Altitude and performance
A lot of persons believe the oxygen is rare in altitude, it is false. The oxygen proportion in the air is the same everywhere around the globe, almost 21%.
What it is changing with altitude, is the atmospheric pressure. The more the altitude is high the more the pressure is low, so the same volume of air contains less molecules of oxygen.
Our body requires then to breathe a bigger volume of air to capture the same quantity of oxygen and supply the same quantity of energy.
In reaction, everyone could believe that the body is going to generate more red corpuscles and become more powerful. That's also a false idea. Some studies even have demonstrated the opposite, particularly for the high level sportsmen who often have, of course, a high rate of red corpuscles.
Furthermore, training in altitude is delicate (more difficult effort, losses of marks or sensations because of lower performances, immunizing fragility, etc.) which thwarts the potential advantages.
There are a lot of controversies on this subject but, nevertheless, the last studies are in favour of "live high, train low" which means to live in altitude but to train in the valley, which is not always easy to do.