220 minus your age in years
Ah, this old thing. It exists for several reasons:-
* that formula is the best fit,
population wide, for an equation of the form "X - age". Any other value than 220 gives a worse fit
population wide* there are better formulae (for a
population wide fit) if you move to second order polynomials, but they're more difficult for the average person to calculate
* individuals vary massively, I'm sure many will post their anecdata to show this (it certainly is way off for me)
* in the absence of any other data it's the best thing to start off to use
* as soon as you have other data (i.e. from your HRM) then you can throw the old value away and use the new value
Since you obtain 165 from the formula, but have seen 178 on your HRM then use 178 as you working HR
max.
As you get fitter you'll be able to push yourself faster and harder and you may see even higher numbers. If so, redo the calculations based on those.
The actual value of your HR
max has very little to do with your "fitness" level. You can't compare it to others and, in my experience, it doesn't really change whether I'm as fit as I've been for years, or after a period of months of being a slob. What changes for me is that I do the same run at the same speed (with roughly the same weather) and when I'm 'fitter' my max and avg HR is lower. Or I'll do the same run (with roughly the same weather) and have the same avg and max HR as before but when I'm 'fitter' I'll do it faster than before. (although, for me, 'fitter' often includes being lighter which obviously requires less energy and therefore a slightly lower HR.)
tl;dr use the max value you've seen on your HRM, if you see a higher value use that, don't use a HR
max value that you haven't actually hit within the last 12 months