I can't remember where I read it, but it was in a scientific paper which stated that you cannot increase your max HR. It is what it is and it will decrease with age. A better calculation for HR max is (210-(0.5 x age)) - 5% body weight in pounds +4 for male, 0 for female. For me at age 76 and weighing 215 pounds, it works out at 165 and I haven't been able to exceed this (unless I was in a-fib!).
On the other hand, as you get fitter, your resting HR will decrease, but this decrease may also be as a result of sick sinus syndrome due to aging.