I’m not 100% confident in this but starting from first principles……..
At seal level the amount of oxygen in the atmosphere is 21%. Are you go higher the the atmosphere becomes dense so the amount of oxygen take in with each breath will decrease.
The “effective” amount of oxygen available at 13,000ft is 12.7%
The “effective” amount of oxygen available at 4000ft is 17.9%
So the air is 40% denser at 4000ft which means 40% more O2 molecules taken in with each breath. It stands to reason that the same person in identical conditions would be able to produce 40% more aerobic power at 4000ft than she would at 13,000ft.
Sports like swimming a running have adjustment factors for times run at altitude and the adjustment factors correlate directly with the density of the air at the racing altitude. At 5000ft the air is about 25% less dense than at sea level and the correct factor is about 25%.
I hope this helps.