Right, the formula is based on the general population, but there are athletes in the general population. The simple formula is a simple formula, and frankly that. It gives you a framework for what to expect. It might be spot on for you (it is for me, like withing 1-2 bpm for max, all out efforts), but there are others that crank up their heart rate. Realistically, HR is is simply a number, and not a metric of fitness relative to other individuals. Now, if you get on a treadmill (on the Bruce protocol) and reach 100% of your predicted max HR withing 2 min, then you’re probably out of shape, or a “deconditioned response to exercise.” However, if you get on the treadmill and your it takes you 21 minutes to reach that same heart rate, then you’re in much better shape. Again, though, this is very individualized.
The other major component of how well you can pump blood around your body (in fact the other component of Cardiac Output) is stroke volume, or the amount of blood pumped out of your left ventricle (i.e. your heart) on a beat to beat basis. So think about it. If you have a massive left ventricle and you can pump out 100 mL per beat then you may not need to get your heart rate as high as someone else that has smaller left ventricular stroke volume. But this also depends on how much blood your muscles need. The key point is that every one is different and heart rate can be affected by many factors.
And, are there different formulas? Yep, see this Lifehacker article here as an example. No, Lifehacker is not scientific, but they’ve summed up the major points. There are more examples but this is easy to read and understand, and the key point that they illustrate at the end of the article: Test yourself. That’s all that really matters.