The important distinction here, however, is that intensity can be thought of as either a cause or an effect. With that in mind, power output is always the “cause” while variables like heart rate and perceived exertion are always the “effect” or result. Said another way, heart rate and perceived exertion depend on the power output. That is, for a given individual at a given fitness level in a given environment, the heart rate and perceived exertion are a result of the power output, not vice versa.
Because power output is the sole independent measure of exercise intensity, and not a dependent response like heart rate and perceived exertion, power is the ultimate gold standard for understanding exercise intensity and measuring training load. But that doesn’t mean that heart rate or perceived exertion don’t have value. On the contrary, power by itself doesn’t tend to mean anything unless it’s put into the context of how one feels or how one responds to a given training stimulus. For example, riding at 150 watts and feeling either good or bad says a lot more about one’s fitness or health from day to day than just the power alone. Likewise, having power can add a lot of context to one’s heart rate response or perceived exertion. Although, there is generally a strong relationship between heart rate, RPE, and power for a given individual, it’s ultimately the dissociation between the two that are both the benefit and Achilles heel of each measure. In the end, they work best together.
If, however, you don’t have the luxury of having a power meter, realize that RPE and HR can still be very valuable. In fact, having a lot of data on any given day to describe training is much less important in the big picture than having a few simple metrics to track your training every single day. With that in mind a variable like Perceived Exertion is the only estimate of exercise intensity that can be used every single day, regardless of the type of exercise. You just have to ask yourself how hard you think you went. That simple question, along with the duration of exercise, can give someone rich information about their day-to-day training load. Even if not as accurate as something like power output, big picture, less accurate but consistent data is always more valuable than more accurate inconsistent data.