I find the driver to be my toughest club to control dispersion, although it's weird because it was my most reliable off the tee and I would use it at every opportunity before I improved my iron play by a good margin. I even bought a new lower spin driver last year after a fitting and it seemed to be solved and was nearly always in the fairway but that only lasted a couple of months and I developed a bad hook. When I do a lesson it seems to be ok and the instructor says I have the right loft setting and shaft and spin is good but on the course it becomes very unpredictable. As a result I use 3w off most tees and if there is trouble a 4 iron. It seems with the 3w I can swing as hard as I like, whereas with driver I have to really slow things down. I would really like the extra distance back though as I find it means I have short irons or wedges instead of mid/long irons in. I have another lesson lined up, as well as a fitting session (hit my irons very high) so hopeful for recovering the use of driver. I also ordered a shot scope to hopefully get a better understanding of misses/dispersion etc.
I apply Scott Fawcett´s strategy approach since 2016. The number 70 is the dispersion for a tour pro at 270 yards carry were 90-95% of their golf shots ends.
In your 15 ball test, take the 2nd fardest away from the target. That´s your dispersion divided by 2. Apply scott´s strategy with that number, and not 70.
As an example mine is 80 yards (40 left, 40 rigth) wide at 270 yards carry+roll.