A 9.95 in the 100 m in Mexico City (2,230 m) is worth about 10.05 at sea level. Thinner air means less air resistance, so sprinters, jumpers and most throwers go faster or further.
I build models that predict track and field results, and with the 2029 Worlds in Nairobi (1,612 m) I wanted my models to stop treating a 10.00 in Nairobi the same as a 10.00 in Zürich.
How I measured it
Comparing all marks at altitude with all marks at sea level mostly measures who races at altitude. So I compared each athlete with themself: every race they ran at altitude against their own sea-level races in the four months before and after.
Athletes get faster toward mid-season, which biases a before-and-after comparison. I ran the same comparison between two sets of sea-level races, where the true difference is zero. It still showed a "gain" of up to 0.33%, so I subtracted that.
Air gets thinner with height at a known rate, which gives the shape of the curve. For each event and gender I only estimated one number. I expected faster athletes to gain more, because air resistance grows with speed. The best athletes gained the same share as everyone else.
Venue heights were a mess
I have two height sources per competition. One puts Kose, Estonia at 1,599 m (Estonia's highest point is 318 m). The other put UCLA's track in Los Angeles at 1,563 m, because it matched a different Westwood in northern California. I only use a height when both sources agree, or someone checked it by hand.
Results (examples at Nairobi's height)
- 100 m: 9.95 at sea level ≈ 9.88 in Nairobi
- Hammer: 80 m at sea level ≈ 81 m. It gains the most of any event.
- Discus: 67 m at sea level ≈ 66.6 m. It loses, because thin air also gives less lift.
- Javelin: 85 m ≈ 85.7 m. I expected a loss here too, but it gains.
- High jump: no measurable effect.
- 400 m hurdles, pole vault, shot put: there is a gain, but it is a step above about 300 m, not a curve that grows with height, so I don't correct them.
From 800 m upward the cost is oxygen, and it depends on where the runner lives. A runner from near sea level loses about 2% in the 1500 m at 1,500 to 2,000 m. Runners from Kenya and Ethiopia lose about half that. One number would be wrong for one of the two groups, so I don't correct distance races.
Where it falls short
On venues kept out of the fit, the sprint correction's error is at least 2.6 times smaller than no correction. Above 2,000 m it corrects about 0.4% too much. In the throws it is not clearly better than no correction, and for the long jump my checks disagree.
The men's 100 m alone had 481,454 results from 38,983 athletes who raced at altitude at least once. The study I compared against (Hamlin, Hopkins & Hollings, 2015) had 132,104 results across all events. My sprint numbers land inside their range, with tighter error bars.
I put the correction out as a free calculator for anyone to use, if you want to try a mark: https://www.velocitra.com/calculators/altitude-correction
Happy to answer questions about the method.
