Also, forgive me if this is obvious to many, but buying extra glory packs is also a good way to build up your arcane collection over time. If you collect tributes often, you should eventually reach a point where you easily get more arcanes per week from troop packs than are necessary to trait said troops. Over a long enough period of time (assuming we don’t have huge periods where one arcane is conspicuously not represented for months, like Arcane Dark was until this week), you’ll slowly build up what you need to get kingdom stars, especially if you focus on “cheaper” traits. Base mythics, however, will usually require more extra than you can earn from stockpiling (using the stones on mythics means 2-3 epics/legendaries from a kingdom wont get traited right away). Don’t commit traits if you arent going to use the troop and you dont immediately get a (odd numbered) kingdom star from it, since new troops becoming available in the kingdom makes the entire starring process much easier.
If you are focusing on a specific troop you are going to use, though, unless you know the stone is coming up or is on the current week’s troop pack Explore is still by far your best bet. The only way to speed up the farming at that point is to speed up your clear times.