Start · the lane board
Six courses, the planted answer, and what each method found
Each lane is one course. The first column is the penalty written into
src/build_data.py; the next three are the estimates from
src/analysis.py, all in seconds slower than Berlin for the same runner.
Bars share one scale, and the planted value is the tick.
Negative estimates (faster than Berlin) have no bar. Full width is 110 s.
Why simulate · a test with a known answer
Race results can't tell you whether a method is right
Nobody knows the true penalty of a course, so an estimate from race results has nothing to be checked against. The build script makes one up. It draws 400 men and 400 women with a fixed flat-course ability and sends 150 of them to each race, weighted toward the faster athletes. Each finish time is ability, plus the course penalty, plus a weather penalty, plus normal noise with a 90-second standard deviation. The top 100 per gender are kept: 10,800 results over 54 editions, with 2020 left out.
The planted penalties follow the courses' reputations: Berlin 0, Chicago 12, Tokyo 28, London 35, New York 85, Boston 105 seconds. The weather is a hand-entered table of start temperature, humidity and wind for every edition, which the script describes as anchored to reported race-day conditions (Boston 2018 at 3.9°C with 40 km/h wind, London 2018 at 23.5°C).
On average, the simulated weather costs more than the course on every Major
Seconds the simulation's weather term adds to a 2:10 runner in each edition, with the planted course penalty as a dashed line. Hover, tap, or focus the chart and use the arrow keys.
Temperature, humidity and wind from data/race_weather.csv, run through
weather_multiplier() in src/analysis.py (the same curve build_data.py
uses), times 7,800 s.
The average edition's weather costs 36 seconds in Tokyo and 209 in Berlin, where every race starts between 12 and 18°C, above the curve's 10°C floor. London 2018 adds 530 seconds, five times Boston's planted course penalty. A method that misreads the weather by a few percent would swamp the course signal, which is why methods 2 and 3 divide it out first.
Method 2 · within-runner paired
Same runner, two courses, 18 months apart at most
For every athlete who ran two different Majors within 18 months, each finish time is divided by its race's weather multiplier and the difference is taken. Ordinary least squares then fits one offset per course, with Berlin fixed at zero, over all 42,567 pairs. A 2,000-resample bootstrap gives the intervals, which come out near ±2 seconds for every course.
The method lands within 7.3 seconds of every planted value, and below it each time: by 0.6 s on Chicago, 4.0 on Boston, 4.3 on London, 7.0 on Tokyo and 7.3 on New York. Only Chicago's interval contains its planted value. On the other four the shortfall is too large for sampling noise, so it is a bias, and the code doesn't test where it comes from.
src/analysis.py.Methods 1 and 3 · terrain and weather
One method agrees with the paired fit; the other reads only the map
The weather-normalized method averages each edition's top 10 per gender, divides by the same Maughan / El Helou style multiplier (0.5% per °C above 10°C, 0.2% per °C below 5°C, plus small humidity and wind terms), and averages across years. It puts Boston at +100.1 s and New York at +80.3 s, and misses worst on Tokyo (16.9 against 28).
The grade-adjusted method integrates the Minetti et al. (2002) energy-cost polynomial over each course, treating it as 40% climbing at the average up-grade, 40% descending and 20% flat, with small extra penalties for grades over 1.5% and for courses with many turns. It never sees a race result. On these profiles it scores Boston 89 s faster than Berlin and Tokyo 17 s faster. The simulation has no elevation term, so the gap between this column and the planted one says nothing about whether the model is right about Boston.
The composite · course difficulty index
The weights decide whether Boston or New York comes out hardest
Each method's offset becomes a factor on a 7,800-second (2:10) reference, and the index is 0.15 × grade-adjusted + 0.50 × paired + 0.35 × weather-normalized. The order is Boston 1.0092, New York 1.0089, London 1.0034, Tokyo 1.0018, Chicago 1.0012, Berlin 1.0000. Boston's composite is only 72 seconds over Berlin, against 101 from the paired fit alone, because the elevation model's negative number pulls it down. The weights are a judgment call in the code, so the chart below lets you set your own.
At the script's weights, Boston leads New York by 3 seconds
Composite = 1 + (w1·grade-adjusted + w2·paired + w3·top-10) / 7,800 s,
the formula in compute_cdi(). Like the script, the chart does not rescale weights that don't add to 1.
Per-method offsets from outputs/analysis_results.csv; planted penalties from
COURSE_PENALTY in src/build_data.py. The planted tick is only a fair
comparison when the weights add to 1.
The script's own sensitivity runs agree with the chart. Dropping the grade-adjusted method (the "drop elevation" preset) raises Boston to 1.0110. Restricting the paired fit to men's pairs with both times under 2:10 gives 1.0088. The third run swaps the top two: with a simpler gain-and-loss elevation model in place of Minetti, New York moves to 1.0166, above Boston at 1.0131.
src/analysis.py.Limitations · what this doesn't show
None of these numbers measures an actual course
The athletes and results are generated by src/build_data.py with seed 42.
The names are combinations of real elite first and last names with a number attached,
and the countries are drawn at random. An earlier version of this page presented
Boston's +101 s as a finding about the real course; it is the paired method's estimate
of a penalty that was set to 105 in code.
The test is also kinder than race data would be. The weather correction divides by the same curve that generated the times, so it is exactly right by construction. The simulation also leaves out pacing strategy, fatigue that depends on where the hills fall, and differences in who chooses to race where. Actual fields have all three.
The course profiles (gain, loss, maximum grade, turn count) are typed into
data/course_profiles.csv, and the 40/40/20 split is a rough stand-in for a
segment-by-segment integration. Sydney and Cape Town appear only under the
grade-adjusted method.
Finish · how it was built
Where the numbers come from
- Results
- Simulated: 10,800 top-100 finishes, 6 courses × 9 years × 2 genders, seed 42
- Pairs
- 42,567 same-athlete course pairs within 18 months, derived from the results
- Weather
- 54 hand-entered editions: start temperature, humidity, dew point, wind
- Elevation
- Eight hand-entered course profiles: gain, loss, net drop, maximum grade, turns
- Energy cost
- Minetti et al. (2002), J. Appl. Physiol. 93:1039–1046
- Heat penalty
- Curve after Maughan (2010) and El Helou et al. (2012), PLOS ONE 7(5)
- Techniques
- Least-squares fixed effects, bootstrap intervals, weighted composite index, sensitivity analysis
- Reproduce
python src/build_data.pythenpython src/analysis.py; matches the committed results